Igor Chudinovich

THE CAUCHY PROBLEM IN THE THEORY OF PLATES WITH TRANSVERSE SHEAR DEFORMATION

The Cauchy problem for an infinite plate with transverse shear deformation is studied by means of an area potential and some special initial potentials. This is a fundamental step in the construction of the potential theory for dynamic problems for plates, since such results make it possible to reduce various initial-boundary value problems for the equations of motion to analogous ones for the homogeneous system, which can then be solved by means of retarded potentials.

Boundary Integral Equations in Dynamic Problems for Elastic Plates

Initial-boundary value problems with Dirichlet and Neumann conditions arising in the theory of bending of plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of layer potentials. The solvability of these equations is then investigated in Sobolev-type spaces.

Potential Representations of Solutions for Dynamic Bending of Elastic Plates Weakened by Cracks

The existence of distributional solutions is investigated for the boundary integral equations associated with the motion of a thin elastic plate weakened by a crack.

The Solvability of boundary integral equations for the Dirichlet and Neumann problems in the theory of thin elastic plates

The existence, uniqueness, and continuous dependence on the data are investigated for the weak solutions of boundary integral equations arising in the interior and exterior Dirichlet and Neumann problems for plates with transverse shear deformation treated by means of potential methods.

Existence and uniqueness of weak solutions for a thin plate with elastic boundary conditions

Abstract Robin-type problems are studied for thin elastic plates with transverse shear deformation. These problems are reduced to analogous ones for the corresponding homogeneous equilibrium equation, whose solutions are then represented as single and double layer potentials. The unique solvability of the systems of boundary integral equations yielded by this procedure is discussed in Sobolev spaces.

Existence and integral representations of weak solutions for elastic plates with cracks

The existence and continuous dependence on the data are investigated in Sobolev spaces for the problem of bending of a Reissner-Mindlin-type plate weakened by a crack when the displacements or the moments and force are prescribed along the two sides of the crack. The cases of both an infinite and a finite plate are considered, and representations are sought for the solutions in terms of single layer and double layer potentials with distributional densities.

Non-stationary integral equations for elastic plates

Abstract The weak solvability is discussed of dynamic problems with Dirichlet and Neumann data in the theory of bending of elasticplates with transverse shear deformation. The problems are thenreduced to boundary integral equations, which are solved in spacesof distributions.

Solution of Bending of Elastic Plates by means of Area Potentials

The solvability of the mathematical problem of bending of at elastic plate with transverse shear deformation is discussed in Sobolev spaces, and a representation of the solution is constructed in terrns of an area potential. This potential is then used to reduce the interior and exterior Dirichlet and Neumann problems for plates to analogous boundary value problems for the homogeneous equilibrium equation.

Transmission Problems for Thermoelastic Plates with Transverse Shear Deformation

An initial-boundary value problem for bending of a piecewise homogeneous thermoelastic plate with transverse shear deformation is studied, and its unique solvability in spaces of distributions is proved by means of a combination of the Laplace transformation and variational methods.

The direct method in time-dependent bending of thermoelastic plates

The initial-boundary value problems with Dirichlet and Neumann boundary conditions arising in the theory of bending of thermoelastic plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of the Somigliana representation formulas. The solvability of these equations is then investigated in Sobolev-type spaces.