# A duality principle and related computational method for a class of structural optimization problems in elasticity

## TL;DR

This paper introduces a duality principle and a computational method for optimizing the topology of elastic structures to minimize internal energy, using convex analysis and duality theory, with numerical examples demonstrating its effectiveness.

## Contribution

It develops a novel duality-based computational approach for structural topology optimization in elasticity, avoiding filtering steps to ensure critical point solutions.

## Key findings

- The method successfully finds critical points for the optimization problem.
- Numerical examples validate the theoretical duality approach.
- The approach is applicable to various elastic structural problems.

## Abstract

In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its structural inner energy resulting from the action of external loads to be specified. The main results are obtained through standard tools of convex analysis and duality theory. We emphasize our algorithm do not include a filter to process the results, so that the result obtained is indeed a critical point for the original optimization problem. Finally, we present some numerical examples concerning applications of the theoretical results established.