{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T01:45:39Z","timestamp":1778031939798,"version":"3.51.4"},"reference-count":114,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T00:00:00Z","timestamp":1701475200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/145425\/2019"],"award-info":[{"award-number":["SFRH\/BD\/145425\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Serra H\u00fanter Research Program (Spain)","award":["SFRH\/BD\/145425\/2019"],"award-info":[{"award-number":["SFRH\/BD\/145425\/2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Topology optimization has evidenced its capacity to provide new optimal designs in many different disciplines. However, most novel methods are difficult to apply in commercial software, limiting their use in the academic field and hindering their application in the industry. This article presents a new open methodology for solving geometrically complex non-self-adjoint topology optimization problems, including stress-constrained and stress minimization formulations, using validated FEM commercial software. The methodology was validated by comparing the sensitivity analysis with the results obtained through finite differences and solving two benchmark problems with the following optimizers: Optimality Criteria, Method of Moving Asymptotes, Sequential Least-Squares Quadratic Programming (SLSQP), and Trust-constr optimization algorithms. The SLSQP and Trust-constr optimization algorithms obtained better results in stress-minimization problem statements than the methodology available in ABAQUS\u00ae. A Python implementation of this methodology is proposed, working in conjunction with the commercial software ABAQUS\u00ae 2023 to allow a straightforward application to new problems while benefiting from a graphic user interface and validated finite element solver.<\/jats:p>","DOI":"10.3390\/app132312916","type":"journal-article","created":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T13:45:41Z","timestamp":1701524741000},"page":"12916","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Stress-Constrained Topology Optimization for Commercial Software: A Python Implementation for ABAQUS\u00ae"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2708-2160","authenticated-orcid":false,"given":"Pedro","family":"Fernandes","sequence":"first","affiliation":[{"name":"INEGI\u2014Institute for Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1011-0230","authenticated-orcid":false,"given":"\u00c0lex","family":"Ferrer","sequence":"additional","affiliation":[{"name":"CIMNE\u2014International Center for Numerical Methods in Engineering, Campus Nord UPC, S\/N 08034 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3126-6365","authenticated-orcid":false,"given":"Paulo","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute for Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3326-6345","authenticated-orcid":false,"given":"Marco","family":"Parente","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute for Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"},{"name":"FEUP\u2014Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4869-131X","authenticated-orcid":false,"given":"Ricardo","family":"Pinto","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute for Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6486-3954","authenticated-orcid":false,"given":"Nuno","family":"Correia","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute for Science and Innovation in Mechanical and Industrial Engineering, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Kikuchi","year":"1988","journal-title":"Comput. 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