矩形内弹性理论非均质边值问题的精确解

IF 0.6 4区物理与天体物理 Q4 MECHANICS Doklady Physics Pub Date : 2024-03-01 DOI:10.1134/S102833582311006X

M. D. Kovalenko, A. P. Kerzhaev, I. V. Menshova, Yu. N. Karnet

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摘要

摘要本文提出了一种方法，用于建立矩形区域内有加强筋的弹性理论边界值问题（不均匀问题）的精确解。解以帕普科维奇-法德尔特征函数序列的形式呈现，系数明确确定。该方法基于帕普科维奇正交关系和已开发的矩形（双谐波问题）弹性理论同质边界值问题中帕普科维奇-法德尔特征函数的展开理论。以矩形的偶对称问题为例，说明了求解顺序，矩形的边是自由的，外部载荷沿位于矩形对称轴上的加强筋作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact Solutions to Inhomogeneous Boundary Value Problems of the Theory of Elasticity in a Rectangle

A method is proposed for building exact solutions to boundary value problems of the theory of elasticity in a rectangle with stiffeners located inside a region (the inhomogeneous problem). The solutions are presented as series in Papkovich–Fadle eigenfunctions with explicitly determined coefficients. The method is based on the Papkovich orthogonality relation and the developed theory of expansions in the Papkovich–Fadle eigenfunctions in homogeneous boundary value problems of the theory of elasticity in a rectangle (the biharmonic problem). The solution sequence is demonstrated by the example of an even symmetric problem for a rectangle in which the sides are free and an external load acts along a stiffener located on the axis of symmetry of the rectangle.

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来源期刊

Doklady Physics 物理-力学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

4-8 weeks

期刊介绍： Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.