Keywords: parallel computing, topology optimization, stress constraints, minimum weight, OpenMP.

The traditional approach in structural topology optimization involves the statement of a maximum stiffness objective due to the computational advantages that they offer. However, in engineering applications it is much more appropriate to use different formulations that minimize the weight or the cost of the structure and include stress constraints since this criterion is the most widely used in real structures and the feasibility of the solution is assured, since the failure stress of the material is not exceeded. According to that, different approaches have been proposed to solve topology optimization problems with stress constraints [1,2,3].

These minimum weight with stress constraints approaches produce suitable results but require higher computational requirements than maximum stiffness approaches [1,2,3] since the number of highly non-linear stress constraints is very large. Thus, it is necessary to analyze different techniques in order to reduce the computing time. These methods must be numerical and computational since computational improvements are usually related to specific and improved numerical algorithms. In this paper we develop a parallel code with OpenMP directives to solve the topology optimization problem with stress constraints. This parallelization is performed by studying specific algorithms for the topology optimization of structures (the structural analysis, the sensitivity analysis and the optimization algorithm) that offer very important computational advantages. Thus, we identify different goals in the optimization process that require almost the total computing time and we discuss different alternatives to develop the parallelization of the numerical approaches proposed and their implementation in the source code. Finally an application example is presented in order to verify the efficiency of these techniques. This problem is solved by using an increasing number of processors in order to determine the real speed-up obtained with the techniques proposed.

1

F. Navarrina, I. Muiños, I. Colominas, M. Casteleiro, "Topology optimization of structures: a minimum weight approach with stress constraints", Advances in Engineering Software, 36, 599-606, 2004. doi:10.1016/j.advengsoft.2005.03.005

2

J. París, F. Navarrina, I. Colominas, M. Casteleiro, "Topology optimization of continuum structures with local and global stress constraints", Structural and Multidisciplinary Optimization, 2008. doi:10.1007/s00158-008-0336-2

3

J. París, F. Navarrina, I. Colominas, M. Casteleiro, "Block aggregation of stress constraints in topology optimization of structures", Computer Aided Optimum Design of Structures X, Myrtle Beach (SC), USA, 2007. doi:10.2495/OP070031

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)