By Fridtjov Irgens
This publication offers an creation into the total technological know-how of Continuum Mechanics in 3 elements. The presentation is smooth and entire. Its creation into tensors is particularly light. The e-book includes many examples and routines, and is meant for scientists, practitioners and scholars of mechanics.
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Additional resources for Continuum Mechanics
However, in some derivations it is advantageous to distinguish between Tik and Tki . According to Cauchy’s lemma the stress vectors are equal to −ti on the sides of a coordinate surfaces for which the normals are −ei . We may also let the coordinate stresses Tik represent the components of these stress vectors, see Fig. 5. Then we have the following sign rule for coordinate stresses. A positive coordinate stress acts in direction of a positive coordinate axis on that side of a material coordinate surface facing the positive direction of a coordinate axis.
16) [abc] = ei jk ai b j ck = det ⎝ b1 b2 b3 ⎠ c1 c2 c3 The base vectors are related according to: [e1 e2 e3 ] = 1, [e3 e2 e1 ] = −1 etc. 17) This relation may be taken to define an orthogonal right-handed system of unit vectors. 3 Coordinate Transformations Vectors and tensors, which will be defined in Chap. 4, are coordinate invariant quantities, which in any coordinate system we have chosen are represented by their components. It is important to determine the relations between sets of components relative to different coordinate systems.
In special situations it becomes necessary to add to the two types of forces introduced above, body couples, given as couple per unit mass, and surface couples or couple stresses on the surface of the body, given as couple per unit area. Body couples are for instance present as a result of an elastic strain wave passing through a body exposed to an electromagnetic field. Another example of the presence of body couples is given by the effect of the magnetic field of the earth on the needle of a compass.
Continuum Mechanics by Fridtjov Irgens