Topological Optimization Design And Analysis Of The Uncertain Structures

In a large number of practical engineering problems,the material properties,geometric parameters and loads were uncertain due to the uncertainty of measurement errors,manufacturing levels,environmental conditions and so on.During the optimization solution process,the reliability-based topological optimization design,in which the structural reliability was taken as a constraint condition,were merged the structural reliability theory with topology optimization technique.The design results become more reasonable since various uncertainties,which affected the properties of the structures,were considered quantitatively,therefore the disadvantages of traditional structure optimization design were overcome effectively.However,at present the relevant research on the reliability-based topological optimization design was mainly concentrated on the force field while little attention had been paid to temperature field.It was of great theoretical significance and practical values to carry out optimization design in the temperature field.Besides,because some composites were subjected to heat loads,it was important to evaluate the reliability of composite structure by using randomly homogenezing thermal analysis method.It would be helpful to predict the properties of inhomogeneous materials by describing the microstructure characteristic and macro-transformation properly.The main research works could be described as follows:In the first part non-probabilistic reliability topology optimization design of steady-state heat conduction structure was investigated.Since both the thermophysical parameters and heat loads were interval ones,the computational expressions of mean value and mean square error of dissipation of heat transport potential capacity were presented according to interval factor method and interval calculation rules.The topology optimization model of heat conduction structure was constructed,in which the relative thermal conductivity of elements was the design variables and non-probabilistic reliability with dissipation of heat transport potential capacity was constrainted.Evolutionary structural optimization method was used in the optimization process.The numerical examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.In the second part topology optimization design of steady-state heat conduction structure was discussed when the the thermophysical parameters and heat load were considered as random variables or fuzzy ones respectively.When the parameters were random ones,according to the random factor method,the computational expressions of numerical characteristics of dissipation of heat transport potential capacity were deduced.The topology optimization model of heat conduction structure under probabilistic reliability with dissipation of heat transport potential capacity constraint was constructed,in which the relative thermal conductivity of elements was the design variables.Evolutionary structural optimization method was used in the optimization process.When the parameters were fuzzy ones,the fuzzy variables were transformed into random ones according to the equal information entropy principle.The topology optimization model of heat conduction structure under fuzzy reliability with dissipation of heat transport potential capacity constraint was constructed,in which the relative thermal conductivity of elements was the design variables.Evolutionary structural optimization method was used in the optimization process.The numerical examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.In the third part the problem of probabilistic and non-probabilistic hybrid reliability-based topology optimization design of heat conduction structures was studied when the thermophysical parameters and heat loads were considered as interval variables and random variables.The function of dissipation of heat transport potential capacity was deduced according to the interval factor method and the random factor method.The probabilistic and non-probabilistic hybrid reliability-based optimization model of the heat conduction structures was constructed,in which the relative thermal conductivity of elements was regarded as the design variables,the total volume of heat conductive material was minimized,and the hybrid reliability index for dissipation of heat transport potential capacity was taken as the constraint condition.The evolutionary structural optimization method was used in the optimization.On the other hand,the interval variables was transformed into random ones and the topology optimization model of heat conduction structure under probabilistic reliability constraint was constructed.The two numerical examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.In the fourth part topology optimization design of planar continuum structures with random-interval-fuzzy hybrid variables under constraint of strain energy or stress was studied.The structural physical parameters,applied loads and allowed flexibility were considered as random variables,interval variables or fuzzy variables.Based on information entropy,the fuzzy variables were transformed into equivalent random variables with normal distribution.According to the probabilistic reliability analysis method,the hybrid reliability index containing random variables and interval variables was obtained.On this basis,the topology optimization model of planar continuum structures was constructed,in which the presence or absence of elements was regarded as the design variables,the total volume of the structures was minimized,and the hybrid reliability index with strain energy or stress was taken as the constraint condition.The evolutionary structural optimization method was used in the optimization.The two numerical examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.In the fifth part random homogenization analysis for the effective thermal properties of a three-dimensional composite material with unidirectional fibers was presented by combining the equivalent inclusion method with Random Factor Method(RFM).The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters were completely accounted for,and stochastic effective thermal properties of thermal expansion coefficients as well as their correlation were then sought.Results from the RFM and the Monte-Carlo Method(MCM)were compared.The impact of randomness and correlation of the micro-structural parameters on the random homogenized results was revealed by two methods simultaneously,and some important conclusions were obtained.