# Topology optimization for transient response of structures subjected to dynamic loads

## TL;DR

This paper develops a topology optimization framework for structures under transient dynamic loads, enabling tailored responses through advanced numerical methods and material interpolation techniques.

## Contribution

It introduces a gradient-based optimization approach using MMA, adjoint sensitivities, and stabilization methods for transient structural problems.

## Key findings

- Optimized designs effectively tailor transient responses.
- The framework handles both static and dynamic loading cases.
- Numerical stabilization improves manufacturability of designs.

## Abstract

This paper presents a topology optimization framework for structural problems subjected to transient loading. The mechanical model assumes a linear elastic isotropic material, infinitesimal strains, and a dynamic response. The optimization problem is solved using the gradient-based optimizer Method of Moving Asymptotes (MMA) with time-dependent sensitivities provided via the adjoint method. The stiffness of materials is interpolated using the Solid Isotropic Material with Penalization (SIMP) method and the Heaviside Projection Method (HPM) is used to stabilize the problem numerically and improve the manufacturability of the topology-optimized designs. Both static and dynamic optimization examples are considered here. The resulting optimized designs demonstrate the ability of topology optimization to tailor the transient response of structures.