Asymptotic Analysis of Spatial Problems in Elasticity

Description

The book presents homogeneous solutions in static and dynamical problems of anisotropic theory of elasticity, which are constructed for a hollow cylinder. It also offers an asymptotic process for finding frequencies of natural vibrations of a hollow cylinder, and establishes a qualitative study of several applied theories of the boundaries of applicability. Further the authors develop a general theory for a transversally isotropic spherical shell, which includes methods for constructing inhomogeneous and homogeneous solutions that allow the characteristic features of the stress–strain state of an anisotropic spherical shell to be revealed. Lastly, the book introduces an asymptotic method for integrating the equations of anisotropic theory of elasticity in variable thickness plates and shells. Based on the results of the author and researchers at Baku State University and the Institute of Mathematics and Mechanics, ANAS, the book is intended for specialists in the field of theory of elasticity, theory of plates and shells, and applied mathematics. Front Matter ....Pages i-vi Asymptotic Theory of a Cylindrical Shell (Magomed F. Mekhtiev)....Pages 1-62 Constructing Homogeneous Solutions to a Transversally-Isotropic Spherical Shell (Magomed F. Mekhtiev)....Pages 63-121 Constructing Homogeneous Solutions for a Truncated Hollow Cone (Magomed F. Mekhtiev)....Pages 123-133 Asymptotic Behavior of the Solution to an Axially Symmetric Problem of Elasticity Theory for a Transversally-Isotropic Hollow Cone (Magomed F. Mekhtiev)....Pages 135-186 Asymptotic Analysis of a Tension-Compression Problem for a Variable Thickness Transtropic Plate (Magomed F. Mekhtiev)....Pages 187-210 Asymptotic Analysis of a Bending Problem for a Variable Thickness Transtropic Plate (Magomed F. Mekhtiev)....Pages 211-241