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  • 1975-1979  (4,369)
  • Organic Chemistry  (3,423)
  • Engineering General  (946)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1090-1094 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the two-dimensional isoparametric 8-node element an additive condition is formulated, so that the function describing the domain boundary is continually differentiable at the common nodes on the boundary. This condition will be satisfied by moving the mid-side nodes into a special position. The advantage in using this modified element will be shown by an example of the elasto-plastic calculation of a double-edge notched specimen.
    Additional Material: 3 Ill.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1095-1099 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical description of the numerical approximation to incompressibility with nearly incompressible displacement finite elements is presented. By the way of functional analysis, it leads to a condition of convergence to the incompressible problem when v is increased up to 0.5, which can be identified with Fried's K1 criterion.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1813-1850 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The computational aspects are examined for the numerical analysis of inelastic structures and continua. In this context, the tracing of quasistatic and dynamic motions is considered with particular emphasis on the interaction of nonlinear and transient problems.In the first part, explicit and implicit solution schemes are developed for the numerical integration of inelastic first-order rte processes governing creep, viscoelasticity and viscoplasticity. In the second part, the exposition is extended to second-order inertial problems and in particular to the field of dynamic plasticity, devoting special attention to the kinematics of finite deformation problems.
    Additional Material: 28 Ill.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1874-1875 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1-9 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element model is presented for the analysis of the thermal stress development in a body with temperature dependent material properties. The thermal model allows a change of phase to occur within the body and an elasto-viscoplastic constitutive relationship is used for the stress analysis. An example is given of the applicability of the technique to the analysis of continuous casting in metals.
    Additional Material: 5 Ill.
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 287-289 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple quadrature rule that precisely integrates products of singular √r and quadratic shape function gradients for a two-dimensional six node triangle and a three-dimensional fifteen node prism is derived.
    Additional Material: 1 Ill.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 292-295 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 109
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 515-529 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion. The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element. The derivation is quite general; consequently, the results can be used for a broad category of cable configurations. Individual helical armourning wires, for instance, may have unique geometric and material properties. In addition, no limit is placed on the number of wire layers. Furthermore, compressibility of the central core element can also be considered. The equations of equilibrium are first derived to include ‘internal’ geometric non-linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element. These equations are then linearized in a consistent manner to give a liner stiffness matrix. Linear elasticity is assumed throughout. Excellent agreement with experimental results for two different cables validates the correctness of the analysis.
    Additional Material: 4 Ill.
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 531-544 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees-of-freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.
    Additional Material: 4 Ill.
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 617-620 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stability analysis of the hyperbolic and parabolic explicit difference schemes presented in our previous paper 1 is improved on. Analysis of the Fourier components gives rise to stability limits that are very near the actual numerical stability limits.
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 629-630 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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  • 113
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 741-755 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.
    Additional Material: 2 Ill.
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 727-740 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the finite element calculation of the stress intensity faactors for plane extension and plate bending problems. On the basis of the plate theory including the effect of transverse shear deformation, the influences of plate thickness, crack length and plate width on the stress intensity faotors are investigated. The numeriacal analyses are carried out using the superposition method of analytical and finite element solutions. It is found that the present stress intensity factors calculated for cracked plates under plane extension as well as bending compare favorably with the analytical ones.
    Additional Material: 10 Ill.
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 769-773 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 757-767 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this paper is to show that a mathematical programming method, due to Maier and his co-workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic-plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.
    Additional Material: 3 Ill.
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  • 117
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 780-784 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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  • 118
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 774-779 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The choice of strain-displacement relations to fomulate curved finite elements for the geometrically nonlinear analysis of deep thin shells of general shape is discussed. It is clearly demonstrated on a simple arch problem how the strain-displacement relations can affect the buckling pressure and it is concuded that inconsistent expressions should be avoided.
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 946-948 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 120
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 942-945 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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  • 121
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 122
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 949-959 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification of the collocation method for the numerical solution of Cauchy-type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A(x - c)α + B(x - c)β, where α 〈 0, 0 〈 β - α 〈 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.
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  • 123
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 961-986 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.
    Additional Material: 10 Ill.
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  • 124
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 987-1000 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new numerical method of calculating unsteady-state heat conduction and thermal stresses by using improved coefficient matrix patterns on the nodal points of a structure is given. Good agreement is obtained between our results and the rigorous results, and this method seems to yield better accuracy than other well-known approximate methods for two-dimensional transient thermal stress problems.
    Additional Material: 9 Ill.
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  • 125
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1001-1019 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The homogeneous Dirichlet problem for the biharmonic operator is solved as the variational formulation of two coupled second-order equations. The discretization by a mixed finite element model results in a set of linear equations whose coefficient matrix is sparse, symmetric but indefinite. We describe a class of preconditioned conjugate gradient methods for the numerical solution of this linear system. The precondition matrices correspond to incomplete factorizations of the coefficient matrix. The numerical results show a low computational complexity in both number of computer operations and demand of storage.
    Additional Material: 8 Ill.
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  • 126
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1021-1035 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank-Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed.
    Additional Material: 9 Ill.
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  • 127
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1051-1061 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of finite element methods to parabolic partial differential equations leads to large linear systems of first-order ordinary differential equations. Very often these systems are stiff and difficulties arise in their numerical solution. We attempt to analyse the problem of how to select numerical methods for the solution of such linear systems.
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  • 128
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1037-1050 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nonlinear impact of a vehicle against a deformable barrier and its subsequent rebound from that barrier are simulated. A one-dimensional elastoplastic model represents the vehicle as a series of rod finite elements and the barrier as a single mass, nonlinear spring. The solution procedure utilizes variable time step integration, contains an error control and eliminates numerical instabilities. A limited study assesses the influence of system parameters on both structure and occupants. The chief objective, however, is to establish the feasibility of the proposed treatment of this class of problems. Some results obtained appear, at first, to contradict intuition. It is observed that modelling a deformable barrier as rigid can lead to unconservative results with respect to structural response of the vehicle.
    Additional Material: 8 Ill.
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  • 129
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1063-1072 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Similar and similarly oriented CST elements have the same stiffness matrix, and therefore similar shapes generated by the assembly of such elements possess the same stiffness matrix. This property and the matrix condensation technique may be judiciously combined to simplify the study of large structures, which may otherwise incur large core requirements and time and involve the solution of a great number of equations. In this paper the idea is developed to indicate its full potential. In illustration, results from examples on the determination of stresses around a small hole in a large plate are presented.
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  • 130
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1073-1078 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for smoothing the transition between structural components modelled with dissimilar finite element meshes is presented. The interface mismatch is assigned a potential of dislocation, which is minimized with respect to selected kinematic parametes of the mating surface. This leads to linear constraints between the caididate representations of the mating surface which essentially dictate a least-square error in dislocaiton. The constraints are enforced by the Lagrange multiplier or reduced stiffness technique. Numerical results indicate gradual transition in the predicted stresses neighbouring the interface. Existing computer codes which permit multipoint constraint specifications are readily available to implement the technique.
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  • 131
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1085-1089 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the order of certain two-dimensional quadrature formulae is discussed and it is shown that their degree and order are not related in the same simple way as they are for one-dimensional rules.
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  • 132
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1079-1084 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The decomposition of a block tridiagonal matrix into the product of block lowe and upper matrices is described. The cost of solving a block tridiagonal system of equations is given and compared to profile gaussian elimination. The desirability of a less expensive method is coupled to physical intuition about a common problem of solving a slowly varying sequence of such systems to motivate an iterative method based on residual correction. The method is described and convergence criteria are derived. An expression of the cost is developed and is shown to compare favourably with decomposition in many cases. Problems and advantages in computer implementation of the method are discussed and results of tests of a particular implementation on a well-known problem are given.
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  • 133
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1100-1104 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This communication presents a simple algorithm to compute the stiffness matrix for a triangular plate bending element, without numerical integration. This brings about a substantial saving in computer time.
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  • 134
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1105-1105 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 135
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    International Journal for Numerical Methods in Engineering 14 (1979) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 136
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1107-1126 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.
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  • 137
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1127-1140 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Reference 1 a class of first-order factorization methods for the solution of large, sparse systems of equations, of which the coefficient matrix is a symmetric M-matrix, was introduced. Asymptotic results for the computational complexity was proved in the case of systems arising from finite difference approximation of second-order self-adjoint elliptic partial differential equation problems in two dimensions with Dirichlet boundary conditions. In this paper the result is extended to cover even mixed boundary conditions and problems with discontinuous material coefficients. Results from numerical experiments with various finite difference and finite element approximations are presented and comparisons with direct and other interative methods are made.
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  • 138
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1165-1182 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical procedure for the solution of metalworking problems of a strain-hardening material. The overall metalworking process is split up into a number of stages and the governing equations for a typical stage are set up in terms of incremental displacements. The incremental deformation occurring in each successive stage is found by an interative numerical procedure based on the concept of piecewise linearization. The ‘composite’ solution yields the distribution of stress and strain in the work material at various stages of the process. Finally, application of the method to finite axisymmetric compression is described.
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  • 139
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1141-1163 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an explicit numerical method for solving transient combined heat conduction and convection problems. Applications include the cooling of many types of engineering plant; for example, stator and rotor windings of turbogenerators and high voltage underground cables. The Du Fort-Frankel and the fully implicit finite difference schemes have been used to solve the conduction and convection equations, respectively. It is shown that, with a suitable order of calculation, the overall method becomes explicit. Computational procedures are outlined and stability, accuracy and convergence are considered. Numerical examples are given to illustrate the use of the method and to validate some of the theoretical points. Results have also been obtained using existing numerical methods and have been compared with those from the proposed method. For certain problems, it is shown that the proposed method uses less overall computing time than other methods such as that devised by Crank and Nicolson.
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  • 140
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1183-1196 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 141
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1221-1239 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 142
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1197-1220 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 143
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1241-1256 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new dynamic substructuring method is presented. The substructures are identified by their fixed-interface modes and the condensed stiffness and mass matrices at zero vibration frequency. Physical co-ordinates are used instead of the modal co-ordinates to make the condition of compatibility between elements applicable. The dimension of the fundamental matrices is equal to the number of interface co-ordinates for each substructure. All information needed to formulate the fundamental matrices may be obtained experimentally. Both discrete and continuous parameter models are considered.A number of numerical examples are given and the method is compared with the other methods of dynamic substructure. It is shown that the numerical accuracy lost in the ordinary eigenvalue economization process may be recovered by the present method.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1262-1267 
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  • 145
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1257-1261 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents and results obtained from the stabilitystudies of plane Poiseuille flow and magnetohydrodynamic flow by the finite element method. Applying Galerkin's weighted residual method and introducing the interpolation function in the exponetial form with respect to time, the governing flow equations are reduced to an eigenvalue problem. This formulation is much simpler than that of the asymptotic expansion method. Solutions are obtained directly in terms of velocity and pressure. Results of the critical Reynolds number obtained by this method compare well with those of other methods for plane Poiseuille flow and magnetohydrodynamic flow.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1268-1270 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In Reference 1 a mistake has been made by the derivation of equation (40). The correct expression is shown in the present note.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1271-1271 
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1272-1272 
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  • 149
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    International Journal for Numerical Methods in Engineering 14 (1979) 
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  • 150
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    International Journal for Numerical Methods in Engineering 14 (1979), S. i 
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  • 151
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1273-1291 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Finite element interpolations of arbitrary polynomial degree which are exactly and minimally C1 continuous across interelement boundaries are studied. A perspective view of the techniques proposed by other authors is presented and some new possibilities are considered. The problem is discussed with reference to the plate and shell finite element approximations, based on the principle of minimum potential energy. The approach also permits identification of sufficient conditions for guaranteeing full rank of stiffness matrices based on modified principles of potential energy. The results of this analysis can be used to investigate the linear dependencies among nodal variables which also occur in the formulation of other fourth-order problems.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1293-1307 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper the computer code Duvorol, dealing with the computation of three-dimensional rolling contact with dry friction, is described. It is based on the variational principle of Duvaut and Lions for dry friction, which leads to an incremental theory. The relevant properties of Duvorol are:1Generality. All half-space steady-state rolling contact problems with Hertzian normal contact can be treated.2Reliability. The total tangential force is always found with reasonable accuracy by a standard discretization.3Speed. On an IBM 370/158 the calculation of a case then takes only several seconds.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1323-1333 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An incremental force-displacement relation is derived using the finite element matrix method to study the inelastic bending of beams including transverse shear. Solutions are obtained for the case of a cantilever beam with a point load and a simply supported beam with distributed loading considering and also ignoring the effect of transverse shear. They show good agreement for those cases where solutions are available. Also, the effect of transverse shear is found to be quite significant.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1309-1321 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An accurate nonlinear analysis procedure for calculating the displacement stresses and system buckling loads of geometrically imperfect truss structures is developed. The investigation considers both local and system imperfections. This nonlinear analysis takes first-order geometrically nonlinear effects into account. The accuracy of the analysis procedure is confirmed by comparison with analytical and experimental results for truss structures drawn from the literature. The results show that local and system imperfections can have strong influence on the behaviour of truss structures and therefore should be taken into account. It is shown that nonlinear effects play a major role in the phenomena and therefore simplified analyses that neglect nonlinear effects are inadequate.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1335-1346 
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    Notes: A new second-order accurate method for the solution of two-point boundary value problems on a uniform mesh is given; the local truncation error is obtained for use with the deferred correction process. The method is compared with existing second-order techniques and is shown to produce more accurate results for a number of linear and nonlinear example problems.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1347-1358 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, yet effective, finite element approach to aerodynamic problems is presented. A better approximation of the geometry is obtained by the mapping of airfoils into near-circles. The mapping serves in homogenizing the gradients of the problem by magnifying regions of high gradients such as the leading and trailing edges while geometrically condensing the lower gradient regions on the main part of the airfoil. The mapping also permits the use of an effective automated mesh generation scheme that greatly reduces the amount of preparatory work involved in finite elements. To limit the size of the solution domain, an asymptotic analytical solution, with unknown coefficients, is assumed on a finite radius outer contour. The coefficients are obtained along with the finite element nodal unknowns. An accrued advantage of this patching asymptotic procedure is its ability to obtain the lift as a solution variable without having to resort to the numerical integration of the pressure field over the body. Solutions to non-lifting and lifting bodies are obtained.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1359-1377 
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    Notes: We introduce a finite element model for stress analysis of threaded connections. Instead of modelling individual threads, the thread zone is replaced by a layer of elements with orthotropic properties. The principal directions of orthotropy depend upon the thread geometry and upon the direction of load, which is not necessarily known a priori. Both conventional and tapered threads are considered. The latter problem is nonlinear, as the number of threads in contact is a function of the load. Numerical results for conventional and tapered threads agree well with theoretical and exeprimental results in the literature.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1379-1398 
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    Notes: Orthogonal base functions that are complete first-order polynomials but contain higher order terms are developed for normalized rectangular and triangular elements. To obtain exact expressions for kinetic energy under rigid body rotation, an internal node is introduced at the centroid of each element. Then the corresponding mass matrix is both diagonal and consistent. A mixed variational formulation is used in the derivation of spatially discretized field equations. Central Difference time integration is utilized to provide sample results which are compared with other numerical or analytical solutions.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1399-1412 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A combination of a two-dimensional finite element process and a Fourier series in the third dimension, well known in linear applications, is shown to be a possible and efficient way of analysing plastic and visco-plastic behaviour. The economy of the process as contrasted with full three-dimensional solutions is illustrated.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1428-1429 
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1421-1427 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It is shown here that certain interpolating polynomials of degrees four and five may not always be uniquely defined on triangular-shaped elements which have one curved side. Conditions which indicate non-uniqueness are given, together with some geometrical interpretations concerning the location of the node on the curved side. A numerical example is given to demonstrate that there ar curves for which every point is unsuitable to be chosen as a node.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1413-1420 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the light of recent contributions by Batoz1 and Hibbitt,2 two aspects of finite element formulations for shell stability analysis are examined. The first is the consistency of the shell strain-displacement equations employed; the second is the proper representation of ‘follower forces’ - pressures that are always normal to the deforming surface. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted buckling loads. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted bukling loads.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1430-1430 
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1430-1430 
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    International Journal for Numerical Methods in Engineering 14 (1979) 
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1461-1476 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1431-1448 
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    Notes: The higher order dynamic correction terms for the stiffness and inertia matrices associated with a triangular plane stress-strain finite dynamic element are developed in detail. Numerical results presented indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structures when compared with the analysis based on the usual finite element procedure.A FORTRAN IV computer program listing of the various relevant element matrices is also presented in the Appendix.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1449-1460 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model is proposed to simulate the space-time behaviour of a low-density plasma in a linear multipole. Semi-discrete Galerkin techniques are used in conjunction with triangular finite elements. For both space and time discretizations, special techniques are developed to numerically separate the effect of rapid diffusion along the field lines from the slow perpendicular diffusion. Numerical results are exhibited to show how these techniques succeed in eliminating the problems caused by the strong anisotropy of the diffusion coefficient in the strongly curved and very inhomogeneous multipole configuration.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1477-1497 
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    Notes: Some tools are presented that may be used when implementing an application oriented software system. FEMSYS, a system for calculations based on the finite element method, will serve as example. Features of a simple problem oriented language and its parsing are treated and also a generally applicable data structure for both internal and external data storage. It is indicated how a system can be implemented which is suited to the solution of both standard and non-standard problems.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1499-1509 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An isoparametric Hermite cubic element is developed for calculating compressible flows past complex aerofoils in two dimensions. A simple intermediate transformation is used to derive an isoparametric transform whose Jacobian is always non-zero and which attains very high accuracy on the boundary. Application of the method and assessment of the error is illustrated by flow past a circular cylinder.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1511-1524 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Three weighted residual methods are used to analyse several linear and nonlinear model problems related to the stream function-vorticity formulation of the Navier-Stokes equations. These methods are then used to solve the driven cavity problem. The results obtained at Reynolds numbers of 100 and 400 compare very favourably with those obtained by finite difference and spline methods on meshes using at least four times as many mesh points.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1525-1544 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Various singularity finite elements proposed so far are reviewed and their correlations are discussed. The method adopted in the comparative study is based on the singularity mapping or transformation technique. It is suggested that a compact design of computational routines is materialized by using the element which embodies singularity transformation and can be compatible with the notion of using the variable-number-nodes element in the general-purpose computer programs.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1545-1557 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The reasons for the presence of spurious modes in plane isoparametric elements are examined. Eigenvalue and eigenvector analyses of stiffness matrices for single elements and unconstrained and constrained meshes reveal the types of mechanisms and near-mechanisms that can be expected when reduced or selective integration techniques are used with quadrilateral elements in the analysis of plane strain problems.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1559-1562 
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    Notes: Approximate and exact methods are presented for computing a function, related to complete elliptic integrals of the first kind, which arise in the theory of microwave transmission lines. The method can be implemented on programmable hand calculators.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1563-1566 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is presented for inverting an n × n complex matrix M = A + jB by using a real matrix inversion. The approach avoids the requirements of inverting a 2n × 2n real matrix as well as non-singularity assumptions placed on A or B, or A + B, or A - B, as required by earlier methods.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1574-1574 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper a new, one-point iterative formula for solution of equations is presented.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1567-1573 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a finite difference method for two-point boundary value problems described by fourth-order ordinary differential equations which results in consistency of truncation errors. It is demonstrated that the order of the formulae used to approximate the boundary conditions must be higher than those used for similar derivative terms in the differential equation. A generalization of the method to differential equations of order n is discussed. The procedure is illustrated with a numerical example.
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1575-1579 
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  • 180
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1581-1596 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Possibility of the application of the finite element method to some problems of nonlinear optics is investigated in this paper. The self-action of a light beam in a nonlinear medium is considered. The general approach to the cretion of conservative computation schemes is presented, based on varitional principles. Definite schemes, which are applicable for the problem of thermal self-action, are described in detail both in the case of cylindrical and or rectangular co-ordinates. The accuracy and convergence of the models are analysed. The results of computation of the self-action problems in motionless and moving media are presented.
    Additional Material: 10 Ill.
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  • 181
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1613-1626 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi-Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
    Additional Material: 1 Ill.
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  • 182
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1597-1612 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic response of strip footings resting on a soil medium, idealized as an elastic halfspace, is obtained using the finite element discretization technique with constant strain rectangular elements consisting of 4CST elements. Boundary stresses have been computed using a combination of Rayleigh wave absorbing boundaries (RAB) and standard vicous boundaries (SVB). The influences of contact pressure distributions at the footing - soil interface, mass and frequency ratios on the dynamic response of a strip footing are studied. Effects of embedment, static surcharge, nonhomogeneity and nonlinear constitutive relations are shown. Results are compared with the existing solution and are presented graphically.
    Additional Material: 11 Ill.
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  • 183
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1627-1641 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two properties of hybrid element method for diffraction and radiation of water waves are examined. For long waves in shallow water the method is shown to give a unique solution for all frequencies. Thus, unlike several other known methods, there are no irregular frequencies for which the approximating matrix equation is singluar. For a sea of arbitrary depth, it is shown that all known global identities such as reciprocity and energy theorems are preserved by the discrete solution. Thus, satisfaction of these identities by the numerical solution is only a necessary but by no means sufficient condition for accuracy.
    Additional Material: 5 Ill.
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  • 184
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1653-1663 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The concept of fictitious external loading being in exact equilibrium with the internal stresses in a structure is introduced. It is employed in conjunction with the principle of virtual work in an effort to examine certain details of the finite element displacement method in an alternative way.
    Additional Material: 5 Ill.
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  • 185
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1643-1651 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several examples are presented to illustrate how standard finite differnce schemes for the wave eqation (e.g. Lax-Wendroff, Leafrog, etc.) can be developed from finite element analysis. The development of the diffrence schemes from the element schemes is made possible by using Galerkin's method on both the spacial and temporal dimensions.
    Additional Material: 10 Ill.
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  • 186
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1665-1678 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of local mesh refinements for the generation of meshes for the finite element or finite difference methods is studied. A class of rectangular meshes which admit restricted local refinements, referred to as irregular rectangular meshes, is introduced and its representation discussed. Properties of algorithms for mesh refinements are discussed from the viewpoints of termination with a mesh in the specified class, memory utilization, symmetry and fragmentation of the mesh.
    Additional Material: 8 Ill.
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  • 187
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1679-1692 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Transform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi-dimensional case.
    Additional Material: 10 Ill.
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  • 188
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1707-1709 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent property of the discrete solution to certain one-dimensional problems is examined in the context of the weighted residual difference equations and their conservation properties. The difference equations are shown to satisfy the differential equation exactly at nodes and reproduce the derivatives at boundary nodes. The exact values for the first derivative at interior nodes follow from the conservation property when applied locally.
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  • 189
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1715-1725 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 190
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1693-1706 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness-derivative method of Parks1 for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector field2,3 which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3 on the weight function and of Zienkiewicz4 on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back-substitution on the already-factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three-dimensional configurations is outlined.While this manuscript was under review, the authors became aware of the recent work of Vanderglas,21 in which the same approach as ours is used to extend the stiffness derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vanderglas noted.
    Additional Material: 6 Ill.
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  • 191
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1710-1714 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification of the numerical techniques of solution of Cauchy-type singular integral equations and determination of stress intensity factors at crack tips in plane elastic media is proposed. This technique presents some advantages under appropriate geometry conditions.
    Additional Material: 2 Tab.
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  • 192
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1726-1731 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Transient heat conduction in a composite slab is investigated in the present work by using the orthogonal collocation method. The present numerical method is found to be quite efficient and highly stable even for the power-type temperature dependence of thermal conductivity which often cuases severe computational instability to many numerical methods.
    Additional Material: 3 Ill.
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  • 193
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1732-1733 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 194
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1732-1733 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 195
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1735-1738 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 196
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1734-1734 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 197
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    International Journal for Numerical Methods in Engineering 14 (1979) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 198
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1734-1734 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 199
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1739-1760 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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  • 200
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    International Journal for Numerical Methods in Engineering 14 (1979), S. 1761-1783 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The selection of the set of active constraints does not introduce any difficulty and is achieved correctly in all cases. The subdivision of the design variables in an active and passive group is intrinsically contained in the dual formulation. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results.
    Additional Material: 8 Ill.
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