This paper presents the study of the plane strain problem of an infinite isotropic elastic medium subjected to far-field load and containing multiple Gurtin–Murdoch material surfaces located along straight segments. Each material segment represents a membrane of vanishing thickness characterized by its own elastic stiffness and residual surface tension. The governing equations, the jump conditions, and the surface tip conditions are reviewed. The displacements in the matrix are sought as the sum of complex variable single-layer elastic potentials whose densities are equal to the jumps in complex tractions across the segments. The densities are found by solving the system of coupled hypersingular boundary integral equations. The approximations by a series of Chebyshev’s polynomials of the second kind are used with the square root weight functions chosen to satisfy the tip conditions automatically. Numerical examples are presented to illustrate the influence of dimensionless parameters and to study the effects of interactions.

中文翻译：

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沿直线段包含多个 Gurtin-Murdoch 材料表面的弹性矩阵的平面应变问题

本文研究了无限各向同性弹性介质在远场载荷作用下的平面应变问题，该介质包含沿直线段布置的多个 Gurtin-Murdoch 材料表面。每个材料片段代表厚度消失的膜，其特征在于其自身的弹性刚度和残余表面张力。回顾了控制方程、跳跃条件和表面尖端条件。矩阵中的位移被视为复变量单层弹性势的总和，其密度等于跨段的复牵引力的跳跃。通过求解耦合超奇异边界积分方程组可以找到密度。一系列第二类切比雪夫多项式的近似值与选择的平方根权重函数一起使用，以自动满足尖端条件。给出了数值例子来说明无量纲参数的影响并研究相互作用的影响。