Computational Continuum Mechanics

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Cambridge University Press, Mar 10, 2008 - Science
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This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.
 

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Contents

Kinematics
51
Forces and Stresses
103
Constitutive Equations
131
Plasticity Formulations
177
LargeDeformation
231
SmallDeformation
286
References
321
Index
327
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Page 3 - The determinant of the product of two matrices is equal to the product of the determinants of the two matrices.
Page 3 - One can show that the determinant of a matrix is equal to the determinant of its transpose, that is.
Page 6 - Therefore, the number of columns in A must be equal to the number of rows in B. If A is an mxn matrix and B is an nxp matrix, then C is an mxp matrix.
Page 2 - Use the last exercise to show that every square matrix can be written as the sum of a symmetric matrix and a skew—symmetric matrix.
Page 2 - ... is said to be square; otherwise the matrix is said to be rectangular or nonsquare.

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