New Extrapolation Technology In Bidirectional Frequency Evolutionary Structural Optimization Method

The evolutionary structural optimization method is a numerical method applied on structural topology optimization recently. The method is based on the idea that by gradually removing the inefficient material, the residual shape of structure will evolve towards an optimum.Because only element removing is allowed in traditional evolutionary structural optimization method, when given a poor initial design, it may produce a final structure undesirable. The improved evolutionary structural optimization method used in this paper allows materials to be added as well as removed, and it is therefore called bidirectional evolutionary structural optimization method.In every step of the evolutionary process, bidirectional evolutionary structural optimization method needs to find all of the deleting and adding elements. The deleting elements are the parts of the present structure. The displacements of the deleting elements' nodes are known. As to the unknown displacements of the nodes on the boundary of the structure, traditional bidirectional evolutionary structural optimization method adopts extrapolation methods. Traditional extrapolation method can only be applied on regular rectangle element or cuboidal element. If the structure is dispersed by irregular elements, the method will encounter difficulties.This paper is consist of two parts work. In regard to the first part of the work, this paper studies the influence of two different extrapolation methods, linear and quadratic, for Eight-node Quadrilateral element on the final design. An example is given and it is shown that in bidirectional evolutionary structural optimization method, extrapolation methods have significant influence on the accuracy of sensitivity number.In allusion to the limitation of the above-mentioned method, the paper brings forward a new method to estimate the unknown displacements of the boundary additional elements. The method is based upon a new idea. After the normal modes analysis, according as the known displacements of the nodes in the intra-domain, unknown displacements of the nodes on the boundary of the structure will be calculated by linear static method. The article puts forward two linear static extrapolation method. They are total linear static extrapolation method and one by one elemental linear static extrapolation method. The article discusses their advantage and disadvantage. The displacements estimated by total linear static extrapolation method has more integral quality, but the sensitivity number estimated by one by one elemental extrapolation method are more close to the modified structural element's real sensitivity number. The method can be popularized on arbitrarily elements, and the computational result has explicit mechanical significance. The example demonstrates that the method is effective. The method is proved that it has preferably applied worthiness.