Fundamentals Of The Mechanics Of Solids

This distinctive textbook aims to introduce readers to the basic structures of the mechanics of deformable bodies, with a special emphasis on the description of the elastic behavior of simple materials and structures composed by elastic beams. The authors take a deductive rather than inductive approach and start from a few first, foundational principles. A wide selection of exercises, many with hints and solutions, are provided throughout and organized in a way that will allow readers to form a link between abstract mathematical concepts and real-world applications. The text begins with the definition of bodies and deformations, keeping the kinematics of rigid bodies as a special case; the authors also distinguish between material and spatial metrics, defining each one in the pertinent space. Subsequent chapters cover observers and classes of possible changes; forces, torques, and related balances, which are derived from the invariance under classical changes in observers of the power of the external actions over a body, rather than postulated a priori; constitutive structures; variational principles in linear elasticity; the de Saint-Venant problem; yield criteria and a discussion of their role in the representation of material behavior; and an overview of some bifurcation phenomena, focusing on the Euler rod. An appendix on tensor algebra and tensor calculus is included for readers who need a brief refresher on these topics. Fundamentals of the Mechanics of Solids is primarily intended for graduate and advanced undergraduate students in various fields of engineering and applied mathematics. Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics.

As the theories and methods have evolved over the years, the mechanics of solid bodies has become unduly fragmented. Most books focus on specific aspects, such as the theories of elasticity or plasticity, the theories of shells, or the mechanics of materials. While a narrow focus serves immediate purposes, much is achieved by establishing the common foundations and providing a unified perspective of the discipline as a whole. Mechanics of Solids and Shells accomplishes these objectives. By emphasizing the underlying assumptions and the approximations that lead to the mathematical formulations, it offers a practical, unified presentation of the foundations of the mechanics of solids, the behavior of deformable bodies and thin shells, and the properties of finite elements. The initial chapters present the fundamental kinematics, dynamics, energetics, and behavior of materials that build the foundation for all of the subsequent developments. These are presented in full generality without the usual restrictions on the deformation. The general principles of work and energy form the basis for the consistent theories of shells and the approximations by finite elements. The final chapter views the latter as a means of approximation and builds a bridge between the mechanics of the continuum and the discrete assembly. Expressly written for engineers, Mechanics of Solids and Shells forms a reliable source for the tools of analysis and approximation. Its constructive presentation clearly reveals the origins, assumptions, and limitations of the methods described and provides a firm, practical basis for the use of those methods.

Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based.Develop Intuitive Ability to Identify and Avoid Physically Meaningless PredictionsApplied Mechanics o

Introduction to the Mechanics of Deformable Solids: Bars and Beams introduces the theory of beams and bars, including axial, torsion, and bending loading and analysis of bars that are subjected to combined loadings, including resulting complex stress states using Mohr’s circle. The book provides failure analysis based on maximum stress criteria and introduces design using models developed in the text. Throughout the book, the author emphasizes fundamentals, including consistent mathematical notation. The author also presents the fundamentals of the mechanics of solids in such a way that the beginning student is able to progress directly to a follow-up course that utilizes two- and three-dimensional finite element codes imbedded within modern software packages for structural design purposes. As such, excessive details included in the previous generation of textbooks on the subject are obviated due to their obsolescence with the availability of today’s finite element software packages.

The complete primer to micromechanics Fundamentals of Micromechanics of Solids is the first book integrating various approaches in micromechanics into a unified mathematical framework, complete with coverage of both linear and nonlinear behaviors. Based on this unified framework, results from the authors' own research, as well as existing results in the literature are re-derived in a logical, pedagogical, and understandable approach. It enables readers to follow the various developments of micromechanics theories and quickly understand its wide range of applications of micromechanics. This helpful guide is a powerful tool for learning the most fundamental ideas and approaches, basic concepts, principles, and methodologies of micromechanics. Readers will find: * Vigorous derivations of the mathematical framework * Introductions to both linear and nonlinear material behavior * Unique coverage of brittle damage, shape memory alloys, and TRIP steels * Large numbers of problems and exercises to support teaching and learning the concepts * Lists of references and suggested readings in each chapter

Engineering Solid Mechanics bridges the gap between elementary approaches to strength of materials and more advanced, specialized versions on the subject. The book provides a basic understanding of the fundamentals of elasticity and plasticity, applies these fundamentals to solve analytically a spectrum of engineering problems, and introduces advanced topics of mechanics of materials - including fracture mechanics, creep, superplasticity, fiber reinforced composites, powder compacts, and porous solids. Text includes: stress and strain, equilibrium, and compatibility elastic stress-strain relations the elastic problem and the stress function approach to solving plane elastic problems applications of the stress function solution in Cartesian and polar coordinates Problems of elastic rods, plates, and shells through formulating a strain compatibility function as well as applying energy methods Elastic and elastic-plastic fracture mechanics Plastic and creep deformation Inelastic deformation and its applications This book presents the material in an instructive manner, suitable for individual self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The authors provide generous explanations, systematic derivations, and detailed discussions, supplemented by a vast variety of problems and solved examples. Primarily written for professionals and students in mechanical engineering, Engineering Solid Mechanics also serves persons in other fields of engineering, such as aerospace, civil, and material engineering.

It covers all the basic topics of mechanics of deformable bodies generally taught in these courses. The text presents the topics in a clear, simple, practical, logical and cogent fashion that provides the students with insights into theory as well as applications to practical problems. It uses an abundance of worked examples to impart a high level of comprehension of concepts and helps master the process of calculations, manipulations and that of making appropriate inferences. Well-labelled diagrams have been used throughout the text for a sound comprehension of the fundamentals of the subject. Most of the examples and chapter-end problems have been formulated in parametric form making them independent of units and suitable for practical applications. An extensive set of problems along with hints and answers is provided at the end of each chapter for practice. Since the book aims at covering the topics generally taught in engineering curriculum of several disciplines, an interdisciplinary approach has been followed. Some advanced topics such as thick pressure vessels, skew bending, curved members, beam-columns, etc. have also been included for the benefit of postgraduate students.

Experimental solid mechanics is the study of materials to determine their physical properties. This study might include performing a stress analysis or measuring the extent of displacement, shape, strain and stress which a material suffers under controlled conditions. In the last few years there have been remarkable developments in experimental techniques that measure shape, displacement and strains and these sorts of experiments are increasingly conducted using computational techniques. Experimental Mechanics of Solids is a comprehensive introduction to the topics, technologies and methods of experimental mechanics of solids. It begins by establishing the fundamentals of continuum mechanics, explaining key areas such as the equations used, stresses and strains, and two and three dimensional problems. Having laid down the foundations of the topic, the book then moves on to look at specific techniques and technologies with emphasis on the most recent developments such as optics and image processing. Most of the current computational methods, as well as practical ones, are included to ensure that the book provides information essential to the reader in practical or research applications. Key features: Presents widely used and accepted methodologies that are based on research and development work of the lead author Systematically works through the topics and theories of experimental mechanics including detailed treatments of the Moire, Speckle and holographic optical methods Includes illustrations and diagrams to illuminate the topic clearly for the reader Provides a comprehensive introduction to the topic, and also acts as a quick reference guide This comprehensive book forms an invaluable resource for graduate students and is also a point of reference for researchers and practitioners in structural and materials engineering.