Local stress‐constrained and slope‐constrained SAND topology optimisation

Summary We study the alternative ‘simultaneous analysis and design’ (SAND) formulation of the local stress‐constrained and slope‐constrained topology design problem. It is demonstrated that a standard trust‐region Lagrange–Newton sequential quadratic programming‐type algorithm—based, in this case, on strictly convex and separable approximate subproblems—may converge to singular optima of the local stress‐constrained problem without having to resort to relaxation or perturbation techniques. Moreover, because of the negation of the sensitivity analyses—in SAND, the density and displacement variables are independent—and the immense sparsity of the SAND problem, solutions to large‐scale problem instances may be obtained in a reasonable amount of computation time. Copyright © 2016 John Wiley & Sons, Ltd.