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  • 1
    Electronic Resource
    Electronic Resource
    An implementation of mixed enhanced finite elements with strains assumed in Cartesian and natural element coordinates using sparse B (overline)-matrices (2000)
    Bradford : Emerald
    Engineering computations 17 (2000), S. 933-949 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu-Washizu variational formulation with orthogonal stress and strain functions is considered. The use of orthogonal functions leads to a formulation with B (overline) -strain matrices which avoids numerical inversion of matrices. Depending on the choice of the stress and strain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P-S of Pian-Sumihara or the Trefftz-type element QE2 of Piltner and Taylor. With the mixed formulation discussed in this paper a simple extension of the high precision elements P-S and QE2 to general non-linear problems is possible, since the final computer implementation of the mixed element is very similar to the implementation of a displacement element. Instead of sparse B-matrices, sparse B (overline) -matrices are used and the typical matrix inversions of hybrid and mixed methods can be avoided. The two most efficient four-node B (overline) -elements for plane strain and plane stress in this study are denoted B (overline)(x, y)-QE4 and B (overline)(?, ?)-QE4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400010379776
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  • 2
    Electronic Resource
    Electronic Resource
    Comment on “Series solutions for a transversely loaded and completely clamped thick rectangular plate based on the three-dimensional theory of elasticity” by I. A. Okumura and Y. Oguma, Archive of Applied Mechanics, 68, 103–121 (1998) (2000)
    Springer
    Archive of applied mechanics 70 (2000), S. 670-670 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004190000108
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  • 3
    Electronic Resource
    Electronic Resource
    Trefftz-type boundary elements for the evaluation of symmetric coefficient matrices (1994)
    Springer
    Computational mechanics 15 (1994), S. 137-160 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The classical Trefftz-method can be generalized such that different types of finite elements and boundary elements are obtained. In a Trefftz-type approach we utilize functions which a priori satisfy the governing differential equations. In this paper the systematic construction of singular Trefftz-trial functions for elasticity problems is discussed. For convenience a list of solution representations and particular solutions is given which did not appear together elsewhere. The Trefftz-trial functions with singular expressions on the boundary are constructed such that the physical components (stresses, strains, displacements) remain finite in the solution domain and on the boundary. The unknown coefficients of the linearly independent Trefftz-trial functions for the physical components can be obtained by using a variational formulation. The symmetric coefficient matrix in the discussed procedure can be obtained from the evaluation of boundary integrals. As an application of the proposed boundary element algorithm, the symmetric stiffness matrices of subdomains (finite element domains) are calculated. For the numerical example the solution domain is decomposed into triangular subdomains so that a standard finite element program could be used to assemble the system of equations. The chosen example is meant as a simple test for the proposed algorithm and should not be understood as a proposal for a new triangular finite element. Using the proposed boundary element techniques, symmetric stiffness matrices for irregular shaped subdomains (finite elements) can be derived. However, in order to use the method in a finite element package for the coupling of irregular shaped subdomains some program modifications will be necessary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00372566
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  • 4
    Electronic Resource
    Electronic Resource
    An alternative version of the Pian–Sumihara element with a simple extension to non-linear problems (2000)
    Springer
    Computational mechanics 26 (2000), S. 483-489 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  The stiffness matrix for the Pian–Sumihara element can be obtained in a different way than originally presented in Pian and Sumihara (1984). Instead of getting the element matrix from a hybrid stress formulation with five stress terms one can use a modified Hu–Washizu formulation using nine stress and nine strain terms as well as four enhanced strain terms. Using orthogonal stress and strain functions it becomes possible to obtain the stiffness matrix via sparse B¯-matrices so that numerical matrix inversions can be omitted. The advantage of using the mixed variational formulation with displacements, stresses, strains, and enhanced strains is that the extension to non-linear problems is easily achieved since the final computer implementation is very similar to an implementation of a displacement element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660000198
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  • 5
    Electronic Resource
    Electronic Resource
    The application of a complex 3-dimensional elasticity solution representation for the analysis of a thick rectangular plate (1988)
    Springer
    Acta mechanica 75 (1988), S. 77-91 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Recently a complex representation of the stresses and displacements for the three-dimensional field equations of elasticity was developed such that the complex formulas of Muskhelishvili [1] for plane strain are included as special cases [2], [3], [4]. The solution is given in terms of six arbitrary complex valued functions. The complex variables in the formulation contain parameters, which can be considered as discrete parameter values or parameter functions. In this paper the use of the complex formulation for the case of discrete parameter values is illustrated within the example of a thick rectangular plate, where the boundary conditions on the side faces are chosen to be the vanishing deflection, normal stress and tangential displacements. Assuming these three-dimensional boundary conditions for the evaluation of the according conditions of a two-dimensional Reissner-model gives a set of boundary conditions which was treated by Salerno and Goldberg [9]. The Reissner-results are used for the sake of comparison with the three-dimensional solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174629
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  • 6
    Electronic Resource
    Electronic Resource
    Special finite elements with holes and internal cracksThis work has been supported by the DFG (Deutsche Forschungsgemeinschaft). (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1471-1485 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210809
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  • 7
    Electronic Resource
    Electronic Resource
    A boundary element algorithm using compatible boundary displacements and tractions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1323-1341 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the aid of Muskhelishvili's complex plane elasticity solution representation compatible displacement and stress fields are constructed. The complex functions in these formulas are represented by Cauchy integrals, which are discretized along the boundary with the aid of complex shape functions for each boundary element. The constructed displacement and stress functions satisfy the Navier equations and the equilibrium equations, respectively. The use of fifth order complex basis functions with continuous second complex derivatives gives numerical results of high accuracy.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290614
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  • 8
    Electronic Resource
    Electronic Resource
    A quadrilateral hybrid-Trefftz plate bending element for the inclusion of warping based on a three-dimensional plate formulation (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 387-408 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived without ad hoc assumptions from the three-dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co-ordinate z, is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy, a priori, the three-dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin plates.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330210
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  • 9
    Electronic Resource
    Electronic Resource
    A quadrilateral mixed finite element with two enhanced strain modes (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 1783-1808 
    Details
    ISSN: 0029-5981
    Keywords: finite elements ; enhanced strain method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved plane strain/stress element is derived using a Hu-Washizu variational formulation with bilinear displacement interpolation, seven strain and stress terms, and two enhanced strain modes. The number of unknowns of the four-node element is increased from eight to ten degrees of freedom. For linear and non-linear applications, the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element, which is denoted by QE2. The excellent performance of the proposed element is demonstrated using several linear and non-linear examples.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381102
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