A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.
This is an advanced modern textbook on thermal stresses. It serves a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering. This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis. This 2nd enhanced edition includes a new chapter on Thermally Induced Vibrations. The method of stiffness is added to Chapter 7. The variational principle for the Green-Lindsay and Green-Naghdi models have been added to Chapter 2 and equations of motion and compatibility equations in spherical coordinates to Chapter 3. Additional problems at the end of chapters were added.
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detailed derivations for the mass, stiffness and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems and the third one presents the three dimensional transient heat conduction problems. The programs are written in C++ environment.
This comprehensive volume introduces educational units dealing with important topics of modern applied mathematics. Chapters include comprehensive information on different topics such as: Methods of Approximation for Mapping in Probability Spaces, Mathematical Modelling of Seismic Sources, Climate Variability, Geometry of Differential Equations, Modelling of Particle-Driven Gravity Currents, Impulsive Free-Surface Flows, Internal Wave Propagation, Isogroups and Exact Solutions of Higher Order Boltzman Equation, Molecular and Particle Modelling, Asymptotic Behaviour of Solutions of Nonlinear Partial Differential Equations, Mixed Boundary Value Problems, Dual Integral Equations, Dual Series Equations and their Applications, Evolutionary Mechanisms of Organization in Complex Systems, Zero-Sum Differential Games, Bernoulli Convolutions, Probability Distribution Functions, O.D.E. Approach to Stochastic Approximation, Bayesian Inference on the Long Range Dependence.