Solving the problem of stretching an elastic-plastic strip weakened by cuts and holes

In this paper, the boundary between elastic and plastic regions in a stretchable strip is con-structed. The band is weakened by side slits and holes. Such tasks are still relevant, since its solution allows us to make an assessment of the limiting state of the structure under consideration. Cuts can have an arbitrary shape, their number is not limited. For simplicity, only sections with rectilinear boundaries are considered in the article. The holes may have an arbitrary shape and be located anywhere in the strip. In operation, only circular holes are considered for simplicity. Numerical methods are currently very often used to solve such a problem, unfortunately, often without much justification. Therefore, analytical methods for solving such problems are becoming more and more relevant. In this paper, the conservation laws of differential equations are used. The conserved current is linear in the first derivatives. The task is solved in two stages. At the first stage, Dirichlet is solved for the Laplace equation, and at the second stage, the technique of conservation laws is used. Their use makes it possible to reduce the finding of the components of the stress tensor at each point to a contour integral along the boundaries of the region un-der consideration. And this makes it possible to build an elastic-plastic boundary.