Reliability-Based Topology Optimization Using Variable Density Method And Performance Measure Approach

Topology optimization is to achieve a specific goal by modifying the layout of structural materials under the certain constraints.Deterministic topology optimization ignores or uses a single safety factor to consider the parameter uncertainty in the optimization process,which results in conservative or dangerous structure.Compared with reliability-based size optimization and shape optimization,the studies in reliability-based topology optimization(RBTO)are relatively few because the design variables in RBTO are quite a lot.This paper performs RBTO for 2-D and 3-D rigid structures,heat conduction structures and compliant mechanisms based on variable density method and performance measure approach.The main contents are as follows:(1)Compare the material interpolation model,filter function and optimization algorithm which are commonly used in topology optimization.Introduce the basic knowledge of reliability theory,establish the reliability-based topology optimization model and draw the iterative flow chart.(Chapter 2)(2)Through examples of four-corner-supported flat panel,L-shaped structure,simply-supported beam and 2-D and 3-D cantilever beam,the effects of target reliability index,and the number and coefficient of variation of random variables on the topological configuration and volume fraction are analyzed.The results show that RBTO can obtain a rigid structure that meets both the optimal force-transferring-path and the reliability requirements.(Chapter 3)(3)Through examples of 2-D and 3-D heat conduction structures,the change of topological configuration and volume fraction due to the change of target reliability index,and the number and coefficient of variation of random variables are observed.The results show that RBTO which considering the uncertainties of heat conductivity coefficient and heating loads can obtain a heat conduction structure that meets both the optimal heat-transferring-path and the reliability requirements compared with the deterministic topology optimization.(Chapter 4)(4)The 2-D and 3-D inverse displacement mechanisms are calculated,and the results show that the method of RBTO in this paper is applicable to simple compliant mechanism.(Chapter 5)...