Independent continuous and mapping method of structural topology optimization based on global stress approach

Abstract

There are three difficulties in topology optimization of continuum structures. 1) The topology under multiple load case is more difficult to be optimized than under single load case, because the former becomes a multiple objective based on compliance objective functions. 2) With local constraints, such as an elemental stress limit, the topology is more difficult to be solved than with global constraints, such as the displacement or frequency limits, because the sensitivity analysis of the former has very expensive computation. 3) With the phenomenon of load illness, which is similar with stiffness illness in the structural analysis, it is not easy to get the reasonable final topological structure, because it is difficult to consider different influences between the loads with small forces and big forces, and some topology paths of transferring small forces may disappear during the iteration process. To overcome difficulties above, four measures are adopted. 1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises strength theory, all elements’ stress constraints are transformed into a structural energy constraint. 3) The phenomenon of load illness is divided to classify into three cases. 4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of load illness are solved in terms of different complementary approaches. Several 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 load illness can be solved well by the weighting method that takes the structural energy as a weighting coefficient.