The Research And Application Of Shape Optimization Numerical Method

It is a task of shape optimization in some sense to improve the characteristic of structure, which it is more to minimizing stress concentration, to improve stress-distributing status, by changing the geometry shape of structure regions, and requiring certain physics value to meet some condition in the boundary.First, we reviewed the previous method of shape optimization design in this paper. The geometric parameter of structure had been chosen as the design variables, such as coordinates of nodes, coefficients of polynomials and splines. The seeking object were that the used material was minimizing, minimum weight and maximum fatigue life. Whatever object was sought, its' final calculation was achieved by stress analysis. There exist different methods of sensitivity analysis, but its' final sensitivity calculating was fulfilled by making use of the difference method or divided different scheme.Secondly, a sets of fictitious load applying on structure "control point" is chosen as the design variable of shape optimization, the minimizing maximum Von Mises stress of globe or local structure is chosen as the object function of optimization. The structure discretization is carried out using high accuracy eight node isoparametric elements. By controlling grids nodal maximum deformation, we can deal better with the distortion of finite element meshes that appear in the shape optimization, and a new numerical method of sensitivity analysis was produced, based on the fictitious load variables, by use of a linear relationship between node displacement and loads. Two examples are tested successfully, the optimizing result tally better with the theory.In the end, the effect of the maximum displacement was discussed, and the other salient feature relating with fictitious load are researched in the shape optimization. The suggestions are presented in the shape optimization based on fictitious load variables.