The plane strain problem of an elastic matrix subjected to uniform far-field load and containing a Steigmann–Ogden material surface with circular arc cross-section is considered. The governing equations and the boundary conditions for the problem are reviewed. Exact complex integral representations for the elastic fields everywhere in the material are provided. The problem is further reduced to the system of real variables hypersingular boundary integral equations in terms of the first component of the surface stress tensor (surface stress) and the remaining component of that tensor and its second derivative, along with various problem parameters. The two unknowns are then approximated by the series of trigonometric functions that are multiplied by the square root weight functions to allow for automatic incorporation of the tip conditions. The unknown coefficients in series are found from the system of linear algebraic equations that is solved using standard collocation method. The numerical examples are presented to illustrate the influence of dimensionless parameters. The connection of the problem with that of rigid circular arc is discussed.

考虑了承受均匀远场载荷且包含圆弧截面 Steigmann-Ogden 材料表面的弹性基体的平面应变问题。回顾了问题的控制方程和边界条件。提供了材料中各处弹性场的精确复积分表示。该问题进一步简化为由表面应力张量的第一个分量（表面应力）和该张量的剩余分量及其二阶导数以及各种问题参数组成的实变量超奇异边界积分方程组。然后通过一系列三角函数乘以平方根权重函数来近似这两个未知数，以允许自动合并尖端条件。串联的未知系数是从使用标准配置方法求解的线性代数方程组中找到的。数值例子说明了无量纲参数的影响。讨论了该问题与刚性圆弧问题的联系。