Potential. Solution of Poisson's Equation, Equations of Continuity and Elasticity

Details Potential. Solution of Poisson's Equation, Equations of Continuity and Elasticity Potential. Solution of Poisson's Equation, Equations of Continuity and Elasticity

2010-11-22

arxiv.org/abs/1011.4723v1

Physics

General Physics

24 pages

Scientific paper

The modern theory of the potential does not give a solution of Poisson's equation. In the present work its solution has been found via generalized functions and a nonpotential solution of the continuity equation has been obtained. The method is demonstrated by the solution of elasticity equations using the example of a crack in the infinite specimen and a surface crack. Their elastic energies have been calculated. In has been shown that there is no critical condition for a crack in the infinite specimen and the crack always closes. Only the surface crack possesses the critical condition.

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