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TOPress3D: 3D topology optimization with design-dependent pressure loads in MATLAB

December 2024
Optimization and Engineering

Authors:

Indian Institute of Technology Hyderabad

This paper introduces “TOPress3D," a 3D topology optimization MATLAB code for structures subjected to design-dependent pressure loads. With a primary focus on pedagogical objectives, the code provides an easy learning experience, making it a valuable tool and practical gateway for newcomers, students, and researchers towards this topic. TOPress3D uses Darcy’s law with a drainage term to link the given pressure load to design variables that, in turn, is converted to consistent nodal loads. Optimization problems focused on compliance minimization under volume constraints with pressure loads are solved. Load sensitivities arising due to design-dependent nature of the loads are evaluated using the adjoint-variable approach. The method of moving asymptotes is used to update the design variables. TOPress3D is constituted by six main parts. Each is described in detail. The code is also tailored to solve different problems. The robustness and success of the code are demonstrated in designing a few pressure load-bearing structures. The code is provided in Appendix B and is available with extensions in the supplementary material and publicly at https://github.com/PrabhatIn/TOPress3D.

Element i nomenclature. Lface, Rface, BTface, Tface, Fface and Bface represent left, right, bottom, top, front, and back faces, respectively. Herein, these faces respectively contain 1,2,5,6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 1,\,2,\,5,\,6\right\} $$\end{document}, 3,4,7,8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 3,\,4,\,7,\,8\right\} $$\end{document}, 1,2,3,4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 1,\,2,\,3,\,4\right\} $$\end{document}, 5,6,7,8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 5,\,6,\,7,\,8\right\} $$\end{document}, 2,3,6,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 2,\,3,\,6,\,7\right\} $$\end{document} and 1,4,5,8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ 1,\,4,\,5,\,8\right\} $$\end{document} nodes

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Design domain for a loadbearing lid structure. Pressure load is applied on the top surface, and all its edges are fixed

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Optimized pressure loadbearing lid structure in different views. The domain is parameterized using 48×24×24\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$48\times 24 \times 24$$\end{document} FEs. The density value of the isosurface displayed is 0.3

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Convergence plot for the loadbearing lid structure

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Design domain for an externally pressurized structure. The pressure load is applied on the top surface. The bottom, front and back faces get zero pressure loading. The left and right edges of the bottom face are fixed. The left and right faces slid in the vertical direction

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Optimization and Engineering

https://doi.org/10.1007/s11081-024-09931-2

RESEARCH ARTICLE

TOPress3D: 3D topology optimization with

design-dependent pressure loads in MATLAB

Prabhat Kumar1

Received: 11 April 2024 / Revised: 26 August 2024 / Accepted: 20 September 2024

Abstract

This paper introduces “TOPress3D," a 3D topology optimization MATLAB code

for structures subjected to design-dependent pressure loads. With a primary focus

on pedagogical objectives, the code provides an easy learning experience, making

it a valuable tool and practical gateway for newcomers, students, and researchers

towards this topic. TOPress3D uses Darcy’s law with a drainage term to link the

given pressure load to design variables that, in turn, is converted to consistent nodal

loads. Optimization problems focused on compliance minimization under volume

constraints with pressure loads are solved. Load sensitivities arising due to design-

dependent nature of the loads are evaluated using the adjoint-variable approach. The

method of moving asymptotes is used to update the design variables. TOPress3D is

constituted by six main parts. Each is described in detail. The code is also tailored to

solve different problems. The robustness and success of the code are demonstrated in

designing a few pressure load-bearing structures. The code is provided in Appendix B

and is available with extensions in the supplementary material and publicly at https://

github.com/PrabhatIn/TOPress3D.

Keywords Topology optimization ·Design-dependent pressure loads ·MATLAB

code ·Compliance minimization

1 Introduction

This paper introduces “TOPress3D," a MATLAB code (158-line) designed for per-

forming 3D topology optimization on structures subjected to design-dependent ﬂuidic

pressure loads. While such loads are prevalent in various applications, addressing

them within a topology optimization framework presents distinct challenges as they

change direction, location and/or magnitude with design evolution (Hammer and

Olhoff 2000; Kumar et al. 2020). These challenges become more pronounced for 3D

BPrabhat Kumar

pkumar@mae.iith.ac.in

1Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad,

Telangana 502285, India

123

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TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads

Article

Apr 2023

Prabhat Kumar

In a topology optimization (TO) setting, design-dependent fluidic pressure loads pose several challenges as their direction, magnitude, and location alter with topology evolution. This paper offers a compact 100-line MATLAB code, TOPress, for TO of structures subjected to fluidic pressure loads using the method of moving asymptotes. The code is intended for pedagogical purposes and aims to ease the beginners’ and students’ learning toward the TO with design-dependent fluidic pressure loads. TOPress is developed per the approach first reported in Kumar et al. (Struct Multidisc Optim 61(4):1637–1655, 2020). The Darcy law, in conjunction with the drainage term, is used to model the applied pressure load. The consistent nodal loads are determined from the obtained pressure field. The employed approach facilitates inexpensive computation of the load sensitivities using the adjoint-variable method. Compliance minimization subject to volume constraint optimization problems is solved. The success and efficacy of the code are demonstrated by solving benchmark numerical examples involving pressure loads, wherein the importance of load sensitivities is also demonstrated. TOPress contains six main parts, is described in detail, and is extended to solve different problems. Steps to include a projection filter are provided to achieve loadbearing designs close to 0-1. The code is provided in Appendix 2 and can also be downloaded along with its extensions from https://github.com/PrabhatIn/TOPress.

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Soft robots are made of compliant materials that perform their tasks by deriving motion from elastic deformations. They are used in various applications, e.g., for handling fragile objects, navigating sensitive/complex environments, etc., and are typically actuated by Pneumatic/hydraulic loads. Though demands for soft robots are continuously increasing in various engineering sectors, due to the lack of systematic approaches, they are primarily designed manually. This paper presents a systematic density-based topology optimization approach to designing soft robots while considering the design-dependent behavior of the actuating loads. We use the Darcy law with the conceptualized drainage term to model the design-dependent nature of the applied pressure loads. The standard finite element is employed to evaluate the consistent nodal loads from the obtained pressure field. The robust topology optimization formulation is used with the multi-criteria objective. The success of the presented approach is demonstrated by designing a member/soft robot of the pneumatic networks (PneuNets). The optimized member is combined in several series to get different PneuNets. Their CAD models are generated, and they are studied with high-pressure loads in a commercial software. Depending upon the number of members in the PneuNets, different output motions are noted.KeywordsSoft robotsTopology optimizationDesign-dependent loadsCompliant mechanisms

TOPress3D: 3D topology optimization with design-dependent pressure loads in MATLAB

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