By Professor Oscar Gonzalez, Professor Andrew M. Stuart

ISBN-10: 0511455135

ISBN-13: 9780511455131

ISBN-10: 0521714249

ISBN-13: 9780521714242

ISBN-10: 0521886805

ISBN-13: 9780521886802

ISBN-10: 1282389947

ISBN-13: 9781282389946

A concise account of vintage theories of fluids and solids, for graduate and complex undergraduate classes in continuum mechanics.

Show description

Read or Download A First Course in Continuum Mechanics PDF

Similar fluid dynamics books

Cavitation in Non-Newtonian Fluids: With Biomedical and by Emil Brujan PDF

Non-Newtonian homes on bubble dynamics and cavitation are essentially various from these of Newtonian fluids. the main major impact arises from the dramatic bring up in viscosity of polymer options in an extensional stream, corresponding to that generated a couple of round bubble in the course of its progress or cave in section.

Read e-book online Transport Phenomena, 2nd Edition PDF

Cautious cognizance is paid to the presentation of the fundamental conception. * improved sections all through textual content offer a lot more impregnable origin than the 1st variation. * Literature citations are given all through for connection with extra fabric

Read e-book online Fox and McDonald’s Introduction to Fluid Mechanics PDF

Fox & McDonald’s advent to Fluid Mechanics ninth version has been essentially the most greatly followed textbooks within the box. This highly-regarded textual content maintains to supply readers with a balanced and entire method of gaining knowledge of severe strategies, incorporating a confirmed problem-solving method that is helping readers enhance an orderly plan to discovering definitely the right answer and touching on effects to anticipated actual habit.

Additional resources for A First Course in Continuum Mechanics

Example text

4. By the change of basis tensor from {ei } to {ei } we mean the tensor A defined by A = Aij ei ⊗ ej where Aij = ei · ej . 11) We could also define a change of basis tensor B from {ei } to {ei } by B = Bij ei ⊗ ej where Bij = ei · ej . All that we say for A will also apply to B. However, for convenience, we work only with A. Using the components of A we can express the basis vectors of one frame in terms of the other. For example, a basis vector ej may be expressed in the frame {ei } as ej = (e1 · ej )e1 + (e2 · ej )e2 + (e3 · ej )e3 = (ei · ej )ei , 20 Tensor Algebra e3 e 3/ e 2/ e2 o v e1 e1/ Fig.

Then there exists a right-handed, orthonormal basis {ei } for V consisting of eigenvectors of S. The corresponding eigenvalues λi are the same (up to ordering) for any such basis and form the full set of eigenvalues of S. The dyadic representation of S in any such basis is 3 λi ei ⊗ ei , S= i=1 and the matrix representation is  λ1  [S] = 0 0 0 λ2 0  0 0 . λ3 The principal invariants of a second-order tensor S are three scalars defined by I1 (S) = tr S, I2 (S) = 1 2 (tr S)2 − tr(S 2 ) , I3 (S) = det S.

7 (a) For arbitrary v we have S(a ⊗ b)v = S(b · v)a = (b · v)Sa = ((Sa) ⊗ b)v, which implies S(a ⊗ b) = (Sa) ⊗ b. (b) For arbitrary v we have (a ⊗ b)Sv = (b · Sv)a = (S T b · v)a = (a ⊗ S T b)v, which implies (a ⊗ b)S = a ⊗ (S T b). Selected Answers 39 (c) For arbitrary u and v we have u · (a ⊗ b)T v = (a ⊗ b)u · v = (b · u)(a · v) = u · (b ⊗ a)v, which implies (a ⊗ b)T = (b ⊗ a). 9 (a) P T = P and P P = P , thus perpendicular projection. (b) P T = P , thus not perpendicular projection. (c) Perpendicular projection.

Download PDF sample

A First Course in Continuum Mechanics by Professor Oscar Gonzalez, Professor Andrew M. Stuart


by Ronald
4.1

Rated 4.92 of 5 – based on 43 votes