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Author : Simon Raphael Eugster
Publisher :
Page : pages
File Size : 46,10 MB
Release : 2014
Category :
ISBN :
Author : C. S. Jog
Publisher : Morgan & Claypool
Page : 0 pages
File Size : 25,53 MB
Release : 2007
Category : Continuum (Mathematics)
ISBN : 9781842654422
After providing the necessary mathematical background needed, the book discusses kinematics, balance laws and constitutive relations for simple materials. Major emphasis is placed on discussing relatively new ideas such as material frame-indifference, the implications of the second law of themodynamics, material symmetry etc. The text shows how under suitable assumptions the classical theories of fluid mechanics, solid mechanics (including the linear theory of elasticity), and rigid-body dynamics follow from the general continuum equations. This book is intended as an advanced undergraduate (or a graduate level) textbook in continuum mechanics and its applications. NEW TO THE SECOND EDITION: A number of new topics have been discussed, some of which are: * Higher-order (in particular, fourth-order) tensors * Differentiation of tensors * Exact solutions to problems in nonlinear linearized elasticity * Components of tensors and their derivatives with respect to curvilinear coordinates * Conversion of tensorial expressions to engineering form
Author : Simon R. Eugster
Publisher : Springer
Page : 146 pages
File Size : 23,32 MB
Release : 2015-03-19
Category : Science
ISBN : 3319164953
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Author : Fridtjov Irgens
Publisher : Springer Science & Business Media
Page : 667 pages
File Size : 20,37 MB
Release : 2008-01-10
Category : Science
ISBN : 3540742980
This book presents an introduction into the entire science of Continuum Mechanics in three parts. The presentation is modern and comprehensive. Its introduction into tensors is very gentle. The book contains many examples and exercises, and is intended for scientists, practitioners and students of mechanics.
Author : Rabindranath Chatterjee
Publisher : Alpha Science Int'l Ltd.
Page : 294 pages
File Size : 21,42 MB
Release : 1999
Category : Mathematics
ISBN : 9788173192449
This text provides an introduction to the theory of continuum mechanics in a logically satisfying form. A simple knowledge of Cartesian tensors is a sufficient prerequisite for this book. The book deals with two major branches of continuum mechanics - the mechanics of elastic solids and the mechanics of fluids providing the basis of civil and mechanical engineering, applied mathematics and physics. Traditional courses in solid mechanics and fluid mechanics are usually taught separately with emphasis on physical behaviour at the cost of rigorous mathematical foundation neglecting the analogies between solids and fluids. The book brings two disciplines under one roof seeking to generalize and unify specialized topics.
Author : C. S. Jog
Publisher : Cambridge University Press
Page : 878 pages
File Size : 15,65 MB
Release : 2015-06-25
Category : Science
ISBN : 1316528383
Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.
Author : Attila Askar
Publisher : World Scientific
Page : 208 pages
File Size : 14,76 MB
Release : 1986-07-01
Category :
ISBN : 9814518956
This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.
Author : Peter Chadwick
Publisher : Courier Corporation
Page : 200 pages
File Size : 18,38 MB
Release : 1999-01-01
Category : Science
ISBN : 9780486401805
Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, efficient notation that fosters quick comprehension and renders these concepts familiar when they reappear in other contexts. Completion of this brief course results in a unified basis for work in fluid dynamics and the mechanics of solid materials, a foundation of particular value to students of mathematics and physics, those studying continuum mechanics at an intermediate or advanced level, and postgraduate students in the applied sciences. "Should be excellent in its intended function as a problem book to accompany a lecture course." — Quarterly of Applied Math.
Author : Esmaeal Ghavanloo
Publisher : Springer Nature
Page : 463 pages
File Size : 25,20 MB
Release : 2021-04-02
Category : Science
ISBN : 3030630501
This book offers a comprehensive and timely report of size-dependent continuum mechanics approaches. Written by scientists with worldwide reputation and established expertise, it covers the most recent findings, advanced theoretical developments and computational techniques, as well as a range of applications, in the field of nonlocal continuum mechanics. Chapters are concerned with lattice-based nonlocal models, Eringen’s nonlocal models, gradient theories of elasticity, strain- and stress-driven nonlocal models, and peridynamic theory, among other topics. This book provides researchers and practitioners with extensive and specialized information on cutting-edge theories and methods, innovative solutions to current problems and a timely insight into the behavior of some advanced materials and structures. It also offers a useful reference guide to senior undergraduate and graduate students in mechanical engineering, materials science, and applied physics.
Author : Victor Berdichevsky
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 41,21 MB
Release : 2009-09-18
Category : Science
ISBN : 3540884696
The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.