摘要:

AbstractA method is presented for the finite element analysis of the interaction of geometrically and materially non‐linear bodies. Interaction is considered at predefined interfaces. Equations for interaction forces are assembled via static condensation, and the solution for these forces is utilized for the full analysis of the problem. An interface function using the interpolating functions is defined to maintain the equilibrium of interaction forces and the displacement compatibility at the interface nodes. The method permits large rotations and slipping as well as the occurrence of new contacts at the interfaces. Additionally, solutions can be found using high‐ or low‐order elements and when nodes at either side of the interface are not al

ISSN:0029-5981    

DOI:10.1002/nme.1620361702

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe boundary discretization of the curl‐free vector variable such as the magnetic field h and the divergence‐free variable such as the surface current density k is discussed. Instead of introducing the scalar variables, the vector variables h and k are discretized by the curl‐conform and the div‐conform triangular edge elements, respectively. The degrees of freedom are associated with the boundary edges. In order to ensure the null curl of h and the null divergence of k, a spanning tree technique is used to identify the independent edges. The triangular edge elements contain the first‐order nodal elements when expressing h or k by the scalar variables. The use of edge elements permits one to solve multiply connected problems if the independent edges are well identified, i.e. the necessary cuts are introduced in multiply connected domains. An automatic tree generation algorithm is presented. It permits one to determine automatically the additional edges on the necessary loops (cuts) of a multiply connected region. Some tree generation examples are illustrated. A numerical application to a three‐dimensional multiply connected eddy current problem is reported at the end o

ISSN:0029-5981    

DOI:10.1002/nme.1620361703

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper describes a parallel implementation ofLDLTfactorization on a distributed‐memory parallel computer. Specifically, the parallelLDLTfactorization procedure is based on a row‐oriented sparse storage scheme. In addition, a strategy is proposed for the parallel solution of a triangular system of equations. The strategy is to compute the inverses of the dense principal diagonal block submatrices of the factorL, stored in a row‐oriented structure. Experimental results for a number of finite element models are presented to illustrate the effectiveness of the parallel solution sc

ISSN:0029-5981    

DOI:10.1002/nme.1620361704

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA new four‐node conforming quadrilateral element (NCQ) for plate bending is Described. The element is based on an earlier free formulation due to Bergan,1,2but extra twist variables are included to make it more accurate. The element geometry is in bilinear polynomials representation, while the displacement functions are described by slight modifications of bicubic polynomials which satisfy energy orthogonality and need not be force‐orthogonal. It is shown that the coupling stiffness between the fundamental deformation modes and its higher‐order deformation modes has been altered. Numerical examples indicate that the element gives a surprisingly accurate sol

ISSN:0029-5981    

DOI:10.1002/nme.1620361705

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper describes a method for the numerical computation of hypersingular integrals as they appear in the boundary element analysis. The proposed method is based on the finite part concept and allows for arbitrary curved boundary elements. Owing to the unknown transformation properties of finite part integrals undergoing a non‐linear co‐ordinate transformation, the definition formula of finite part integrals is applied prior to the transformation into the usual element co‐ordinate system. The resulting integrals are regular and may be evaluated by standard Gaussian quadrature rules. The method is described in detail for the boundary integrals of two‐dimensional linear elastostatics. Numerical examples are inclcded for this type of problem, but the method may easily be adapted to other two‐dimensional

ISSN:0029-5981    

DOI:10.1002/nme.1620361706

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe paper presents the dual hybrid‐Trefftz (HT) element approach devised so as to enforce more strongly the reciprocity of boundary tractions at the element interfaces than the interelement conformity of displacements. As in the standard HT approach,1,2a complete set of Trefftz functions is used to represent the internal displacement field of the element (and, as a consequence, the governing Navier‐Lamé differential equations are aprioriverified over the element). But rather than employing an auxiliary interelement displacement frame field to enforce the conformity on the internal displacements, an auxiliary boundary traction field is adopted to enforce at the element interfaces the reciprocity of tractions derived from the internal displacement field. Provided that the number of Trefftz functions is sufficiently large, this approach yields an opposite bound on the energy in comparison to the standard HT approach based on the displacement frame. As in the standard HT formulation,3the dual HT formulation is particularly well suited for generation of highly accuratep‐version elements. Although presented for solid mechanics, the formulation also holds for other problems. Numerical studies which involve comparisons of the two alternative displacement and traction frame HT element models have been performed by considering the Laplace's equation problem in two dime

ISSN:0029-5981    

DOI:10.1002/nme.1620361707

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA broad class of engineering problems in fracture mechanics, thermal/fluid transport and electromagnetic theory involve the evaluation of two‐dimensional finite part integrals of the formA method for evaluation of such integrals is developed by deriving an equivalent integral using Fourier transformation. This equivalent integral does not involve a kernel with singular behaviour. Consequently, standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations. The accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometrie

ISSN:0029-5981    

DOI:10.1002/nme.1620361708

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA three‐dimensional (3‐D) time‐domain boundary integral equation method (BIEM) is presented for transient elastodynamic crack analysis. A non‐hypersingular traction BIE formulation is used with the crack opening displacements and their derivatives as unknown quantities. A collocation method in conjunction with a time‐stepping scheme is developed to solve the non‐hypersingular time‐domain BIEs. To simplify the analysis and to describe the proper behaviour of the unknown quantities at the crack front, a constant spatial shape function is applied for elements away from the crack front, while a spatial ‘square‐root’ crack‐tip shape function is adopted for elements near the crack front. A linear temporal shape function is used in the time‐stepping scheme. Numerical calculations, have been carried out for penny‐shaped and square cracks. Results for the elastodynamic stress intensity factors are presented as functions of the temporal and the spatial variables. For the test examples considered, good agreement between the present results and those of

ISSN:0029-5981    

DOI:10.1002/nme.1620361709

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIn engineering applications often problems with symmetric system and symmetric loading occur. It is well known that these symmetry conditions can be used to reduce the computational effort. Thus, only a symmetric reduced system is treated with sufficient boundary and loading conditions. Especially for non‐linear problems this procedure is very effective. Such a strategy allows the computation of solution paths with the constraint that the solution has to be symmetric. Consequently in a stability analysis, only limit points and bifurcation points with associated symmetrical eigenvectors can be found. Often the stability behaviour is dominated by symmetry‐breaking bifurcation points which cannot be detected considering only the tangent stiffness matrix of the reduced system. Hence, in case of stability considerations a calculation of the complete system is necessary. This paper introduces a special form of stability analysis of the complete system using only certain matrices known from the symmetric reduced system, and some transformations concerning the topology of the total system. The proposed methods base on a substructure technique for symmetry under reflections and rotations, and are formulated for the finite element method. Numerical examples are given to show the efficiency of the proposed procedures and algorit

ISSN:0029-5981    

DOI:10.1002/nme.1620361710

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620361711

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY