Bouwer, Johann M.Kok, SchalkWilke, Daniel Nicolas2023-11-082023-11-082023Johann M. Bouwer, Schalk Kok & Daniel N. Wilke (2023) Challenges and solutions to arc-length controlled structural shape design problems, Mechanics Based Design of Structures and Machines, 51:7, 4088-4119, DOI: 10.1080/15397734.2021.1950549.1539-7734 (print)1539-7742 (online)10.1080/15397734.2021.1950549http://hdl.handle.net/2263/93201This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous objective function is often handled by zero-order methods. However, we opt to solve the optimization problems using gradient-only optimization. Numerical examples demonstrate that function value based methods can misinterpret discontinuities as minima and terminate prematurely. In contrast, gradient-only algorithms are demonstrated to be insensitive to numerical discontinuities, and locate the correct solutions reliably.en© 2021 Taylor & Francis Group, LLC. This is an electronic version of an article published in Mechanics Based Design of Structures and Machines, vol. 51, no. 7, pp. 4088-4119, 2023, doi: 10.1080/15397734.2021.1950549. Mechanics Based Design of Structures and Machines is available online at: https://www.tandfonline.com/loi/lmbd20.Shape sensitivityGradient-onlyDiscontinuitiesOptimizationArc Length Control (ALC)Engineering, built environment and information technology articles SDG-04SDG-04: Quality educationEngineering, built environment and information technology articles SDG-09SDG-09: Industry, innovation and infrastructureEngineering, built environment and information technology articles SDG-11SDG-11: Sustainable cities and communitiesEngineering, built environment and information technology articles SDG-12SDG-12: Responsible consumption and productionChallenges and solutions to arc-length controlled structural shape design problemsPostprint Article