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

Alexander Ivanchin

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arXiv · 1011.4723

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

Alexander Ivanchin

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Abstract

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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Alexander Ivanchin. 2010-11-22. Potential. Solution of Poisson's Equation, Equations of Continuity and Elasticity. https://arxiv.org/abs/1011.4723

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