摘要:

AbstractThis paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2‐D linear‐elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analy

ISSN:0029-5981    

DOI:10.1002/nme.1620381202

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA strategy for the efficient solution of non‐linear shape optimization problems is developed. This strategy employs an integrated element‐by‐element approach to the solution of the governing partial differential equations, and, more particularly, to the computation of the necessary gradients of the objective function and constraints using an adjoint formulation. This proves to be a very efficient strategy and also is relatively easy to implement, because the local effect of design changes can be exploited. The method is tested with an application involving the design of the shape of electromagnet poles in order to obtain a desired field in the interpolar r

ISSN:0029-5981    

DOI:10.1002/nme.1620381203

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co‐ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non‐linear system of differential‐algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton–Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody d

ISSN:0029-5981    

DOI:10.1002/nme.1620381204

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractBased on a two‐phase fluid model for immiscible displacement in a porous medium, we develop and analyse numerical solution techniques for certain non‐linear phenomena. Two different solution strategies for the treatment of gravity effects, which are non‐trivial to model by existing solution techniques and may be of great influence in many practical flow situations, are presented. The solution procedures are based on an operator‐splitting technique, combining the modified method of characteristics with finite element techniques and adaptive grid ref

ISSN:0029-5981    

DOI:10.1002/nme.1620381205

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe investigate the generalized mid‐point algorithms for the integration of elastoplastic constitutive equations for the pressure‐dependent Gurson–Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid‐point algorithms is derived for the Gurson–Tvergaard model. The generalized mid‐point algorithms, together with the consistent tangent moduli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the Gurson–Tvergaard model for the plane strain tension case is given and the performances of the generalized mid‐point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid‐point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid‐point algorithm (α = 0·5) the most accurate one. Considering the extra non‐symmetrical property of the consistent tangent moduli of the algorithms with α<1, the Euler backward algorithm (α = 1) is,

ISSN:0029-5981    

DOI:10.1002/nme.1620381206

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second‐order elliptic partial differential equations in two dimensions in the vicinity of singular points. The singularities may be caused by re‐entrant corners and abrupt changes in boundary conditions or material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes.This paper addresses the problem of determining the eigenpairs numerically on the basis of the Steklov formulation. Numerical results are presented for several cases. Importantly, the method is applicable to three‐dimensional

ISSN:0029-5981    

DOI:10.1002/nme.1620381207

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe deformation behaviour of a rectangular block under tension is investigated for a rate‐ and temperature‐dependent solid using the finite element method. Isotropic behaviour is assumed and the effect of deformation‐induced heat generation is studied in conjunction with heat conduction. Localization into diffuse necking is examined by applying the instability criterion defined for the particular rate‐dependent behaviour. The influence of different thermal boundary conditions on the deformation mode considered, is demonstrated by means of parametric

ISSN:0029-5981    

DOI:10.1002/nme.1620381208

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractFor the displacement‐based Lagrangian Mindlin plate elements oriented arbitrarily under uniform isoparametric mapping without internal distortion, a theoretical interpretation on the conventional shear‐reduced integration is presented by introducing the concept of reduced minimization. It reveals that the conventional shear‐reduced integration such as URI and SRI prevents the unmatched coefficients of shear strains from becoming spurious constraints. Thus, the shear‐reduced integration eliminates spurious constraints and prevents

ISSN:0029-5981    

DOI:10.1002/nme.1620381209

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper is devoted to the development of efficient preconditioners for an iterative solution of equation sets arising in the Boundary Element Method (BEM). A standard collocation system of equations is transformed to a new basis associated with an auxiliary coarse division model for boundary unknowns and solved in this basis. New systems have rapidly decreasing coefficients and by neglecting a large number of them it is possible to construct readily invertible, sparse preconditioners for iterative procedures. The specific features of the transformed matrix can be attributed to the analytical properties of integral equations. Although the transformation is based on an auxiliary coarse division model, it does not require any additional operations with boundary elements. All manipulations necessary to construct the mapping are performed on the level of algebraic equations. Numerical experiments included in the paper confirm a high rate of convergence of the developed iterative scheme.

ISSN:0029-5981    

DOI:10.1002/nme.1620381210

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620381211

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY