{"title":"Assessment of multi-cracked non-uniform FGM beams using an equilibrium-based finite element formulation","authors":"H.A.F.A. Santos , V.V. Silberschmidt","doi":"10.1016/j.prostr.2024.11.070","DOIUrl":null,"url":null,"abstract":"<div><div>A novel, simple and effective finite element formulation is introduced for the quasi-static analysis of functionally graded nonuniform Timoshenko beams with multiple and open concentrated cracks. This formulation relies on a complementary variational approach based on a set of approximations that satisfy all equilibrium conditions of the boundary-value problem in a strong form. As a result, this formulation is naturally free from the well-known shear-locking phenomenon. The effectiveness of the formulation is numerically demonstrated through its application to various problems, with the obtained results analysed and discussed.</div></div>","PeriodicalId":20518,"journal":{"name":"Procedia Structural Integrity","volume":"66 ","pages":"Pages 195-204"},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Procedia Structural Integrity","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2452321624011247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/31 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A novel, simple and effective finite element formulation is introduced for the quasi-static analysis of functionally graded nonuniform Timoshenko beams with multiple and open concentrated cracks. This formulation relies on a complementary variational approach based on a set of approximations that satisfy all equilibrium conditions of the boundary-value problem in a strong form. As a result, this formulation is naturally free from the well-known shear-locking phenomenon. The effectiveness of the formulation is numerically demonstrated through its application to various problems, with the obtained results analysed and discussed.
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