Parallel computing in topology optimization of structures with stress constraints

• We apply a minimum weight with stress constraints topology optimization formulation.
• Important drawbacks of conventional topology optimization formulations are avoided.
• The sensitivity analysis and the optimization algorithm are computed in parallel.
• OpenMP parallelization directives are used.
• Suitable speed-up is obtained in conventional multi-core computers.

Minimum weight formulations with stress constraints have been recently proposed as an alternative to the traditional maximum stiffness statements for the topology optimization of structures. These minimum weight approaches offer some advantages and avoid unwanted phenomena associated to maximum stiffness approaches, e.g. mesh dependency, checkerboard layouts. In addition, minimum weight formulations analyze more usual statements from a practical point of view in engineering since they reduce the cost of the structure and impose stress constraints. The minimum weight formulation with stress constraints proposed in this paper guarantees the feasibility of the optimal solutions obtained while the cost is minimized.However, these formulations also require bigger computing effort than the traditional maximum stiffness statements since the number of highly non-linear stress constraints is drastically increased while the number of design variables is analogous. Thus, it is necessary to introduce numerical methods and computational techniques that allow to reduce the resources required.In this paper, we propose the use of parallelization techniques in order to reduce the computing time required to solve the topology optimization problem with stress constraints proposed.