Some static and dynamic boundary value problems in isotropic elastic media

In this dissertation, we present the solution of various boundary value problems in both homogeneous and nonhomogeneous elastic media that may have potential applications in engineering.; In Chapter 1, we have given a brief outline of the linear theory of elasticity focusing on the derivation of the basic equations that are useful in formulating a boundary value problem in linear elasticity.; Chapter 2 presents a brief summary of the various Torsion and Crack problems in elasticity that are relevant to the present study.; In Chapter 3 the solution of the torsion problem of semi-infinite composite elastic cylindrical shell composed of two materials of different rigidity modulus is presented. By utilizing the method of Fourier transforms, the expression for the stresses and displacement fields are derived and numerical results are displayed graphically.; In Chapter 4 we discuss the anti-plane shear problem of a mode III crack travelling with constant velocity at the interface of two dissimilar homogeneous materials bonded through a thin layer of non-homogeneous interfacial region. Integral transform method is used to reduce the problem to the solution of a singular integral equation which is further reduced using Chebyshev polynomials, to a system of algebraic equations. Numerical results for the sum intensity factor and energy release rate for the case of two half-spaces are displayed in tabular form. A special case of the problem is compared with the already published results.; In Chapter 5, a plane strain problem of determining the stress intensity factor for a moving Griffith Crack in homogeneous elastic layer with moving punches situated along the boundaries of the layer is considered. The problem is reduced to the solution of a pair of simultaneous singular integral equations with Cauchy type singularities. The integral equations are then solved approximately by the use of Chebyshev polynomials. Numerical results for the stress intensity factors are presented graphically for some particular cases of the problems.; Finally, in Chapter 6, a model is constructed to evaluate the stress intensity factor for a non-homogeneous multi-layered composite with an interlaminar penny-shaped crack subjected to an axially symmetric torsion. The mixed boundary value problem is reduced to solving a Fredholm integral equation of the second kind. Numerical results for the stress intensity factor are presented in the form of graphs.