Reinforcement of a plate weakened by multiple holes with several patches for different types of a plate-patch attachment

TL;DR

This paper develops a comprehensive method for reinforcing plates with multiple holes using various patch attachment strategies, introducing a new numerical approach that improves convergence and reduces computational effort.

Contribution

It presents a general framework for plate reinforcement with multiple patches and holes, and introduces a novel numerical procedure for solving the associated integral equations.

Findings

New numerical method improves convergence

Reduces computational effort compared to previous methods

Applicable to various patch attachment configurations

Abstract

The most general situation of the reinforcement of a plate with multiple holes by several patches is considered. There is no restriction on the number and the location of the patches. Two types of the patch attachment are considered: only along the boundary of the patch or both along the boundary of the patch and the boundaries of the holes which this patch covers. The unattached boundaries of the holes may be loaded with given in-plane stresses. The mechanical problem is reduced to the system of singular integral equations which can be further reduced to the system of Fredholm equations. A new numerical procedure for the solution of the system of singular integral equations is proposed in this paper. It can be observed that this procedure provides a noticeable improvement from the one presented in Zemlyanova \cite{Zem2007}, Zemlyanova and Silvestrov \cite{ZemSil2007}, \cite{ZemSil2009} and allows to achieve a significantly better numerical convergence with less computational effort.