Sounak Kabasi , Allan L. Marbaniang , Siddhartha Ghosh
{"title":"Integrated design of tensile membrane structures using scientific machine learning including wrinkling considerations","authors":"Sounak Kabasi , Allan L. Marbaniang , Siddhartha Ghosh","doi":"10.1016/j.mechrescom.2025.104468","DOIUrl":null,"url":null,"abstract":"<div><div>Tensile membrane structures (TMS) are extremely popular these days owing to their aesthetic appeal, lightweight and their ability to cover large expansive areas. However, the design of TMS involves two computationally challenging steps: (a) form-finding — to find the initial equilibrium shape subjected to the given prestress and boundary conditions and (b) Load analysis — to determine whether the obtained form can resist design loads. Furthermore, the membrane wrinkling phenomena causes even more difficulties in load analysis frameworks. Traditional mesh-based analysis frameworks suffer from ill-conditioned stiffness matrix and convergence issues that can arise due to wrinkling. Hence, in this study a mesh-less framework for load analysis is proposed by posing the load analysis problem as a direct energy minimization problem and solving it using a Quasi Newton optimizer. Modified potential energy formulations for wrinkling considerations incorporated in the mesh-free approach are also proposed. The analysis is performed by employing gradient-enhanced physics-informed neural networks (gPINN) aided by the theory of functional connections (TFC) ensuring kinetically admissible field variables without the requirement of an additional loss function for enforcing the essential boundary conditions. The analysis framework eliminates the requirement of calculation of an explicit stiffness matrix and the penalty parameter as well. Additionally, a vectorized implementation is incorporated, making the proposed approach computationally feasible. Finally, an integrated sequential form-finding and load analysis framework for seamless design and analysis of frame-supported and cable-supported TMS is proposed. Extensive numerical case studies are performed to test the efficacy of the proposed framework. The computational efficiency of the proposed method in comparison to a traditional mesh-based method is also noted.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104468"},"PeriodicalIF":1.9000,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics Research Communications","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0093641325001016","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Tensile membrane structures (TMS) are extremely popular these days owing to their aesthetic appeal, lightweight and their ability to cover large expansive areas. However, the design of TMS involves two computationally challenging steps: (a) form-finding — to find the initial equilibrium shape subjected to the given prestress and boundary conditions and (b) Load analysis — to determine whether the obtained form can resist design loads. Furthermore, the membrane wrinkling phenomena causes even more difficulties in load analysis frameworks. Traditional mesh-based analysis frameworks suffer from ill-conditioned stiffness matrix and convergence issues that can arise due to wrinkling. Hence, in this study a mesh-less framework for load analysis is proposed by posing the load analysis problem as a direct energy minimization problem and solving it using a Quasi Newton optimizer. Modified potential energy formulations for wrinkling considerations incorporated in the mesh-free approach are also proposed. The analysis is performed by employing gradient-enhanced physics-informed neural networks (gPINN) aided by the theory of functional connections (TFC) ensuring kinetically admissible field variables without the requirement of an additional loss function for enforcing the essential boundary conditions. The analysis framework eliminates the requirement of calculation of an explicit stiffness matrix and the penalty parameter as well. Additionally, a vectorized implementation is incorporated, making the proposed approach computationally feasible. Finally, an integrated sequential form-finding and load analysis framework for seamless design and analysis of frame-supported and cable-supported TMS is proposed. Extensive numerical case studies are performed to test the efficacy of the proposed framework. The computational efficiency of the proposed method in comparison to a traditional mesh-based method is also noted.
期刊介绍:
Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide:
• a fast means of communication
• an exchange of ideas among workers in mechanics
• an effective method of bringing new results quickly to the public
• an informal vehicle for the discussion
• of ideas that may still be in the formative stages
The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.