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©2012 Civil-Comp Ltd |
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N. Strömberg
Department of Mechanical Engineering, Jönköping University, Sweden
Keywords: potential energy, unilateral contact, prescribed displacements.
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The modelling of the boundary conditions is crucial in topology optimisation. Small changes in these conditions will typically imply new optimal layouts of material. In many situations the design domain is connected to an assembly of components using contact interfaces. In order to generate proper layouts for this type of design domain one must treat these contact interfaces accurately in the topology optimisation procedure.
The bottle-neck in topology optimisation of non-linear structural problems, such as contact problems, is to solve the state equations and the adjoint equations. By choosing the potential energy as the objective the latter equations are not needed in the sensitivity analysis. In this paper topology optimization of contact problems including non-zero prescribed displacements by maximizing the potential energy is performed. For contact problems with zero initial contact gaps and zero prescribed displacements this is equivalent to minimising the compliance, which is the standard approach in topology optimisation. However, when the compliance is used as objective in topology optimisation of contact problems an extra adjoint equation must be solved. This is not needed in the formulation presented in this paper.
The efficiency of the approach is demonstrated by studying three different problems, two problems in two-dimensions and one in a three-dimensional setting. The method is implemented by using Matlab and Intel Fortran, where the Fortran code is linked to Matlab as mex-files. The implementation can be downloaded as a toolbox (Topo4abq). The three problems have beensolved using this toolbox on a laptop with an Intel Core i7 2.67 GHz processor and a 64 bit version of Windows. It is shown that the CPU-time is reduced as much as 25% compared to an adjoint approach developed in previous works.
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