Research On Topological Optimization Method Of Two-scale Structure Based On Intelligent Distribution Of Materials

Structural optimization refers to the use of mathematical principles to transform a given optimization problem into a mathematical programming problem.It involves the search for an optimal material distribution,subject to specified constraints,to satisfy certain usage requirements such as maximizing structural stiffness or minimizing maximum stress.At present,traditional optimization algorithms often appear grayscale and checkerboard phenomena.In addition,the results of most optimization algorithms can only achieve local optima,and cannot obtain the global optimal solution in the design domain.In order to effectively solve the twoscale optimization problem,improve the global search ability of the algorithm,and ensure the stability of the convergent solution,this paper integrates the Fast Non-dominated Sorting Genetic Algorithm II(NSGA-II)into the traditional two-scale optimization algorithm,and introduces the idea of the Bi-directional Evolutionary Structural Optimization(BESO)to guide the unit.additions and deletions.At the same time,for the multi-phase material layout and multi-objective optimization problems in engineering problems,the corresponding solutions are given by using the proposed algorithm.The main research work of this paper is as follows:(1)Aiming at the problems existing in the traditional topology optimization algorithm,in order to improve the global search ability of the topology optimization algorithm,this paper combines NSGA-II with the two-scale optimization method based on BESO,which is called JESO-NSGA-II.In this method,the units in the traditional optimization algorithm are represented by binary strings,and the crossover mutation operator is used to adjust the binary strings to guide the addition and deletion of units,which greatly expands the global search range and reduces the number of units.Accidental deletion phenomenon.The effectiveness of the JESO-NSGA-II algorithm in structural optimization is verified by analyzing the examples of cantilever beams and L-shaped beams.(2)Secondly,for the layout problem of multiphase materials in engineering,the optimization method is extended to multiphase materials,a material interpolation scheme with weighting factors is introduced,and a sensitivity calculation formula with penalty factors is derived by using the improved density interpolation function.In addition,in order to ensure good connectivity between each microstructure unit,a boundary optimization mechanism is introduced in the optimization process.For multiphase material optimization problems,density values need to be considered.The classic calculation example of cantilever beam is introduced to discuss the problem of mass constraint and volume constraint.The results show that under the same parameter conditions,considering the density value and mass constraint can ensure the best optimization effect of the structure.(3)Most of the mechanical system failures in engineering problems are caused by the strength failure and fatigue failure of the structure,which can be attributed to the stress problem.Therefore,in order to realize the optimal design of stiffness and stress at the same time,a twoobjective optimization strategy is proposed.In order to verify the effectiveness of the proposed algorithm in two-objective optimization problems,the feasibility of the method is verified by analyzing three classic examples and comparing with the single-objective optimization algorithm and similar research results of foreign scholars.