Topology Optimization of Continuum Structure With Globalization of Stress Constraints

There are three difficulties in the topology optimization problem of continuum structure:1) The problem under multiple load case is not easy to be approached than that under single load case, because the former becomes a multiple objective problem on the basis of compliance objective function. 2) The problem with local constraints, such as elemental stress limit, is not easy to be solved than that with global constraints, such as displacement or frequency limits, because sensitivity analysis of the former has too expensive computation. 3) The problem with a phenomenon of ill-conditioned load, which is similar to ill-conditioned stiffness matrix in the structural analysis, is not easy to get reasonable final topological structure, because the former is difficult to consider different influences between the loads with small forces and the loads with big forces, and some of topology paths of transferring small forces may disappear during the process of iteration. To overcome the above difficulties, some measures are adopted as follows:1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises criteria in theory of elastic failure, all element's stress constraints are transformed into a structural energy constraint, namely, a global constraint substitutes for lots of local constraints. 3) The phenomenon of the ill-conditioned load is divided into three cases: (a) Ill-condition exists between load cases, but not within each load case; (b) Ill-condition exists within some load case; (c) Ill-condition exists not only between load cases, but also within some load case. (4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the three cases of ill-conditioned load mentioned above are solved in term of different complementary approaches one by one. Numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of ill-conditioned load can be solved well by the weighting method which takes structural energy as weighting coefficient.