Error Analysis Of Sensitivity And Research On Rejection Criterion In ESO Method

Evolutionary structural optimization method has the advantages of simply thoughts, easy to be combined with the result of finite element analysis program and the high computational efficiency, so the method has a good prospect in engineering applications. ESO has been widely studied at home and abroad, and it has become one of the main areas of topology optimization. However, ESO method still has shortages in theoretical foundation and implementation of the application to be solved, like the problem of checkerboard、performance index and the rationality of sensitivity calculation. In this paper, a debate is focused on sensitivity calculation and deletion strategies what are mainly concerned about in algorithm research and engineering application of the evolutionary structural optimization method, and the results obtained improve the versatility and practicality, which are significant for the theoretical study and practical application of the ESO method.The high-order items are ignored in the sensitivity analysis of original evolutionary structural optimization(ESO), what may result in the iteration failure in some topological optimization procedures, such as Tie-Beam problem. It is known from matrix perturbation theory that the ignorance of high-order items in calculation may bring big sensitivity errors when the stiffness matrix of the structure is ill-conditioned. This paper noted that there were differences in the sensitivity calculation error between different elements, and it closely related to the element location in the structure; specifically, the greater the role of its force transmission, the greater the sensitivity calculation error; and evaluated whether or not the matrix of a structure is ill-conditioned by using condition number, introduces a concept of true sensitivity and deduces its equations included the high-order items. Numerical examples demonstrate that the proposed sensitivity algorithm can effectively avoid the failure of optimization iteration caused by sensitivity errors.Regarding to the problem of deletion criterions in evolutionary structural optimization method, this paper researches on two kinds of criterions in ESO based on element strain energy and sensitivity. The relationship between the strain energy and sensitivity is discussed in the article. The expression of strain energy and sensitivity is derived and results show that they are not equal in numerical size. Based on this, the paper points out the traditional approach that treated element strain energy as sensitivity to guide the element removal is wrong. Whether it is from the optimal topology and structure parameter value, numerical examples demonstrate that the optimization results of two methods are different. So, the ESO for problems with stiffness constraints or based on element strain energy applied two kinds of deletion strategies, and traditional practice is unreasonable that treated element strain energy as the sensitivity to guide the element deletion. The Internal relation of the two methods is that both of them judge inefficient elements from the perspective of structure Compliance, and they have their own advantages for different application requirements engineering.