A generalized discrete fiber angle optimization method for composite structures: Bipartite interpolation optimization

Abstract

This paper proposes a novel fiber angle optimization method for composite, termed bipartite interpolation optimization (BIO), to address high‐dimensional design variables and inefficient fiber orientation optimization. The weighting functions of BIO are constructed with the help of multiphase material topology optimization approach. Various permutations and combinations of n design variables are utilized to represent 2n discrete candidate angles. Since the weighting functions of the way automatically satisfy the sum constraint, it is unnecessary to address the sum constraints during the optimization process. Compared with the traditional discrete material optimization strategy and solid isotropic material with penalization scheme, the BIO method reduces the dimension of the mathematical model for optimizing fiber angles. Compared to the shape functions with penalization scheme, the BIO method can be extended to the optimization problem of 2n candidates. Numerical examples of different types demonstrate that the proposed method has higher solution efficiency in the optimization problem of fiber orientation selection and is suitable for three‐dimensional shell optimization problems. It provides a new technical means for the structural optimization design of composite laminates.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

“…Recently, Zhang et al [93] and Yan et al [94] applied the SQP with approximate Hessian in discrete material optimization. Referring to Powell's work [95], the Hessian matrix is replaced by an approximate matrix B (k) :…”

Multi‐material topology optimization method for transient thermal structure with constraint on permissible temperatures

“…Besides these, many studies for multi-material interpolation have been done to deal with the large number of design variables for multi-material topology optimization. A series of new multi-material interpolation schemes based on traditional material interpolation schemes and other material function model have been proposed, [6][7][8][9][10][11] which could characterize a variety of material properties by fewer variables. After decades of development, multi-material topology optimization method have matured and been applied to structure design in various physical fields, including thermal fields.…”