2010/11/22 by Alexander Ivanchin, Ivanchin, Alexander
Engineering · Physics and Astronomy · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Physical sciences #General Physics (physics.gen-ph) #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1011.4723
24 pages
arxiv created 2010/11/22 · openalex publication_date 2010/11/22 · arxiv updated 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.