Research On Evolutionary Structural Optimization Method And Its Application

Evolutionary Structural Optimization method (ESO) proposed in that last decade is promising in engineering structural shape and topology designs. Its further theoretical development and introduction into new engineering fields are of apparent significance. For the practical engineering requirements of structural designs, this thesis made researches on the evolutionary structural optimization method and its application. The major contributions in this study are as follows.In order to make the optimum structural topology obtained being of near same stress level in every part of it, and its maximum stress achieving its minimum among all possible topologies at the same time, this thesis proposed an improved bi-directional structural topology optimization method and its procedure, based on the idea of minimizing the maximum structural stress and the full stress design, and the derivation of stress sensitivity numbers, and combining stresses with their sensitivity numbers.For the combined topology optimization design problem of continuum structures with discrete topology and size design variables, in order to consider structural size and topology variables all together in each optimization iteration step, relative difference quotients for topology and size variables of continuum structures with several different types of components were formulated, respectively. And combining structural element stress level with the relative difference quotients, a set of optimum criteria for the combined topology optimization problem of continuum structures with size and topology variables was established, and its topology optimization procedure was formulated, based on a bi-directional evolutionary structural optimization method idea. This method correctness and efficiency were verified by use of two examples. Then, a structural topology optimization method considering structural tensional & compression stress, static displacement and frequency requirements was proposed, and design simulations of two types of bridges were completed.In order to accurately describe the changing quantities of displacement and stress constraint functions, which are generated by adding an element to the optimized structure, and in order to improve the conventional bi-directional evolutionary structural optimization method to solve the structural optimization problem with static stress and displacement constraints, this thesis proposed an idea that man-made material is inserted around structural cavities and boundaries. Being based on the idea and stress sensitivity numbers, a set of criteria for adding and removing finite elements, was set. And another kind of new topology optimization procedure was given. Then, the proposed method was extended to topology optimization design problems dealing with mechanics structures under multiple loads, truck frame structures and etc.Two sets of formulations for mean square random dynamic responses and their sensitivity numbers of structures, under white-noise excitations and narrow-band random excitations, were respectively derived. And the evolutionary structural optimization method was successfully extended to structural dynamic topology optimization problems. Moreover, a set of optimum criteria for closely-spaced eigenvalues and repeated eigenvalues was established, based on the built sensitivity numbers of the first multiple eigenvalues. And an improved method for evolutionary structural optimization against buckling was proposed for maximizing the critical buckling load of a structure of constant weight.For the topology optimization problem of complex three-dimensional structures with a lot of mesh elements, this thesis adopted a measure that man-made material finite elements are inserted around structural cavities and boundaries, and successfully overcome the structural optimization model singularity problem. Strategies and algorithms of three-dimension structural topology optimization designs, respectively for the stress, the displacement and the frequency requirements, were proposed.The above-mentioned evolutionary optimization procedures were implemented and a set of software dealing with the two-dimensional and three-dimensional structural topology optimizations was developed. And a lot of simulation designs for mechanical and automobile components, bridge and etc. structures, were given. The results demonstrate that the methods proposed in this thesis are correct and efficient, and are of better engineering application value than the conventional evolutionary structural optimization method.