Elasticity with Mathematica an Introduction to Continum Mechanics and Linear Elasticity

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This book is intended for researchers, engineers and students in solid mechanics, materials science and physics who are interested in using the power of modern computing to solve a wide variety of problems of both practical and fundamental significance in elasticity. Extensive use of Mathematica in the book makes available to the reader a range of recipes that can be readily adjusted to match particular tastes or requirements, to visualize solutions, and to carry out symbolic and numerical analysis and optimization.

Fundamentals of Continuum Mechanics

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This textbook offers a concise yet rigorous treatment of continuum mechanics at the introductory level. It differs from traditional textbooks by combining tensor analysis with mechanical analysis and teaching the former's basics within a single chapter. Readers of this book are not required to have learned tensor analysis in the context of engineering mathematics beforehand. The basic objectives of continuum mechanics are included in this textbook to facilitate an easy and thorough understanding of the concepts of continuum mechanics and elasticity. In addition, the mathematics and physics of deformation and kinematics are introduced and studied from the concept of stretch rather than from the traditional approach of strain. The large deformation problem of new smart soft materials is also introduced. This textbook provides illustrative examples and problem sets that enable readers to test their understanding of the subject matter and utilize the tools developed in the formulation of engineering problems. It is suitable for students whose undergraduate disciplines are non-mechanics-related fields. It also helps students or engineers who use the finite element method (FEM) to analyze problems to interpret the results produced by FEM software. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction Mathematical Fundamentals: Vectors and Tensors Kinematics of a Continuum Stress Measures The Fundamental Laws of Continuum Mechanics The Constitutive Equations of Continuum Constitutive Models of Soft Materials: Hydrogels and Shape Memory Polymers Applications of Continuum Mechanics Readership: Undergraduate and postgraduate students, and professional engineers interested in learning about continuum mechanics, particularly those from non-mechanics-related disciplines.

MATERIAL GEOMETRY: GROUPOIDS IN CONTINUUM MECHANICS

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This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials. The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline. Sample Chapter(s) Preface Chapter 2: Continuum Mechanics: Elastic Simple Bodies Contents: Preface About the Authors Introduction Fundamentals: Continuum Mechanics: Elastic Simple Bodies Groupoids Algebroids Material Groupoid: Material Algebroid Characteristic Distributions and Material Bodies Appendices: Foliations and Distributions Covariant Derivatives Principal Bundles and Connections Bibliography Index Readership: Graduate and postgraduate students interested in Continuum Mechanics, Mathematical Physics and Differential Geometry. Researchers in Elasticity, Applied Mathematics and Differential Geometry. And those taking a master or doctorate course that seeks the interaction between mathematics and mechanical engineering.