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Topology optimization of sheets in contact by a subgradient method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1997年第7期40卷 1295-1321页

作者： Petersson, J Patriksson, M LINKOPING UNIV DEPT ENGN MECH DIV MECH S-58183 LINKOPING SWEDEN UNIV WASHINGTON DEPT MATH SEATTLE WA 98195 USA

We consider the solution of finite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the stiffness of a sheet subject to constraints on the admissible designs and unilateral contact conditions on the displacements. The model allows for zero design volumes, and thus constitutes a true topology optimization problem. We propose and evaluate a subgradient optimization algorithm for a reformulation into a nondifferentiable, convex minimization problem in the displacement variables. The convergence of the method and its low computational complexity are established. An optimal design is derived through a simple averaging scheme which combines the solutions to the linear design problems solved within the subgradient method. To illustrate the efficiency of the algorithm and investigate the properties of the optimal designs, the algorithm is numerically tested on some medium- and large-scale problems. (C) 1997 by John Wiley & Sons, Ltd.

关键词： optimum sheet unilateral contact non-differentiable convex programming subgradient optimization algorithm

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TOPOLOGY OPTIMIZATION OF SHEETS IN CONTACT BY A SUBGRADIENT METHOD

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International Journal for Numerical Methods in Engineering 1998年第7期40卷

作者： JOAKIM PETERSSON MICHAEL PATRIKSSON Department of Mechanical Engineering Division of Mechanics Linköping Institute of Technology S-581 83 Linköping Sweden Department of Mathematics Box 354350 University of Washington Seattle WA 98195-4350 U.S.A.

We consider the solution of finite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the stiffness of a sheet subject to constraints on the admissible designs and unilateral contact conditions on the displacements. The model allows for zero design volumes, and thus constitutes a true topology optimization problem. We propose and evaluate a subgradient optimization algorithm for a reformulation into a non-differentiable, convex minimization problem in the displacement variables. The convergence of the method and its low computational complexity are established. An optimal design is derived through a simple averaging scheme which combines the solutions to the linear design problems solved within the subgradient method. To illustrate the efficiency of the algorithm and investigate the properties of the optimal designs, thealgorithm is numerically tested on some medium- and large-scale problems. © 1997 by John Wiley & Sons, Ltd.

关键词： optimum sheet unilateral contact non-differentiable convex programming subgradient optimization algorithm

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