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  • 1990-1994  (1,941)
  • 1920-1924
  • 1830-1839
  • 1994  (1,074)
  • 1990  (867)
  • Engineering General  (1,226)
  • Physical Chemistry  (471)
  • Mathematics and Statistics  (244)
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  • 1990-1994  (1,941)
  • 1920-1924
  • 1830-1839
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  • 1
    Electronic Resource
    Electronic Resource
    Beyond quenching for singular reaction-diffusion problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1-9 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) 〉 0,f′ ≥ 0,f″ ≥ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non-negative ut, in the region where u 〈 c and with continuous ux for the problem: uxx - ut = - f(u)χ({u 〈 c}), 0 〈 x 〈 a, 0 〈 t 〈 ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫0cf(u) du 〈 ∞, then as t tends to infinity, all solutions tend to the unique steady-state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x) ≡ c by the same amount. For illustration, examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170102
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  • 2
    Electronic Resource
    Electronic Resource
    Approximating sequences for heteroclinic orbits (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 71-76 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170106
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  • 3
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170201
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  • 4
    Electronic Resource
    Electronic Resource
    The existence of solutions of a general boundary value problem for the divergence (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 95-105 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the question of necessary and sufficient conditions to find a vector field V∊ Γ(TM) solving the equation div V = Φ under inhomogeneous boundary conditions V|∂M = Z|∂M with Z∊ Γ (TM) An existence and regularity result is given for an arbitrary Riemannian manifold with boundary, M. The proof is based on the Hodge theory of differential forms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170203
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  • 5
    Electronic Resource
    Electronic Resource
    Local compactness for linear elasticity in irregular domains (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 107-113 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector-valued L2-functions whose symmetrized Jacobians are square-integrable should be compactly embedded in L2. For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170204
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  • 6
    Electronic Resource
    Electronic Resource
    Mathematical problems of liquid crystal flows (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 171-188 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius-Duhem inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170303
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  • 7
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170401
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  • 8
    Electronic Resource
    Electronic Resource
    Landesman-Lazer resonance problems and saddle point methods (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 229-238 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170402
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  • 9
    Electronic Resource
    Electronic Resource
    The stationary and non-stationary stokes system in exterior domains with non-zero divergence and non-zero boundary values (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 269-291 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In an exterior domain Ω⊂∝n, n ≥ 2, we consider the generalized Stokes resolvent problem in Lq-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫∂Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L5(0, T;Lq(Ω)) for 1 〈 s, q 〈 ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170405
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  • 10
    Electronic Resource
    Electronic Resource
    Finite element approximation of a microstructure evolution (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 377-393 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The evolution model of a microstructure described as appropriately generalized Young measures, which was developed in [11], is discretized here by means of a suitably adapted finite element method. The convergence of the approximate solutions is proved, and a one-dimensional example is treated to discuss some implementation experience and to show some illustrative results.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170505
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  • 11
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170601
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  • 12
    Electronic Resource
    Electronic Resource
    Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 451-476 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov-Poisson system. First, we regularize the system in order to apply a fixed-point theorem. Then we pass to the limit using an energy estimate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170604
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  • 13
    Electronic Resource
    Electronic Resource
    Optimal control for parabolic systems with competitive interactions (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170703
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  • 14
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170801
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  • 15
    Electronic Resource
    Electronic Resource
    Local existence of solutions to the Landau-Maxwell system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 613-641 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study here the Landau-Maxwell system in its classical form. We prove the local existence of weak solution with initial data of unrestricted size. The main tools consist of an approximation method and a regularity result for velocity averages of solutions of some general linear transport equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170804
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  • 16
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170901
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  • 17
    Electronic Resource
    Electronic Resource
    A finite element method and stabilization method for a non-linear tricomi problem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 681-695 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove using the Faedo-Galerkin method the existence of a generalized solution of an initial-boundary value problem for the non-linear evolution equation0 ≤ Q ≤ 2, in a cylinder QT = Ω × (0, T), where T u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170903
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  • 18
    Electronic Resource
    Electronic Resource
    On a semi-coercive problem in a porous journal bearing with cavitation problem as boundary condition and subject to an integral condition (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 765-785 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a non-linear problem in pressure saturation modelling of a free boundary problem, arising in self-lubricating bearings, with Neumann boundary conditions for the pressure and a non-local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo-characteristics discretization method and semi-coercive variational inequalities.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171003
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  • 19
    Electronic Resource
    Electronic Resource
    On stationary flow of asymmetric fluids with diffusion (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 837-854 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ∝3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171102
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  • 20
    Electronic Resource
    Electronic Resource
    Control problems with state constraints for shape memory alloys (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 943-952 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, two different control problems with state constraints for shape memory alloys are considered: in the non-isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first-order conditions of optimality are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171204
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  • 21
    Electronic Resource
    Electronic Resource
    Quantitative error estimates for coefficient idealization in linear elliptic problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 971-987 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171206
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  • 22
    Electronic Resource
    Electronic Resource
    An approximate Gidas-Ni-Nirenberg theorem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1045-1052 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study positive solutions u to Δu + f(u) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity f and on the topologies in which perturbations are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171304
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  • 23
    Electronic Resource
    Electronic Resource
    Diffusion limit for the linear boltzmann equation of the neutron transport theory (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1071-1087 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ∊ related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(∊2) accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171306
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  • 24
    Electronic Resource
    Electronic Resource
    Stability analysis of the phytoplankton vertical steady states in a laboratory test tube (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 551-575 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro-differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170705
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  • 25
    Electronic Resource
    Electronic Resource
    Non-linear stability for the Vlasov-Poisson system - the energy-Casimir method (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1129-1140 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of stability of stationary solutions of the Vlasov-Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy-Casimir method has been used to prove non-linear stability for various conservative systems, but no rigorous application to the Vlasov-Poisson system has been given yet. We employ this method to prove non-linear stability of stationary solutions for the plasma physics case in three geometrically different settings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171404
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  • 26
    Electronic Resource
    Electronic Resource
    Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 339-347 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170503
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  • 27
    Electronic Resource
    Electronic Resource
    General interface problems - II (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 431-450 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We continue the study of general interface problems. We prove regularity and asymptotics of solutions in usual Sobolev spaces for non-constant coefficients operators. We also give the stabilization procedure when unstable decompositions appear near a critical angle.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170603
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  • 28
    Electronic Resource
    Electronic Resource
    On global solvability of non-linear viscoelastic equations in the analytic category (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 477-486 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the global existence of analytic solutions to the non-linear viscoelastic equations of the following type: \documentclass{article}\pagestyle{empty}\begin{document}$$ u_n \, = \,\phi \,(\,||\,\nabla _x \,u\,||^2)\Delta u\, + \,\Psi \,(||\,D_x^\beta \,1\,u\,||^2,\,.\,.\,.\,\,||\,D_{x^N }^\beta \,||)\,\Delta u_t $$\end{document} where φ and ψ are continuous and non-negative functions satisfying some additional conditions. The method of the analytic energy estimates is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170605
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  • 29
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171201
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  • 30
    Electronic Resource
    Electronic Resource
    Stability and instability in adiabatic shearing motions of incompressible fluids (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 933-942 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the effect of temperature dependence of the viscosity on the stability of the adiabatic shearing flows of an incompressible Newtonian viscous fluid between two parallel plates. When the viscosity strongly decreases with temperature, the shearing flow caused by a steady motion of the upper plate (steady shearing) becomes unstable, while the shearing flow caused by a time-dependent body force is found to be stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171203
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  • 31
    Electronic Resource
    Electronic Resource
    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171301
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    Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita-type systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1005-1016 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita-type systems are considered leading to global existence and finite time blow-up results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171302
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    The existence of global in space variables solution for non-linear subelliptic equation of floating water (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1053-1070 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global in space variables solutions for a class of non-linear subelliptic evolution operators is proved. A Cauchy problem and an initial-boundary value problem are considered using the contraction theorem and Galerkin methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171305
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    On the boundary transmission problem of thermoelastostatics in a plane domain with interface corners (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1089-1114 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with bimetal problems of thermoelastostatics. By means of an explicit particular solution a reduction to problems of elastostatics is given. An indirect boundary integral method is applied for solving the traction boundary value problem. The solution is represented by a potential of single layer type having Green's contact tensor as the kernel. Thus, from the first the transmission conditions are satisfied. The Fredholm property of the boundary integral operator as well as the asymptotics of the potential density at an interface corner depend on the symbol of a Mellin convolution operator. The singular functions at corners can be obtained by calculating the potential for terms in the asymptotic expansion of the density.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670171402
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    Stokes flow of a micropolar fluid exterior to several non-intersecting closed surfaces, but contained by an exterior contour (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1115-1127 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double-layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double-layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171403
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    Scattering results for measure potentials with unbounded support (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1213-1230 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The eigenfunction expansion theorem and its application to the scattering operator and the scattering matrix is extended to Schrödinger operators with measure potentials with unbounded support on ∝n that are known to generate wave operators that are strongly complete. Analyticity conditions of the eigenfunctions and the scattering matrix are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171504
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    General interface problems - I (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 395-429 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170602
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    Generalized spherical harmonics and exterior differentiation in weighted sobolev spaces (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1017-1043 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We generalize spherical harmonics expansions of scalar functions to expansions of alternating differential forms (‘q-forms’). To this end we develop a calculus for the use of spherical co-ordinates for q-forms and determine the eigen-q-forms of the Beltrami-operator on SN-1 which replace the classical spherical harmonics. We characterize and classify homogeneous q-forms u which satisfy Δu = 0 on ∝N﹨{0} and determine Fredholm properties, kernel and range of the exterior derivative d acting in weighted Lp-spaces of q-forms (generalizing results of McOwen for the scalar Laplacian). These techniques and results are necessary prerequisites for the discussion of the low-frequency behaviour in exterior boundary value problems for systems occurring in electromagnetism and isotropic elasticity.
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    URL: http://dx.doi.org/10.1002/mma.1670171303
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    Completeness of the wave operators in scattering of classical waves by local perturbations of a cone shaped domain (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1141-1164 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider wave propagation in a cone shaped unbounded domain which contains an inhomogeneous medium with non-smooth coefficients. Existence and completeness of the wave operators are proved in the case of local perturbations of the domain and the coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171405
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    On a mathematical model for hot carrier injection in semiconductors (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1193-1212 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a collisionless transport model for electrons in a semiconductor, and we perform an asymptotic analysis for low temperatures or large applied biases. We derive analytic relations for the built-in potential and for the current which flows through the structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171503
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    Stabilization estimates for penetrative motions in porous media (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 11-20 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The physical model for penetrative convection in porous media is here considered to study the effects of variation of the source parameters on the flow. In this note we study the continuous dependence upon the heat supply and the body force of the classical solutions to the initial-boundary value problem of a heat conducting fluid through a porous solid, both for the (well-posed) forward problem and for the (improperly posed) backward in time one. For the former problem we obtain a result of continuous dependence with respect to the L2 norm; while for the latter we prove a result of Hölder continuity in a suitably constrained class of solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170103
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    Polygonal interface problems for the biharmonic operator (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 21-39 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study some boundary value problems on two-dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder and Nevers [9]. The boundary conditions on the external edges are the classical ones. This class of problem contains the boundary value problems for the biharmonic equation in a plane polygon (see [3, 11, 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a regular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered boundary value problem. Finally, we give the exact formula for the coefficients of these singularities.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670170104
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    Resonance phenomena in infinite strings with periodic ends (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 115-154 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in an infinite string under the assumption that the material properties are p1-periodic for x 〉 a and p2-periodic for x 〈 - a. As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time-periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t1/2 for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non-trivial solutions of the corresponding time-independent homogeneous problem which satisfy certain asymptotic properties (‘standing waves’).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170205
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    Stability and asymptotic behaviour in a reaction-diffusion system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 155-169 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with some qualitative analysis for a coupled system of five reaction-diffusion equations which arises from a physiology model. The uniform boundedness of the time-dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non-negative steady-state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time-dependent solution is proven to converge to a constant steady state determined by the initial functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170302
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    Bifurcations of strongly non-linear self-excited oscillations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 189-207 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Perturbation of a single-degree-of-freedom conservative oscillator leads to the emergence and vanishing of periodic solutions and to various types of self-excited oscillations. Using techniques from dynamical systems theory, in particular a certain Poincaré map, we establish the presence of Hopf bifurcations, various types of homoclinic bifurcations and saddle-node bifurcations of the associated Poincaré map. The corresponding bifurcation sets in parameter space are computed explicitly by perturbation methods. The theory is applied to the generalized van der Pol and the generalized Rayleigh oscillator, and to the case of a non-linear spring attached to a conveyor belt.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170304
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    An approximation theorem in inverse electromagnetic scattering (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 293-303 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the inverse electromagnetic scattering problem for an inhomogeneity of compact support with constant permittivity Colton and Päivärinta suggested an optimization scheme which yields a numerical method for determining the refractive index if the far-field data of the scattering problem is known [1]. We prove the denseness of the Cauchy data to certain interior transmission problems and conclude that the infimum of the optimization scheme is zero even if the permittivity varies. Before proving the denseness result, we investigate a boundary value problem which is needed to prove the denseness result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170406
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    A principle of linearization and the uniform asymptotic stability of solutions of the Navier-Stokes equations for compressible isothermic fluidsThis research was supported by the Alexander von Humboldt Foundation during the stay of the author at the University of Würzburg and the Technical University Darmstadt, FRG. (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 251-267 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the correctness of a principle of linearization in the investigation of the uniform asymptotic stability of a sufficiently smooth, but generally non-steady, solution of the Navier-Stokes equations for compressible fluids in the case of a constant temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170404
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    Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 349-376 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence and uniqueness of classical solutions of the Wigner-Poisson and Schrödinger-Poisson systems of equations for both repulsive and attractive potentials. In the repulsive case, we prove decay estimates for the particle density, the potential and the solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170504
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    A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 487-508 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170702
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    A hyperbolic - parabolic system modelling the thermoelastic impact of two rods (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 901-918 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dynamic thermoelastic impact of two rods is modelled by a coupled system of two quasivariational inequalities and two equalities that reflect a bilateral contact condition and a radiation condition for the temperatures. The existence of a weak solution is established using a penalization method that employs Galerkin approximations and a priori estimates.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670171105
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100101
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    Iterative computation of second-order derivatives of eigenvalues and eigenvectors (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100102
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    Semi-Loof element for plate instability (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 11-19 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100103
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    Least-squares T-elments: Equivalent FE and BE forms of a substructure-oriented boundary solution approach (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100104
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    High-order polynomial interpolation in boundary integral equation analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 167-178 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A sixth-order polynomial shape function is developed for BIE analysis. The function is applied over only three-noded elements, but with the support for the function extending over adjacent elements. This avoids the oscillations near the ends of the range which otherwise are characteristic of high-order polynomial interpolation. Various test problems are explored, and it is shown that results as accurate as those from conventional quadratic elements are obtained with larger nodal spacings, and thus giving the potential for significant reductions in matrix storage requirements and solution times.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100208
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    Accurate finite element method for steady and quasisteady lifting aerofoil (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 155-166 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation based on superposition is proposed for a lifting aerofoil in incompressible potential flow. An accuracy improvement technique for the singularity at the aerofoil trailing edge is discussed. It is shown that the quarter-node quadrilateral element can be readily employed to simulate this singularity. It is also demonstrated that the circulation in the flow field can be easily represented by a single constraint equation rather than introducing an artificial cut line in the mesh. The influence of finite-element mesh size on solution accuracy and the correct form of the boundary condition have been investigated as well. Numerical examples are given for both steady and quasisteady Joukowski aerofoils of various thicknesses and at a range of incidences. In all test cases, good agreement is observed between the analytical solution and the numerical result.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100207
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100301
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    A 3D element for non-linear analysis of solids (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 183-194 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An 8-node element (HMITC) for 3D non-linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100302
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    Space-time oriented streamline diffusion methods for non-linear conservation laws in one dimension (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 203-215 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100304
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    Neural-network-based approximations for solving partial differential equations (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 195-201 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100303
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    Cyclic symmetry in boundary elements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 217-225 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm for consideration of axial and cyclic symmetry in the boundary-element method is presented. The appropriate transformation relationships was derived. The algorithm is then implemented in a boundary element program for the analysis of 2D elastostatic problems. Through analysis of typical problems the validity of the algorithm and its implementation is verified. A high level of accuracy and substantial reduction in computer time and storage was achieved.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100305
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    Explicit variable time-step method for implicit moving boundary problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 227-235 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable-length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100306
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    Boundary-element solution of some structural-acoustic coupling problems using the multiple reciprocity method (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 237-248 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we have developed a new formulation for solution of structural-acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary-value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100307
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    Homogenization and effective elastoplasticity models for periodic composites (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 257-265 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for stress- and strain-controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100309
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    Lagrange multiplier approach for evaluation of friction in explicit finite-element analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 249-255 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for evaluation of friction in general contact-impact interfaces is described. The algorithm is based on an explicit finite-element method. Coulomb's friction law is assumed. The defence node algorithm is used such that the sticking condition can be imposed with the Lagrange multiplier method even in explicit dynamic analysis. The algorithm is supposed to be applicable in general situations, including large deformations of the contact-impact bodies and large relative sliding between the contact-impact boundaries. Numerical results are presented to demonstrate the performance of the algorithm.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100308
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 275-277 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100311
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100401
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    General forming of transition elements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 267-273 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalization of the r(1-m)/m strain singularity of higher-order isoparametric elements is presented. It is shown that, by variable placement of the side nodes between their original and singular positions, the point of singularity sensed by the element can be controlled. The transition elements have a strain singularity outside their domain. The singular and non-singular elements are elements are special cases of the general mapping. The transition elements, together with the singular isoparametric elements, can be used for solving crack problems.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100310
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    Some geometric problems related to fracture-control in complex structures (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 279-290 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the design of members with flaws, it is necessary to keep the stress intensity factor K of any sharp crack below the fracture toughness Kcr of the materials. Stress-intensity factor equations for the more common basic specimen geometries and various loading conditions are available in the literature. The application of these equations to complex structures involves geometric problems such as the identification of the outline of each member and the sizing of the equivalent specimen for each flaw. The paper gives a response to such difficulties.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100402
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    Modified simplex optimization program (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 303-312 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, yet storage-effective ‘linear’ programming code is given. The assumption of non-negative variables is bypassed without increasing the size of the problem. Furthermore, the objective is allowed to be summed over not just linear, but also concave, functions. A specific truss topology optimization example is shown.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100405
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    Fourth-order difference method for quasilinear Poisson equation in cylindrical symmetry (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 291-296 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation \documentclass{article}\pagestyle{empty}\begin{document}$$ Au_{zz} + \frac{1}{r}u_r + Bu_{rr} = f\left({r,z,u,u_r,u_z} \right) $$\end{document} with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method.
    Additional Material: 4 Tab.
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    URL: http://dx.doi.org/10.1002/cnm.1640100403
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    Use of central-difference operators for solution of singularly perturbed problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 297-302 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Singularly perturbed second-order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier-Stokes equations for fluid flow. Numerical methods composed of central-difference operators on special piece-wise-uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100404
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    Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100406
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    Universal matrices with new infinite elements for quasiharmonic equation (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 321-331 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100407
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    Accelerated modified Newton-Raphson iteration-based finite-element solution of structural problems involving non-linear deformation behaviour (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 333-338 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new global secant relaxation (GSR)-method-based improvement procedure is used to improve the overall convergency performance of the modified Newton-Raphson iteration in carrying out the solution of discrete systems resulting from the finite-element discretization of a certain class of structural problems involving non-linear deformation behaviour.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100408
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    A simulation of free-surface electrohydrodynamic flow (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 339-353 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Theoretical and experimental analysis of free-surface electrohydrodynamic flow is fragmented and incomplete. Simulation studies of this phenomenon are further limited by the inherent complexities in the modelling process. In this note a mathematical model is developed to analyse free-surface electrohydrodynamic flow in two dimensions, and preliminary results of the simulation are described. The configurations examined include electrified conducting surfaces, the dielectrophoretic forces, and a conducting jet. The simulation is compared with analytical results in the first two investigations and is shown to be quite accurate. In the last simulation it is demonstrated that in the initial formation of a conducting jet, a 10 per cent increase in applied voltage results in about a 10 per cent increase in fluid velocity.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100409
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 355-357 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100410
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    Announcements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 359-360 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100411
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100501
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    Improvement on dual reciprocity boundary element method for equations with convective terms (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 361-371 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100502
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    A direct solver for the least-squares problem arising from GMRES(k) (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 743-749 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least-squares problem, argminy |Hky - β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least-squares problem.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100909
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    Conference diary (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 759-760 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100911
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    Announcements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 761-762 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100912
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640101001
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    An algorithm for the optimization of directionally stretched triangulations (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1481-1497 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the optimization of stretched triangular grids is described. The method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non-linear spring system. The function is minimized using a gradient method based on the steepest descent. Examples are provided to show the applicability of the method to computational fluid dynamics problems.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620370905
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    Optimum application of the multigrid method in generating body-fitted co-ordinates (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1465-1480 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Multigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body-Fitted Co-ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620370904
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    Node and element resequencing using the Laplacian of a finite element graph: Part II - Implementation and numerical results (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1531-1555 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G· associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620370908
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    The benefits of parallel multibody simulation (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1557-1572 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)-residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed-up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370909
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  • 89
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    A finite volume format for structural mechanics (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 181-201 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370202
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  • 90
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    Element-free Galerkin methods (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 229-256 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
    Additional Material: 26 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370205
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  • 91
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    Large deflection inelastic pseudo-transient analysis of laminated composite plates (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 37-48 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A pseudo-transient (static) linear, geometric, material and combined geometric and material non-linear analyses of composite laminates are presented. A nine-noded isoparametric quadrilateral finite element belonging to the Lagrangiar family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. Elasto-plastic material behaviour is incorporated using the flow theory of plasticity. In particular, a modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for by assuming a constant transverse shear strain across the thickness of the laminate and the geometric non-linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of plastic behaviour through the thickness. A wide range of numerical examples is presented to demonstrate the validity and efficiency of the present approach. The results for combined non-linearity are also presented. The variety of results presented here, which are based on realistic material properties of often-used advanced laminated composite plates, and especially those for combined non-linear analysis, should serve as a reference for future investigations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370104
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  • 92
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    A variationally coupled FE-BE method for transient problems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 91-105 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variationally coupled finite element-boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solutions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370107
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  • 93
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    An accurate shear-deformable six-node triangular plate element for laminated composite structures (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 431-455 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A six-node triangle plate/shell element is developed for the analysis of laminated composite structures. This model is formulated using Hamilton's principle along with a first-order (Reissner/Mindlin) shear deformation theory. The element is based upon an isoparametric representation along with an interdependent interpolation strategy; bicubic polynomials for the transverse displacement and biquadratic polynomials for the element geometry, in-plane displacements and rotations. The resulting element, which is evaluated using exact numerical integration, has correct rank and is free of shear ‘locking’. Numerical results are presented that validate the new element and prove its outstanding convergence capabilities in comparison to existing triangular elements using standardized test problems (elastic eigenvalue analysis, patch test, static simply supported square-plate solutions) and experimentally measured vibration data of cantilevered isotropic and composite plates.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370305
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  • 94
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    Stability of collapsed 8-node 2-D and 20-node 3-D isoparametric finite elements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 475-496 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter-point nor the half-point 8-node two-dimensional (2-D) and 20-node three-dimensional (3-D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter-point element can be constructed which do have additional singularities. Since the general behaviour of the half-point element is not affected by small modifications, this element is better suited to match complex body geometries.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370307
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  • 95
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    Conference diary (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 537-538 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370310
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  • 96
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    Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 517-536 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4-node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9-node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4-node quadrilaterals.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370309
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  • 97
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    A quadrilateral hybrid stress element for Mindlin plates based on incompatible displacements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 279-296 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4-node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co-ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co-ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370207
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  • 98
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    A comparison of Lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 605-621 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, we analyse the computational performance of the Lanczos method and a recent optimization technique for the calculation of the p (p ≤ 40) leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic PDEs. The accelerated conjugate gradient method is used to minimize successive Rayleigh quotients defined in deflated subspaces of decreasing size. The pointwise Lanczos scheme is employed in combination with both the Cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive Lanczos vectors. The three algorithms are applied to five sample problems of varying size up to almost 5000. The numerical results show that the Lanczos approach with Cholesky triangularization is generally faster (up to a factor of 5) for small to moderately large matrices, while the optimization method is superior for large problems in terms of both storage requirement and CPU time. In the large case, the Lanczos-Cholesky scheme may be very expensive to run even on modern quite powerful computers.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370405
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  • 99
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    A new eight-node quadrilateral shear-bending plate finite element (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 387-411 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new eight-node quadrilateral shear-bending Reissner-Mindlin plate finite element for the very thin and thick plates without locking and spurious zero-energy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four- and eight-node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight-node quadrilateral shear-bending plate finite element proposed has been found to be very efficient.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370303
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  • 100
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    A unified theory for formulation of hybrid stress membrane elements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 457-474 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theory is proposed in this paper to explain, in a unified manner, the three rational approaches using the incompatible displacements uλ in the hybrid element formulation. Limited to the plane stress case, the theory suggests that the introduction of uλ is to constrain the total value of the invariant I2(= σxσy - τxy2) of the assumed stresses over the element to zero. In the plane stress case, this is the well-known condition for the stress distributions to be independent of the elastic constants of the material. The theory proposed is also used to explain the closeness of the performances of the four 4-node hybrid stress membrane elements, 5β-I, 5β-II, 5β-A and 5β-C, that have been developed previously. The differences among them are shown to be of the second degree in the distortion measures of the element shape, when they are compared on the basis of the non-vanishing total value of I2 of their respectively adopted assumed stress field. Several numerical examples are used to verify and to illustrate the proposed theory.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370306
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