{"title":"Exact solutions for anisotropic beams with arbitrary distributed loads","authors":"Changwei Tang, Guansuo Dui, Yuyao Fu","doi":"10.1016/j.apm.2024.115735","DOIUrl":null,"url":null,"abstract":"<div><div>The general solution of elasticity for plane anisotropic beams with arbitrary constraints at ends and arbitrary normal and tangential distributed loads on surfaces is derived, which consists of internal forces (i.e., bending moment, shearing force, axial force) and their integrals and derivatives of different orders and load-independent polynomial function sequences of longitudinal coordinates. The method for determining the function sequences is established by resolving the governing equation and boundary conditions of the stress function method. For beams with an elastic symmetry plane, a method for directly determining explicit expressions for all terms of function sequences is provided. Particular solutions of examples are solved using general solution formulas, and the results align excellently with existing exact solutions. Finally, the errors in EBT and TBT when applied to beams made of different materials are analysed.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"137 ","pages":"Article 115735"},"PeriodicalIF":4.4000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematical Modelling","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0307904X24004888","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The general solution of elasticity for plane anisotropic beams with arbitrary constraints at ends and arbitrary normal and tangential distributed loads on surfaces is derived, which consists of internal forces (i.e., bending moment, shearing force, axial force) and their integrals and derivatives of different orders and load-independent polynomial function sequences of longitudinal coordinates. The method for determining the function sequences is established by resolving the governing equation and boundary conditions of the stress function method. For beams with an elastic symmetry plane, a method for directly determining explicit expressions for all terms of function sequences is provided. Particular solutions of examples are solved using general solution formulas, and the results align excellently with existing exact solutions. Finally, the errors in EBT and TBT when applied to beams made of different materials are analysed.
期刊介绍：
Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged.
This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.
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