The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations. Also included are developments made by the authors in the boundary integral formulation of thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is formulated for the first time as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-differential equations.

Finite-element methods are commonly used to evaluate cracked solids. Post-processing methods are used to extract Mode I stress-intensity factor values from finite-element analyses. These methods include the Crack-Opening-Displacement (COD) method, the Force method, the Virtual Crack Closure Technique (VCCT) and the Equivalent Domain Integral (EDI) method. The COD method, Force method and the VCCT appear to require that the finite-element mesh intersect the crack front in an orthogonal manner in order to obtain accurate stress-intensity factor values. The EDI does not appear to require this orthogonality with the crack front to obtain accurate stress intensity factor values. The objectives of this study are to determine if accurate stress intensity factor values can be obtained from finite-element models that lack orthogonality with the crack front and, if accurate values cannot be obtained, to modify the extraction methods so that accurate stress-intensity factor values can be obtained from models without orthogonality at the crack front.

The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods. (Author).