Stress Analysis of an Anisotropic Plate with Embedded Thin Elastic Inclusions

V. Maksimenko, S. Zorin
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Abstract

The stress field in an anisotropic plate containing a system of thin elastic inclusions is studied. It is assumed that ideal mechanical contact occurs between the inclusions and the plate. The inclusion is considered as an elastic plate whose width is much smaller than its length. For the inclusions, boundary conditions are formulated under the assumption that the shear and normal stresses and the derivatives of the displacements are discontinuous at the contact line. Special integral representations of the solution of the problem determined from the boundary conditions at the contact line are constructed. The problem is reduced to a system of integral equations, which is solved by a numerical method. The effect of the stiffness and geometry of the elastic inclusions on the distribution and magnitude of the contact stresses is studied. Numerical results are compared with the data obtained by a simplified model in which the elastic inclusion is considered as a thin thread.
嵌入薄弹性夹杂物的各向异性板的应力分析
研究了含薄弹性夹杂体的各向异性板的应力场。假定夹杂物与板材之间存在理想的机械接触。包裹体被认为是一个弹性板,其宽度远远小于其长度。对于夹杂体,假设切应力和正应力以及位移导数在接触线上不连续,并建立了边界条件。构造了由接触线边界条件确定的问题解的特殊积分表示。这个问题被简化为一个积分方程组,用数值方法求解。研究了弹性夹杂物的刚度和几何形状对接触应力分布和大小的影响。将数值计算结果与将弹性包裹体视为细螺纹的简化模型进行了比较。
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