摘要:

AbstractThis paper presents an improved solution of three‐dimensional plasticity problems using the boundary element method (BEM). The BEM formulation for plasticity requires volume as well as boundary discretizations. An initial stress formulation is used to satisfy the material non‐linearity. Conventionally, the plastic field in the volume element (or cell) is interpolated based on the value of plastic stress at the nodes of the cell. In this paper, the distribution of the plastic field in the cell is based on a number of points interior to the cell. The plastic field is described using regression interpolation polynomials through these interior points. The constitutive relation is satisfied at each interior point. The number of points can be varied in each cell, thus allowing for adaptive volume cells. The plastic stresses are computed at the interior points only, therefore, the need for surface stress computation (which uses numerical derivatives at the surface) is completely eliminated. Three‐dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto‐plasticity problems. In all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation

ISSN:0029-5981    

DOI:10.1002/nme.1620331002

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA solution to a parameter estimation problem in heat conduction with phase change is presented. Specifically, the thermophysical properties of the material are estimated by using the temperature measurements of several sensors located inside the fixed domain.In the parameter estimation problem the error is minimized between given and modelled temperatures at sensor locations over the time interval where the experiment involved variation of the material parameters. The methods are illustrated with several examples. The effects on the solution of the locations of the sensors, the number of the sensors, the time step and the number of time steps are examined.

ISSN:0029-5981    

DOI:10.1002/nme.1620331003

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two‐dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg‐Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated paramet

ISSN:0029-5981    

DOI:10.1002/nme.1620331004

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA solution strategy is proposed and implemented for taking advantage of the hierarchical structure of linear equation sets arising from thep‐type finite element method using a hierarchical basis function set. The algorithm dynamically branches to either direct or iterative solution methods. In. the iterative solution branch, the substructure of the finite element equation set is used to generate a lower order preconditioner for a preconditioned conjugate gradient (PCG) method. The convergence rate of the PCG algorithm is monitored to improve the heuristics used in the choice of the preconditioner. The robustness and efficiency of the method are demonstrated on a variety of three dimensional examples utilizing both hexahedral and tetrahedral mesh discretizations. This strategy has been implemented in ap‐version finite element code which has been used in an industrial environment for over two years to solve mechanical design probl

ISSN:0029-5981    

DOI:10.1002/nme.1620331005

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA general method for shape design sensiti vityi analysis (SDSA) as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method. The sensitivity of a general functional composed of thermal and mechanical quantities is considered. The method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. It is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary. Results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading. The sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences. Optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only, clearly showing the practical importance of the SDSA of thermoelastic systems.

ISSN:0029-5981    

DOI:10.1002/nme.1620331006

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper presents the results of a study on the buckling and postbuckling analyses of layered shear‐deformable composite plates usingp‐version finite strips. The plates are considered to be sufficiently long so that the effect of boundary conditions along the shorter edges is of little significance; this makes it possible to use the ‘exact’ trigonometric functions in the longitudinal direction. The displacement field in the transverse direction is discretized byp‐version finite strips and convergence is studied byp‐extension, i.e. keeping the number of strips relatively small whilst increasing the polynomial order till convergence of the buckling load or the postbuckling stiffness is achieved.Detailed convergence studies are presented and comparison with results of earlier investigations are shown wherever appropriate. The results demonstrate the superior convergence characteristics of thep‐ver

ISSN:0029-5981    

DOI:10.1002/nme.1620331007

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA finite element formulation for geometric non‐linear analysis of elastic straight thin‐walled beams is presented. The updated Lagrangian procedure is used for a stiffness matrix derivation‐to analyse large displacements or buckling behaviour of space frames. The stiffness matrix is developed for a generic cross‐section and is equally efficient for symmetric, monosymmetric or asymmetric open sections. Some non‐linear strain terms usually neglected in the literature have been considered, resulting in a formulation which also includes the initial bimoment and torsion effect for all cross‐sections analysed. The proposed method has been implemented and the results of sample problems ar

ISSN:0029-5981    

DOI:10.1002/nme.1620331008

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractLinear and non‐linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non‐linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non‐linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical exa

ISSN:0029-5981    

DOI:10.1002/nme.1620331009

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe continuity and differentiability of object functions is a basic prerequisite for the application of gradient methods in optimization. However, for parameters defining the shape of an electromagnetic device, the finite element discretization in the field analysis introduces discontinuities into the object function which slow down the convergence rate. Additionally, depending on the geometric parametrizaiion employed, the optimization frequently yields shape contours that are impracticable for manufacturing purposes. This paper investigates the problems inherent in geometric parametrization and shows that the discontinuities in the object function are caused by changes in mesh topology as the geometric parameters vary; these changes inevitably follow from the use of free meshing algorithms. As a solution to these shortcomings a structural mapping technique is outlined that maps surface displacements onto the parameters of the finite element mesh and obtains the parameter dependent geometric variations without a change in mesh topology. This resulting geometric parametrization yields continuous object functions without artificial local minima and results in smooth surface contours of the optimized device. Using this new parametrization technique, design sensitivity analysis, is shown to be a reliable and essential part in the efficient application of gradient methods for shape optimization.

ISSN:0029-5981    

DOI:10.1002/nme.1620331010

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAssumed field‐consistent strain formulations of the displacement finite element procedure can lead to poor convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, i.e. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger–Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field‐consistency and variational' consistency are two complementary but mutually exclusive principles—one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constraine

ISSN:0029-5981    

DOI:10.1002/nme.1620331011

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY