由不同抗拉和抗压材料制成的复杂形状柔性浅壳的非线性变形

IF 0.7 4区 材料科学 Q4 MATERIALS SCIENCE, CHARACTERIZATION & TESTING
O. Z. Galishyn, S. M. Sklepus
{"title":"由不同抗拉和抗压材料制成的复杂形状柔性浅壳的非线性变形","authors":"O. Z. Galishyn, S. M. Sklepus","doi":"10.1007/s11223-024-00624-w","DOIUrl":null,"url":null,"abstract":"<p>A new numerical-and-analytical method is developed for solving geometrically and physically nonlinear problems of bending shallow shells of complex shapes made from materials with different resistance to tension and compression. To linearize the initial nonlinear problem, the method of continuous continuation in the parameter associated with the external load was used. For the variational formulation of the linearized problem, a Lagrange functional was constructed, defined at kinematically possible displacement velocities. To find the main unknowns of the problem of nonlinear bending of a hollow shell (displacements, deformations, stresses), the Cauchy problem for a system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta– Merson method with automatic step selection. The initial conditions are found in the solution to the problem of geometrically linear deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta–Merson scheme were obtained from the solution of the variational problem for the Lagrange functional. The variational problems were solved by the Ritz method in combination with the R-function method. The latter makes it possible to present an approximate solution in the form of a formula, which solution structure exactly satisfies all (general structure) or part (partial structure) of the boundary conditions. The problems of nonlinear deformation of a square cylindrical shell and a shell of complex shape with combined fixation conditions are solved. The influence of the direction of external loading, geometric shape, and fixation conditions on the stress-strain state is investigated. It is shown that failure to consider the different behaviors of the material in tension and compression leads to significant errors in calculating the stress-strain state parameters.</p>","PeriodicalId":22007,"journal":{"name":"Strength of Materials","volume":"48 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Deformation of Flexible Shallow Shells of Complex Shape Made of Materials with Different Resistance to Tension and Compression\",\"authors\":\"O. Z. Galishyn, S. M. Sklepus\",\"doi\":\"10.1007/s11223-024-00624-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A new numerical-and-analytical method is developed for solving geometrically and physically nonlinear problems of bending shallow shells of complex shapes made from materials with different resistance to tension and compression. To linearize the initial nonlinear problem, the method of continuous continuation in the parameter associated with the external load was used. For the variational formulation of the linearized problem, a Lagrange functional was constructed, defined at kinematically possible displacement velocities. To find the main unknowns of the problem of nonlinear bending of a hollow shell (displacements, deformations, stresses), the Cauchy problem for a system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta– Merson method with automatic step selection. The initial conditions are found in the solution to the problem of geometrically linear deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta–Merson scheme were obtained from the solution of the variational problem for the Lagrange functional. The variational problems were solved by the Ritz method in combination with the R-function method. The latter makes it possible to present an approximate solution in the form of a formula, which solution structure exactly satisfies all (general structure) or part (partial structure) of the boundary conditions. The problems of nonlinear deformation of a square cylindrical shell and a shell of complex shape with combined fixation conditions are solved. The influence of the direction of external loading, geometric shape, and fixation conditions on the stress-strain state is investigated. It is shown that failure to consider the different behaviors of the material in tension and compression leads to significant errors in calculating the stress-strain state parameters.</p>\",\"PeriodicalId\":22007,\"journal\":{\"name\":\"Strength of Materials\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Strength of Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1007/s11223-024-00624-w\",\"RegionNum\":4,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATERIALS SCIENCE, CHARACTERIZATION & TESTING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Strength of Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s11223-024-00624-w","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
引用次数: 0

摘要

为解决由具有不同抗拉和抗压性能的材料制成的复杂形状浅壳弯曲的几何和物理非线性问题,开发了一种新的数值和分析方法。为了使初始非线性问题线性化,采用了与外部载荷相关的参数连续延续法。为了对线性化问题进行变分计算,构建了一个拉格朗日函数,该函数定义于运动学上可能的位移速度。为了找到空心壳体非线性弯曲问题的主要未知数(位移、变形、应力),提出了常微分方程系统的 Cauchy 问题。Cauchy 问题采用自动选择步长的 Runge-Kutta- Merson 方法求解。初始条件可在几何线性变形问题的解中找到。与 Runge-Kutta- Merson 方案相对应的载荷参数固定值的微分方程右边是从拉格朗日函数的变分问题求解中得到的。变分问题采用里兹法结合 R 函数法求解。后者能以公式的形式给出近似解,其解结构完全满足边界条件的全部(一般结构)或部分(部分结构)。解决了具有组合固定条件的方形圆柱形壳体和复杂形状壳体的非线性变形问题。研究了外部加载方向、几何形状和固定条件对应力应变状态的影响。结果表明,不考虑材料在拉伸和压缩时的不同行为会导致应力应变状态参数的计算出现重大误差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Nonlinear Deformation of Flexible Shallow Shells of Complex Shape Made of Materials with Different Resistance to Tension and Compression

Nonlinear Deformation of Flexible Shallow Shells of Complex Shape Made of Materials with Different Resistance to Tension and Compression

A new numerical-and-analytical method is developed for solving geometrically and physically nonlinear problems of bending shallow shells of complex shapes made from materials with different resistance to tension and compression. To linearize the initial nonlinear problem, the method of continuous continuation in the parameter associated with the external load was used. For the variational formulation of the linearized problem, a Lagrange functional was constructed, defined at kinematically possible displacement velocities. To find the main unknowns of the problem of nonlinear bending of a hollow shell (displacements, deformations, stresses), the Cauchy problem for a system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta– Merson method with automatic step selection. The initial conditions are found in the solution to the problem of geometrically linear deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta–Merson scheme were obtained from the solution of the variational problem for the Lagrange functional. The variational problems were solved by the Ritz method in combination with the R-function method. The latter makes it possible to present an approximate solution in the form of a formula, which solution structure exactly satisfies all (general structure) or part (partial structure) of the boundary conditions. The problems of nonlinear deformation of a square cylindrical shell and a shell of complex shape with combined fixation conditions are solved. The influence of the direction of external loading, geometric shape, and fixation conditions on the stress-strain state is investigated. It is shown that failure to consider the different behaviors of the material in tension and compression leads to significant errors in calculating the stress-strain state parameters.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Strength of Materials
Strength of Materials MATERIALS SCIENCE, CHARACTERIZATION & TESTING-
CiteScore
1.20
自引率
14.30%
发文量
89
审稿时长
6-12 weeks
期刊介绍: Strength of Materials focuses on the strength of materials and structural components subjected to different types of force and thermal loadings, the limiting strength criteria of structures, and the theory of strength of structures. Consideration is given to actual operating conditions, problems of crack resistance and theories of failure, the theory of oscillations of real mechanical systems, and calculations of the stress-strain state of structural components.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信