TOPOLOGY OPTIMIZATION OF STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BY INDEPENDENT CONTINUUM MAP METHOD

Abstract

We establish topology optimization model in terms of Independent Continuum Map method (ICM), so as to avoid the difficulties caused by multiple objective functions of compliance, owing to referring to weight as objective function. Using the distorted-strain-energy criterion, we transform stress constraints on all elements into structure strain-energy constraints in global sense. Then, the problem of topological optimum of continuum structure subjected to global strain-energy constraints is formulated and solved. The process of optimization is conducted through three basic steps which include the computation of the minimum strain energy of structure corresponding to the maximum strain-energy under the load case due to prescribing weight constraint, the determination of the allowable strain-energy of structure for every load case by using a formula from our numerical tests, as well as the establishment and solution of optimization model with the weight function due to all allowable strain energies. A strategy that is available to cope with complicated load ill-posedness in terms of different complementary approaches one by one is presented in the present work. Several numerical examples demonstrate that the topology path of transferring forces can be obtained more readily by global strain energy constraints rather than local stress constraints, and the problem of load ill-posedness can be tackled very well by the weighting method with regard to structural strain energy as weighting coefficient.