An Improved Guide-Weight Method Without the Sensitivity Analysis

Abstract

This paper proposes an improved guide-weight method, in which the sensitivity analysis does not need to be calculated. Based on the Kuhn-Tucker extreme condition, the general iterative criterion of the improved guide-weight method is derived by importing relational function. The iterative criterion directly constructs an explicit representation between the design variable and the objective function, which does not require sensitivity analysis. Taking the problem of minimum compliance as an example, the iterative criterion between relative density and strain energy of elements is obtained under the condition of mass constraint. Two examples were studied using the two material interpolation models. The results show that the optimal results in the same topological form are obtained from the two material interpolation models. The results are consistent with the optimization results of the guide-weight method, which verifies the feasibility and effectiveness of using the improved guide-weight method to study the topology optimization without the sensitivity analysis. INDEX TERMS Optimization methods, finite element method, mechanical engineering, structural engineering, topology optimization, guide-weight method.

Variable-density topology optimization and bending test of quasi-honeycomb sandwich structures

“…Teimouri and Asgari 17 solved the checker-boarding and mesh dependency by obtaining the sensitivity number of each element from those of the nodes within the elemental filter radius for BESO method. Jiao et al 18 established an explicit relationship between the design variable and objective function in the iterative criteria of SIMP and RAMP models to improve the clarity of topology optimization structure. Zhang et al 19 modified the sensitivity analysis method of SIMP model by Helmholtz-type density filter and hyperbolic tangent function to make the topology structure boundary clear and smooth.…”