摘要:

AbstractThis paper deals with simple and effective C0linear triangular bending elements based on the Hu‐Washizu variational principle. The following key features are inherent in the proposed formulation: extensional, flexural and transverse shear strains and the corresponding stresses are referred to the directions of the triangle sides. The independent variation of displacements, strains and stresses yields discrete approximations consistent with the continuum theory. Furthermore, a proper identification of the deformational modes and the orthogonality requirements between the assumed transverse shear forces and the undesirable strain fields lead to element formulations with important attributes: minimization of superfluous energy, properly justified assumptions, simplicity of formulation and straightforward extension to non‐linear problems. Alternative approximations of strains and stresses, also presented, enhance the element performance in the case of both thick and thin plates and shells. Test examples demonstrate the characteristic properties of the proposed element formulati

ISSN:0029-5981    

DOI:10.1002/nme.1620360202

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe paper describes how several procedures for higher‐order predictions have been introduced in order to improve the convergence speed in a general finite element program for non‐linear structural analysis. In addition to higher‐order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post‐bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re‐creation of the tangential stiffness matrix, used for equilibrium iterations.Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods.The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferr

ISSN:0029-5981    

DOI:10.1002/nme.1620360203

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this paper a boundary element method for two‐dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic‐perfectly plastic or work‐hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three‐noded line elements are used to represent the boundary and eight‐noded quadrilateral or six‐noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load i

ISSN:0029-5981    

DOI:10.1002/nme.1620360204

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non‐singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non‐singular and is shown to be amenable to simple, low‐order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi‐analytical BIE implementation reported

ISSN:0029-5981    

DOI:10.1002/nme.1620360205

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIn distance geometry problems and many other applications, we are faced with the optimization of high‐dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well‐known preconditioning techniques for the conjugate gradient method remain applicable. Very‐large‐scale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the al

ISSN:0029-5981    

DOI:10.1002/nme.1620360206

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.

ISSN:0029-5981    

DOI:10.1002/nme.1620360207

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractLow order finite elements are of vital interest for practical applications in linear and non‐linear structural analysis. The possible discretization errors, when Reissner‐Mindlin shell elements with bilinear shape functions are used, and modifications to prevent these errors are presented. On some numerical examples the influence of these errors and of various modifications on the results is shown. Finally, the case of membrane locking with low order Reissner‐Mindlin elements for particular assumptions concerning the base vectors and methods to prevent this locking are disc

ISSN:0029-5981    

DOI:10.1002/nme.1620360208

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractAn efficient solution procedure for elasto‐plastic analysis of Reissner‐Mindlin plates has been proposed in this work. The main ingredients which render efficiency are: what appears to be an optimally tuned four‐node plate element with assumed shear strains and incompatible bending modes; an elasto‐plastic constitutive model given directly in terms of stress resultants; and efficient computation of plastic flow which simplifies to a solution of a single scalar equation and remaining state update computation. The performance of the element has been proved very satisfying in both elastic singularity‐dominated and elasto‐plast

ISSN:0029-5981    

DOI:10.1002/nme.1620360209

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non‐linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non‐linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. The method is applied to the test problems of a three‐dimensional sphere with an axisymmetric boundary condition and a two‐dimensional

ISSN:0029-5981    

DOI:10.1002/nme.1620360210

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non‐axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluate

ISSN:0029-5981    

DOI:10.1002/nme.1620360211

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY