Keywords: object-oriented programming, parallel programming, finite element method, structural optimization, nonlinear kinematics, CAGD-free optimization, C++.

The world of computational simulation has to face growing multidisciplinary challenges to satisfy the demands for realistic prediction in virtual design. More complex models have to be tackled and coupled-field effects have to be taken into account. Structural optimization can be used as general tool in the design process [1]. However, response functionals of complex models are usually severely nonlinear and non-convex. Thus highly specialized methods from different disciplines must be combined to solve these optimization problems, which results in a crucial demand for flexibility of the computational environment.

This contribution presents computational concepts and algorithmic techniques of the in-house code Carat++ for simulation and gradient-based optimization of large-scale structural finite element models. In order to establish a high level of flexibility and extensibility, object-oriented programming has been the key concept of software design. It is shown that the object-oriented paradigm facilitates and alleviates the application of advanced optimization strategies capable of handling the computational difficulties of complex simulations.

Computer aided geometric design (CAGD)-free optimization methods are used to integrate shape optimization during an early stage of design and to reduce the modelling effort. First order gradient information is computed by an exact semi-analytical approach [2]. To overcome the problem of increasing numerical cost due to large design space, the design sensitivities are evaluated using adjoint formulations. Regularization and filtering is performed to overcome arising singularities due to the highly non-convex design spaces [3]. Nonlinear kinematics is included in both simulation and sensitivity analysis. It is shown that this yields much better designs with extremely efficient load carrying behaviour especially pronounced in the case of highly loaded lightweight structures.

A new parallel computation strategy for sensitivity evaluation is presented which comprises all these techniques and takes advantage of a fully parallelized simulation and optimization environment. The node-cut approach is applied as partitioning concept. Beyond that, each sub-domain is extended by a band of remote-copy elements and nodes that both belong to surrounding partitions. This technique, which has been suggested by Patzak et al. to establish nonlocal constitutive models [4], is used in this contribution to facilitate sensitivity evaluation and filtering in the context of optimization. Two application examples illustrate the method, the applicability to large problems, and the high parallel efficiency.

1

K.-U. Bletzinger, M. Firl, J. Linhard, R. Wüchner, "Optimal Shapes of Mechanically Motivated Structures", Comput. Methods Appl. Mech. Engrg, 199, 324-333, 2010. doi:10.1016/j.cma.2008.09.009

2

K.-U. Bletzinger, M. Firl, F. Daoud, "Approximation of derivatives in semi-analytical structural optimization", Computers and Structures, 86(13-14), 1404-1416, 2008. doi:10.1016/j.compstruc.2007.04.014

3

M. Firl, R. Wüchner, K.-U. Bletzinger, "Regularization of Shape Optimization Problems", Struct. Multidiscip. Optim., submitted.

4

B. Patzak, D. Rypl, Z. Bittnar, "Parallel Explicit Finite Element Dynamics with Nonlocal Constitutive Models", Computers and Structures, 79, 2287-2297, 2001. doi:10.1016/S0045-7949(01)00069-4

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