Research On Structural Topology Optimization Under Multiple Loading Cases

Structural topology optimization has not only greatly improve structural performance, reduce unnecessary waste of materials, but also shorten the development cycle, improve the design efficiency. With the mature of finite element and rapid development of optimization algorithm, lighten weight structure has attracted more and more attention..It has become an important direction of research in the field of topology optimization. At the same time, most of the actual structure is working under a variety of conditions. Therefore, research on multi-load cases topology optimization problem is of great practical significance.First of all, for the stiffness optimization of continuum structure under mult-load cases, we propose the performance index formula, and analyze the advantages and limitations with the conventional ESO method to solve topological optimization problems which is based on the logic AND criterion. Aiming at the multi-load cases optimization essentially belongs to multi-objective problems, we put forward the linear weighted method to solve the problem. The weighting coefficient selection is further analysised and discussed。Weighting coefficient selection formula is proposed under both static and dynamic weighted, which is an effective solution to the multi-load stiffness optimization problem.Secondly, this paper gives an analysis to solve the problems using minimax theory to multi-load topology optimization. It is pointed out that G.P. Steven’s method is applied to the condition where response has the smaller difference. And we improved it for this point. In each case should the ratio of stress(or strain) and average instead of element stress values, to ensure that the structure optimization of containing small load case, is effective to the problem.Lastly, this paper also describes the way of truss structure evolution based on the full stress design. On the basis of full stress design criterion,we apply it to the ESO method.By changing the thickness of the element, the element stress closes to full stress state, making the structure topology optimal.For the multi-load cases topology optimization, we determine the desired element thickness according to the element stress under all load cases, fulfilmenting the renewal of element’s thickness(design variables). Combining with the ESO method by gradually removing the element of smaller thickness, we can obtain the optimical topology structure under multiple load cases.