Optimal Shape Design of Membrane Structures
By: C.W. Lim1 and V.V. Toropov1,2
1School of Civil Engineering
University of Leeds, United Kingdom
2School of Mechanical Engineering
University of Leeds, United Kingdom

Lim-2013 Paper

new-VVT-v3 PPT

This paper deals with stress-based optimization of membrane structures, where constraints on compressive stresses are used to avoid the formation of wrinkles on the membrane surface. The difficulty arises because a large number of constraints must be considered since stress is a local quantity and hence the problem becomes computationally intensive. The strategy of replacing the local compressive stresses by a global measure using the aggregated constraints approach is hence adopted. A shape optimization problem of a prestressed membrane roof is formulated such that the structural stiffness is increased by minimizing the strain energy subject to a single aggregated stress constraint. Further, an unconstrained multi-objective optimization problem is formulated and solved using a multi-objective genetic algorithm to find a representative set of Pareto-optimal solutions. For that purpose, a moving least squares metamodel has been built using sampling from an optimum latin hypercube design of experiments. Comparisons are then made between the single- and multi-objective optimization problem formulations.
Keywords: membranes, wrinkling, shape optimization, aggregated constraints, design of experiments, metamodel, multi-objective optimization

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