Contact Problem for the End of Elastic Half-Strip

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Abstract

The paper considers contact problems for a stamp located at the end of an elastic half-strip without friction under the action of a concentrated force. A practical analogue of this problem is the support zone of a beam or truss on the head of a rectangular column, since the supporting parts of beams or columns have high bending rigidity. The calculation is performed in two stages. At the first stage, the variational-difference method solves the problem of the action of an arbitrarily applied concentrated force on the end of an elastic half-strip. The solution of this problem makes it possible to compose a square matrix of vertical displacements of the points of the end of the half-strip from the action of a single force. At the second stage, the Zhemochkin method solves the contact problem for a stamp arbitrarily located at the end of the elastic half-strip. The coefficients of the canonical equations of the forces method in the Zhemochkin method are based on the previously obtained matrix of vertical displacements of the end points of the elastic half-strip. Three problems for stamps located at the end of an elastic half-strip are considered in the paper. Graphs of the distribution of contact stresses, a plot of bending moments are given and the position of the force causing the translational movement of the stamp located on the edge of the half-strip is determined. The similarity of the obtained is noted with the results for a stamp located on an elastic half-plane.
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弹性半条末端的接触问题
本文研究了在集中力作用下,位于无摩擦弹性半条末端的冲压件的接触问题。这个问题的一个实际类比是矩形柱头部的梁或桁架的支撑区,因为梁或柱的支撑部分具有很高的抗弯刚度。计算分两个阶段进行。在第一阶段,变分差分法解决了弹性半条末端任意施加集中力的问题。这个问题的解决使我们有可能在一个单一的力的作用下,组成一个半条末端各点的垂直位移的方阵。在第二阶段,采用Zhemochkin方法解决弹性半条末端任意位置的冲压件的接触问题。Zhemochkin法中力法正则方程的系数是基于先前得到的弹性半条端点的垂直位移矩阵。本文考虑了弹性半条末端的三个问题。给出了接触应力分布图和弯矩分布图,并确定了引起压痕平移运动的力在半带边缘的位置。所得到的结果与位于弹性半平面上的印章的结果相似。
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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