Transcription of CVEN 5161 Advanced Mechanics of Materials I
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CVEN 5161 Advanced Mechanics of Materials I
CVEN 5161. Advanced Mechanics of Materials I. Instructor: Kaspar J. Willam Revised Version of Class Notes Fall 2003. Chapter 1. Preliminaries The mathematical tools behind stress and strain are housed in Linear Algebra and Vec- tor and Tensor Analysis in particular. For this reason let us revisit established concepts which hopefully provide additional insight into matrix analysis beyond the mere Mechanics of elementary matrix manipulation. Vector and Tensor Analysis (a) Cartesian Description of Vectors: Forces, displacements, velocities and accelerations are objects F , u, v, a <3 which may be represented in terms of a set of base vectors and their components. In the following we resort to cartesian coordinates in which the base vectors ei form an or- thonormal set which satisfies . 1 0 0. ei ej = ij i, j = 1, 2, 3 where [ ij ] = 1 = 0 1 0 ( ).
Chapter 1 Preliminaries The mathematical tools behind stress and strain are housed in Linear Algebra and Vec-tor and Tensor Analysis in particular.
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