{"title":"Explicit determination for exact solutions of elastic rectangular beams","authors":"Changwei Tang, Guansuo Dui, Yuyao Fu","doi":"10.1007/s10999-024-09714-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a method to directly determine explicit expressions of the exact general solutions for isotropic rectangular beam is provided. If the spanwise variation of the bending moment is smooth, the exact solution of the stress function can be expressed in the form of infinite series, whose each term is the product of the bending moment or its higher derivatives and polynomial involving only the longitudinal coordinates, while the polynomials are independent of the distributed loads. First, the explicit exact expression of the stress function is derived by solving recurrence formulae. Then, the convergence and accuracy of the formulae is estimated by retaining different terms. Finally, formulae of the stress and displacement fields are applied to some classical examples with the cases distributed loads in simple polynomials and sine form, and the results obtained are in perfect agreement with the existing exact theory.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"20 6","pages":"1269 - 1289"},"PeriodicalIF":2.7000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s10999-024-09714-8","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a method to directly determine explicit expressions of the exact general solutions for isotropic rectangular beam is provided. If the spanwise variation of the bending moment is smooth, the exact solution of the stress function can be expressed in the form of infinite series, whose each term is the product of the bending moment or its higher derivatives and polynomial involving only the longitudinal coordinates, while the polynomials are independent of the distributed loads. First, the explicit exact expression of the stress function is derived by solving recurrence formulae. Then, the convergence and accuracy of the formulae is estimated by retaining different terms. Finally, formulae of the stress and displacement fields are applied to some classical examples with the cases distributed loads in simple polynomials and sine form, and the results obtained are in perfect agreement with the existing exact theory.
期刊介绍：
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.
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