Thermoelasticity with Finite Wave Speeds


Book Description

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.







Finite Elements Methods in Mechanics


Book Description

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.




Modern Applied Mathematics


Book Description

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.




Thermal Stresses -- Advanced Theory and Applications


Book Description

The authors are pleased to present Thermal Stresses – Advanced Theory and Applications. This book will serve a wide range of readers, in particular, gr- uate students, PhD candidates, professors, scientists, researchers in various industrial and government institutes, and engineers. Thus, the book should be considered not only as a graduate textbook, but also as a reference handbook to those working or interested in areas of Applied Mathematics, Continuum Mechanics, Stress Analysis, and Mechanical Design. In addition, the book p- vides extensive coverage of great many theoretical problems and numerous references to the literature. The ?eld of Thermal Stresses lies at the crossroads of Stress Analysis, T- ory of Elasticity, Thermodynamics, Heat Conduction Theory, and advanced methods of Applied Mathematics. Each of these areas is covered to the extend it is necessary. Therefore, the book is self-contained, so that the reader should not need to consult other sources while studying the topic. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic preparation on the part of the reader in Classical Mechanics, Stress Analysis, and Mathematics, - cluding Vector and Cartesian Tensor Analysis is expected. While selecting material for the book, the authors made every e?ort to present both classical topics and methods, and modern, or more recent, dev- opments in the ?eld. The book comprises ten chapters.




Thermal Stresses—Advanced Theory and Applications


Book Description

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.




Advanced Problem in Mechanics II


Book Description

This book focuses on original theories and approaches in the field of mechanics. It reports on both theoretical and applied researches, with a special emphasis on problems and solutions at the interfaces of mechanics and other research areas. The respective chapters highlight cutting-edge works fostering development in fields such as micro- and nanomechanics, material science, physics of solid states, molecular physics, astrophysics, and many others. Special attention has been given to outstanding research conducted by young scientists from all over the world. This book is based on the 48th edition of the international conference “Advanced Problems in Mechanics”, which was held in 2020, in St. Petersburg, Russia, and co-organized by The Peter the Great St. Petersburg Polytechnic University and the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, under the patronage of the Russian Academy of Sciences. It provides researchers and graduate students with an extensive overview of the latest research and a source of inspiration for future developments and collaborations in mechanics and related fields.







Fractional Thermoelasticity


Book Description




Progress in Physics, vol. 3/2009


Book Description

Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics.