Topology optimisation and simultaneous analysis and design : material penalisation and local stress constraints

[摘要] ENGLISH ABSTRACT: We investigate the simultaneous analysis and design (SAND) formulation of the topology optimisationproblem. The characteristics of the formulation are presented considering the simplecompliance/weight constrained problem and the more complex local stress constrained case.The problems are solved in an efficient sparse sequential approximate optimisation (SAO) frameworkwith the SAND formulation showing an significant reduction in computational requirementscompared to the traditional and inherently expensive nested analysis and design (NAND) approach.In SAND the state equations are included in the optimisation problem as a set of equality constraintsand not solved exactly in each iteration, as would be the case in NAND. Decision and statevariables are thus independent, resulting in an immensely sparse optimisation problem. The availabilityof simple exact analytic expressions for all the constraint functions (via the finite elementmethod) allows for the construction of accurate approximate subproblems with little computationaleffort. Furthermore, material can be removed completely from the design domain with few complications,resulting in a decrease in subproblem size as the algorithm progresses, further reducingcomputation time.The inclusion of void material in the design domain leads to the formulation of stress constraints asso-called 'vanishing' constraints. Furthermore, the SAND formulation provides a new perspectiveon the infamous singularity problem. Amongst other results, we present some test cases that seemto scale linearly in computational requirements for a specific range of problem sizes.

[发布机构] Stellenbosch University