Design Of Asymptotically Concentrated Method For Topology Optimization Based On The SIMLF Interpolation

Structural topology optimization is regarded as a powerful tool for the conceptual design of engineering structures.Topology optimization technique seeks to achieve the best performance of a structure while satisfying various constraints such as a prescribed load,and determine the optimal delivery path for the force.Topology optimization determines the material distribution scheme in the design domain and has a great impact on the structural design.In the meanwhile,topology optimization has a great design space and a good development prospect.Currently,topology optimization has become a hot topic in the field of structural optimization and has been widely studied.However,the theories and methods of topology optimization are not yet fully mature.Therefore,it still deserves further study.In this paper,the Solid Isotropic Microstructures with Penalization(SIMP)and the Optimality Criteria(OC)method are used as prototypes.The asymptotically concentrated topology optimization method based on the Solid Isotropic Material with Logistic Function(SIMLF)interpolation is proposed by analyzing and discussing the advantages and disadvantages of these two methods.Based on the proposed method,the following researches are conducted in this paper.1.The SIMP interpolation model and the interpolation model based on the logistic function are described.In the SIMP interpolation model,some high-related-density elements may be wrongly punished.Although the interpolation based on the logistic function has a reasonable polarization,it can not obtain a complete range of Young's modulus.To solve the above problems,this paper proposes a SIMLF interpolation model with polarization.The SIMLF interpolation can weaken the influence of low-related-density elements,enhance the influence of high-related-density elements and reduce the gray-element in the optimal topology result.Moreover,complete range of Young's modulus can be obtained with the SIMLF interpolation and almost no zero-sensitivity element(the element whose sensitivity equals 0)is generated in the SIMLF interpolation.This means that all elements are involved in the subsequent process of updating the design variables,which can ensure the accuracy of updates,improve optimization efficiency and help achieve better topology optimization results.2.The optimization model for Evolutionary Structural Optimization(ESO)method,Bidirectional Evolutionary Structural Optimization(BESO)method and a new hybrid method(ESO-SIMP)optimization model are briefly described.In order to overcome the deficiencies in the three kinds of evolutionary methods,the asymptotically concentrated method is proposed.The direction of asymptotically concentrated method is the same as the optimization solution,which speeds up the optimization process and improves optimization efficiency.There is no deletion process in the asymptotically concentrated method.The asymptotically concentrated method focuses on asymptotically concentrating the densities of material,so it can effectively avoid the accidental deletion while obtaining centralized density variables and completely clear topology results.3.The balanced parameter method and decremental coefficient method are proposed for the convergence problem of constraints and numerical oscillation of objective function.As a secondary constraint method,the decremental coefficient method can be used to strengthen the constraints.In the balanced parameter method,two parameters the sum of which is 1 are introduced into the OC algorithm to reassign the design variables.The balanced parameter method can effectively compensate for the lack of the ordered SIMP interpolation model and solve the numerical oscillation of the objective function without affecting the optimal value of the objective function.4.The single-material model and multi-material model of asymptotically concentrated topology optimization method based on SIMLF interpolation are established and applied in the field of statics.The examples show that two kinds of results can be obtained by using the proposed method.Based on these two topology results,the asymptotically concentrated method is subdivided into incomplete asymptotically concentrated method and complete asymptotically concentrated method.An optimal structure with clear boundaries and small structural compliance can be obtained by using the proposed method.Moreover,the optimization process is relatively smooth,and there is no numerical oscillation of objective function and volume fraction(in multi-material optimization).5.The asymptotically concentrated topology optimization method based on SIMLF interpolation is applied to the dynamic frequency domain and the dynamic time domain,respectively.For the problem of dynamic topology optimization in frequency domain, structural stability factors are introduced to describe that to some extent the SIMLF interpolation has an effect on ensuring structural stability.For the problem of dynamic topology optimization in the time domain,Newmark-? method is introduced to transform the dynamic problem in the time domain into a quasi-static problem.Newmark-? method calculates the equivalent stiffness and payload to solve the displacement vector,velocity vector,and acceleration vector.The examples show that the proposed method is feasible and effective in the field of dynamic topology optimization and has certain advantages.