Application Of Improved BESO Algorithm In Structural Topology Optimization

Structural optimization has always been a research area widely being studied in the field of structural engineering.Compared with size optimization and shape optimization,topology optimization is the most complicated research area in structural optimization field.Bidirectional Evolutionary Structural Optimization(BESO),which is a topology optimization method with concise theory and high optimization efficiency,has been an important research area in topology optimization theory.The methodology of BESO method was first introduced in this thesis;secondly the implementation of BESO method with multiple constraints was derived;a performance index that can measure the optimization efficiency was then proposed and a self-updating evolution rate that can smooth and accelerate the optimization process was utilized in this thesis;the procedure for the topology optimization on the structural system under dynamic loading was also investigated in the thesis;finally,a large-scale primary and secondary frame-bracing structure was taken as an example to discuss on how to apply the improved topology optimization algorithm to topology optimization design process of practical engineering structural system.The main work of this thesis is as follows:Firstly,the basic theory and process of BESO method was introduced,and the filtering technique about sensitivity analysis in topology optimization was discussed to solve numerical instability problems such as checkerboard and grid dependence.On this basis,three BESO methods with single constraint(including maximum stiffness optimization with volume constraint,minimum volume optimization with displacement constraint,maximum frequency optimization with volume constraint)were introduced.The sensitivity analysis for each element in the optimization domain was conducted and the procedure on topology optimization was introduced as well.Finally,the feasibility of the above three topology optimization cases was verified by several numerical examples.The procedure for BESO method was proposed in Chapter 3 to solve the optimization problem with multiple constraints.The concept of the Lagrange multiplier method in optimization problem with multiple constraints was introduced,then the methodologies and procedures for three different optimization cases(including maximum stiffness optimization problem with displacement and volume constraints,maximum frequency optimization problem with displacement and volume constraints,minimum volume optimization problem with multiple displacement constraints)were derived in this chapter.The sensitivity analysis for each element in the optimization domain was also introduced.Finally the feasibility of the above three topology optimization methods was verified by several numerical examples.A series of examples were adopted to investigate the influence of different fixed Evolution Rates(ER)on the topology optimization results,then a Performance Index(PI)which can measure the optimization efficiency was proposed for the stiffness optimization problem.A self-updating evolution rate(ERi)which can enable the topology optimization process to be more stable and efficient was established from this index.Two examples were demonstrated to verify the effectiveness of the improved method.The topology optimization problem for structural system under dynamic loading was studied in Chapter 5.The basic procedure of topology optimization considering dynamic response was first introduced.By obtaining the equivalent static load from the dynamic response analysis of the optimized structure and utilizing the BESO method for multiple load cases,the implementation methodology for topology optimization on structural system under dynamic loading was proposed as well.Two examples were used to verify the effectiveness of this method in this chapter.Finally,taking a primary-secondary frame-bracing structure as an example,and considering its horizontal equivalent static load induced from dynamic wind loading and seismic effect,the method of topology optimization design of the bracing subsystem using BESO method was discussed in this part.By utilizing the self-updating evolution rate and performance index,stiffness optimization with volume constraint and volume optimization with inter-storey drift and top level drift constraints were performed respectively.By continuously adjusting the optimization design method,the effectiveness and efficiency of the proposed topology optimization process were improved,thus the final optimization design result could meet the requirements of structural design for such complex structural system.