An equilibrium problem for a~Timoshenko plate with a~through crack

N. P. Lazarev

Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 32-43

Résumé

We study the equilibrium problem for an elastic plate (Timoshenko model) with a vertical crack. On the curve defining the through crack we impose a boundary condition as an inequality describing the nonpenetration of the opposite crack edges. We prove the unique solvability of the variational statement of the problem. From the variational statement we deduce a complete system of boundary conditions, which we use to obtain an equivalent differential statement. We establish additional smoothness of the solution in comparison with that given in the variational statement. We prove that the solution functions are infinitely smooth under additional assumptions on the function of external loads and the functions of displacements near the curve describing the through crack.