SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR ANISOTROPIC PLATES AND SHELLS BY BOUNDARY ELEMENTS METHOD

Author:

Velikanov P. G.ORCID,Khalitova D. M.ORCID

Abstract

Modern mechanical engineering sets the tasks of calculating thin-walled structures that combine lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of anisotropic materials and plastics seems justified. The problems of the theory of plates and shells belong to the class of boundary value problems, the analytical solution of which, due to various circumstances (nonlinearity of differential equations, complexity of geometry and boundary conditions, etc.), cannot bedetermined. Numerical methods help to solve this problem. Among numerical methods, undeservedly little attention is paid to the boundary element method. In this regard, the further development of indirect method of compensating loads for solving problems of the anisotropic plates and shells theory based on the applicationof exact fundamental solutions is relevant.The paper considers the application of the indirect boundary element method for solving of an anisotropic plates and shells nonlinear deformation problem. Since the kernels of the system of singular integral equations to which the solution of the problem is reduced are expressed in terms of the fundamental solution and itsderivatives, first of all, the article provides a method for determining the fundamental solutions to the problem of bending and the plane stress state of an anisotropic plate. The displacement vector is determined from the solution of linear equations system describing the bending and plane stress state of an anisotropic plate. The solution of the system is performed by the method of compensating loads, according to which the area representing the plan of the shallow shell is supplemented to an infinite plane, and on the contour that limits the area, compensating loads are applied to the infinite plate. Integral equations of indirect BEM are given. In this paper, the study of nonlinear deformation of anisotropic plates and shallow shells is carried out using the deflection load dependencies. The deflection at a given point on the median surface of the shell was taken as the leading parameter.

Publisher

Samara National Research University

Reference19 articles.

1. Galimov K.Z. Fundamentals of the nonlinear theory of thin shells. Kazan: Izd-vo Kazanskogo un-ta, 1975, 326 p. (In Russ.)

2. Volmir A.S. Nonlinear dynamics of plates and shells. Moscow: Nauka, 1972, 432 p. Available at: https://dwg.ru/lib/1965. (In Russ.)

3. Lekhnitsky S.G. Anisotropic plates. Moscow: OGIZ-Gostekhizdat, 1947, 355 p. Available at: https://lib-bkm.ru/12625. (In Russ.)

4. Kornishin M.S. Nonlinear problems of the plates and shallow shells theory and methods of their solution. Moscow: Nauka, 1964, 192 p. (In Russ.)

5. Hormander (должна быть О с двумя точками наверху) L. The Analysis of Linear Partial Differential Operators I Distribution Theory and Fourier Analysis. Moscow: Mir, 1986, 464 p. Available at: http://www.bookre.org/reader?file=442772. (In Russ.)

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3