Mathematical Modeling in Static Three-Dimensional Boundary-Value Problems: A Skew-Symmetric Problem for a Layer Weakened by a Through Hole with Sliding end Clamping

The authors overview spatial static boundary-value problems of mathematical physics for a layer. The problem for a layer with a non-circular cylindrical through hole is solved using the singular integral equations (SIE) method. A new mathematical model has been constructed; namely, a new method based on a system of three SIEs has been developed and tested numerically. As a result of a high-precision numerical study, it was found that as the thickness of the layer increases, the relative circumferential stress grows. In the case of a circular hole, the maximum relative circumferential stress shifts inside from the ends.