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Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.Issues of stress concentration near holes in transtropic shallow spherical shells made of composite materials and subjected to internal pressure are addressed in [1][2][3][4][5][6][9][10][11][12]. Studies aimed at evaluating the influence of transverse shear stiffness on the stress state of shells with holes are reviewed in [2,11]. In [10,12,13], the effect of shear stiffness in composite shells is analyzed numerically.A Problem Formulation for thin elastic shells compliant to transverse shear was first proposed in [4, 5] based on differential equations of a refined Timoshenko theory that allows for the low transverse shear stiffness of the material [5],

The characteristic special feature of deformation behavior of modern laminated composite materials and structural elements fabricated from these materials, at current levels of loading and operating conditions is the occurrence of the purely three-dimensional stress-deformed state. In this process some specific mechanical phenomena and effects may occur, which is impossible to describe within the framework of applied or approximate approaches existing currently in deformable solid body mechanics. The structure of massive laminated materials may be included in this class of phenomena when the critical parameters of the problem depend only on the ratio between mechanical and geometrical characteristics of single layers and are independent of the dimensions and the form of the total laminated body as a whole. Since this phenomenon may be the beginning of the process of fracture of these materials, and the loss of the load-carrying capacity of structure elements fabricated from them, we consider below, in three-dimensional formulation, the problem of the surface and internal instability in laminated composite materials under compressive surface loads. The classification of the existing types of stability problems is presented for laminated materials and approaches for their solution presented in the literature. On the basis of three-dimensional linearized stability theory, within the framework of the piecewise-homogeneous media model, the general formulation of the most characteristic classes of stability problems of laminated materials is given in Lagrangian coordinates at small and finite, homogeneous and inhomogeneous precritical deformation. Analytic and variational methods of investigation of formulated problems are given with application to various models of laminated bodies models, in accordance with accepted stability criteria. The accuracy of these models is evaluated, based on the example of the solution of certain model problems; the range of application is given for existing applied and approximate approaches to the analysis of formulated problems. Results of solution of specific problems are given; specific mechanical effects, characteristic for the phenomenon considered, are found. Recommendations are formulated for engineering design and computational methods. New promising areas of research are pointed out for the problem of laminated composite materials stability.

The problem of folding in the Earth's stratified crust is addressed within the framework of solid mechanics. The history and formulation of the problem and approaches to its solution are briefly outlined. The initial stage of folding in strata with different mechanical properties is studied in detail using the piecewise-homogeneous medium model and the three-dimensional theory of stability. Conclusions of applied and fundamental importance are drawn from an analysis of solutions to a wide range of specific problems