New PDF release: Computer Methods for Mathematical Computations

By George Elmer Forsythe, Michael A. Malcolm, Cleve B. Moler

ISBN-10: 0131653326

ISBN-13: 9780131653320

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Extra info for Computer Methods for Mathematical Computations (Prentice-Hall series in automatic computation)

Example text

4) contain six unknown components of the state of stress. The compatibility equations should be completed by the equilibrium equations Then the number of equations is equal to the number of the unknowns. Let us consider two particular cases. 7) then the equilibrium equations and Eq. 8) Let us consider some particular cases. e. the Macdonald function. 7). 8) we obtain the following particular integrals:. 11) 54 This case can be interpreted as the action of a temperature nucleus at the origin. Observe that in this case the couple stresses #-113, #-131, #-123' #-132 vanish.

In section 2 a few sources of self-stresses will be considered. e. in those materials which consist of particles of one kind only. We shall think of atoms, but they could be molecules just as well. The materials of this kind correspond to the materially uniform bodies of the mathematical theory of elasticity. 23 Generally speaking, the sources of self-stresses are defects in an other-wise regular structure of which the crystal is the best-understood example. The lattice defects have been the object of scientific research for decades and have been found to be responsible for a huge variety of properties of such bodies to which among others all metals belong.

They, too, will be excluded from the notion of self-stresses employed here although the methods to be discussed will suit well to many problems involving such stresses. In section 2 a few sources of self-stresses will be considered. e. in those materials which consist of particles of one kind only. We shall think of atoms, but they could be molecules just as well. The materials of this kind correspond to the materially uniform bodies of the mathematical theory of elasticity. 23 Generally speaking, the sources of self-stresses are defects in an other-wise regular structure of which the crystal is the best-understood example.

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Computer Methods for Mathematical Computations (Prentice-Hall series in automatic computation) by George Elmer Forsythe, Michael A. Malcolm, Cleve B. Moler


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