PRECISION OF ACTIV TASKS FOR A PLATE WHITH OPENING

Abstract

The study of the stress–strain state of plates containing holes of various shapes remains a fundamental and practically significant problem in modern solid mechanics. Holes and cutouts are indispensable in real engineering structures for weight reduction, assembly, or maintenance purposes. However, they inevitably disturb the uniform stress field, producing zones of stress concentration that often serve as the starting points of cracks and fatigue failure. Understanding and predicting these effects is essential for improving the reliability, durability, and efficiency of modern structures in aerospace, mechanical, civil, and energy engineering. Recent progress in this field has been driven by the combined application of analytical methods and numerical techniques, particularly the finite element method. Researchers have achieved significant results in modeling the influence of hole shape, orientation, and boundary conditions on the overall stress distribution. A special focus has been placed on anisotropic materials, which are increasingly used in composite and layered structures due to their high strength-to-weight ratio. Anisotropy of the elastic medium usually introduces considerable additional difficulties in solving boundary-value problems. In the case of rectilinear anisotropy, one must deal with a pair of coupled analytic functions depending on different complex variables. For media with curvilinear anisotropy, the direct application of classical methods based on complex function theory becomes impossible. These difficulties can be overcome only in certain special cases, such as small anisotropy or specific laws governing the variation of elastic properties, while the corresponding isotropic problem is generally considered the simplest benchmark. In this context, the present work provides exact closed-form solutions for two problems concerning the stress–strain state of an orthotropic plate with cylindrical anisotropy. The results contribute to a deeper understanding of the mechanical behavior of anisotropic plates with holes and can serve as reference models for verifying numerical simulations and optimizing engineering designs.