| The purpose of structural optimization is to make the material use more economical and the force distribution more reasonable under the premise of safety.Structural optimization can be divided into size optimization,shape optimization and topology optimization.Among them,topology optimization is currently a hot topic in this field.Topology optimization gives answers to the fundamental question of engineering design: how to place material within a prescribed design domain in order to obtain the best structural performance.Recently,a large number of topology optimization methods have been proposed.Among them,the density-based topology optimization method is easy to understand,and has rather mature basic theory.In this paper,density-based topology optimization is thoroughly discussed and improved from different perspectives.The main contents of this paper are as follows:1.In this paper,some basic theories of topology optimization are introduced,i.e.,the common topology optimization methods,numerical instability problems and solutions in the process of topology optimization,implementation of continuum structure topology optimization based on finite element method,definition of the minimum structure compliance problem and definition of the minimum heat potential capacity problem.(Chapter 2)2.Theoretical knowledge of two basic filtering methods in density-based topology optimization is introduced.Based on the original SIMP(Simplified Isotropic Material Penalization)interpolation model,a modified SIMP interpolation model is proposed.Compared to the original model,the modified SIMP model can provide a base value for derivative of Young's modulus under the premise of ensuring penalization strength,which could decrease the number of zero density elements,so as to weaken the phenomenon that the elements are deleted at early stage of optimization.Three examples are given to show that modified SIMP model could obtain better results with higher efficiency,smaller discreteness and less structural details than original SIMP model.(Chapter 3)3.Three nonlinear density filters,i.e.,Heaviside projection scheme,modified Heaviside projection scheme and volume preserving projection scheme,are discussed.Based on the original volume preserving projection scheme,this paper proposes a modified volume preserving projection scheme.The modified volume preserving projection scheme has a new filter function and a new volume preserving condition.The new filter function has simple form and its gently varied derivative during the iteration assures that the modified volume preserving projection scheme couldpromote quick development at early stage and alleviate oscillations at the end of the iteration process.The new volume preserving condition is that volumes before linear density filtering and after nonlinear density filtering remain the same.This condition could achieve real volume preservation and volume stability of the whole optimization process.Six examples are given to show that modified volume preserving projection scheme not only effectively suppresses the numerical instability phenomenon such as gray elements and checkerboard pattern,but also has clearer topology,smaller objective function and higher efficiency than other methods.(Chapter 4)4.Continuation schemes of density-based topology optimization are introduced.In response to the deficiency of original continuation schemes,this paper proposes a new continuation scheme: mixed cross continuation scheme.The new continuation scheme not only deletes some unnecessary iterations to improve efficiency,but also add Heaviside projection into the optimization to utilize the advantage that the method could provide a minimum length-scale on solid regions.Six examples are given to show that the new continuation scheme could improve efficiency while ensuring discreteness and provide a minimum length-scale on solid regions,which decreases structural details.This improvement is evident in heat potential capacity problem.(Chapter 5)... |
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