Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB

TL;DR

Proportional Topology Optimization (PTO) is a new non-gradient method for topology optimization that is simple, efficient, and accurate, implemented in MATLAB for stress constrained and minimum compliance problems, with publicly available code.

Contribution

The paper introduces PTO, a novel non-gradient topology optimization method, and provides detailed implementation and comparison with existing gradient-based methods.

Findings

PTO achieves comparable accuracy and efficiency to gradient methods.

PTO can produce lower stress and volume fraction but higher compliance.

The MATLAB implementations are self-contained and publicly accessible.

Abstract

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing gradient optimality criteria method. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.