Stress constraints sensitivity analysis in structural topology optimization

Sensitivity Analysis is an essential issue in the structural optimization field. The calculation of the derivatives of the most relevant quantities (displacements, stresses, strains) in optimum design of structures allows to estimate the structural response when changes in the design variables are introduced. This essential information is used by the most frequent conventional optimization algorithms (SLP, MMA, Feasible directions) in order to reach the optimal solution. According to this idea, the Sensitivity Analysis of the stress constraints in Topology Optimization problems is a crucial aspect to obtain the optimal solution when stress constraints are considered.Maximum stiffness approaches usually involve one linear constraint and one non-linear objective function. Thus, the computation of the required sensitivity analysis does not mean a crucial limitation. However, in the topology optimization problem with stress constraints, efficient and accurate computation of the derivatives is needed in order to reach appropriate optimal solutions. In this paper, a complete analytic and efficient procedure to obtain the Sensitivity Analysis of the stress constraints in topology optimization of continuum structures is analyzed. First order derivatives and second order directional derivatives of the stress constraints are analyzed and included in the optimization procedure. In addition, topology optimization problems usually involve thousands of design variables and constraints. Thus, an efficient implementation of the algorithms used in the computation of the Sensitivity Analysis is developed in order to reduce the computational cost required. Finally, the sensitivity analysis techniques presented in this paper are tested by solving some application examples.