The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably sim...The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.展开更多
By using complex variable methods, the boundary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticit...By using complex variable methods, the boundary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticity which, as well-known, may be easily solved by reduction to a Fredholm integral equation. The case of circular plate is illustrated in detail, the solution of which is obtained in closed form.展开更多
The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with ...The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with some symmetry and the same uniform pressures are applied to both of its sides. The problem is reduced to a uniquely solvable singular integral equation on the interface and the crack. The order of singularity at the vertex is considered, which may be determined by a transcendental equation.展开更多
文摘The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.
文摘By using complex variable methods, the boundary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticity which, as well-known, may be easily solved by reduction to a Fredholm integral equation. The case of circular plate is illustrated in detail, the solution of which is obtained in closed form.
文摘The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with some symmetry and the same uniform pressures are applied to both of its sides. The problem is reduced to a uniquely solvable singular integral equation on the interface and the crack. The order of singularity at the vertex is considered, which may be determined by a transcendental equation.
