Boundary Value Problem Of Plate Research Articles

Dirac method for nonlinear and non-homogenous boundary value problems of plates

Dirac method for nonlinear and non-homogenous boundary value problems of plates

An analytical method for nonlinear and nonhomogeneous boundary value problems of plates

An analytical method for nonlinear and nonhomogeneous boundary value problems of plates

Solution of boundary-value problems of plates by the Vekua method for approximations N = 1 and N = 2

In this paper, the problem of bending for an isotropic plate with constant thickness 2h is considered. Problems of bending for infinite plates with a circular hole in which a rigid body is placed in the cases of approximations N = 1 and N = 2 of the Vekua theory are solved. We consider the case where the body is soldered. Problems of bending of circular rings are also solved. The results obtained are compared to the corresponding results obtained by plane classical bending theory.

An analytic method of studying the nonlinearly elastic equilibrium of a rectangular plate of variable thickness under bending

We propose an approximate analytic method of solving three-dimensional boundary-value problems of the physically nonlinear theory of elasticity for thick rectangular plates of variable thickness subject to a transverse load. The method is used to seek a solution of this problem in the form of double power series in small dimensionless parameters. In arbitrary approximation the original problem is reduced to a sequence of linear inhomogeneous boundary-value problems for plates of constant thickness.

Wave solutions of equations of Timoshenko type for the transverse vibrations of plates with parameters periodic on one coordinate

The hyperbolic system of equations that describes the vibrations of plates inhomogeneous along one rectangular coordinate in the context of the Timoshenko theory is presented in canonical hamiltonian form, assuming the solution is periodic on a second coordinate. In the case of periodic inhomogeneity we study the structure of the solutions of certain wave boundary-value problems for plates of this type using the general properties of periodic hamiltonian systems. Bibliography: 6 titles.

Weak solutions of interior boundary-value problems for plates with transverse shear deformation

The existence, uniqueness, and continuous dependence on the data are investigated for the solutions of the equations of bending of plates with transverse shear deformation in a Sobolev space setting.

APPLICATION OF NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS TO BOUNDARY VALUE PROBLEMS OF PLATES AND SHELLS

APPLICATION OF NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS TO BOUNDARY VALUE PROBLEMS OF PLATES AND SHELLS

The equivalence between the wave propagation method and Bolotin's method in the asymptotic estimation of eigenfrequencies of a rectangular plate

The Kirchhoff thin plate equation is an important mathematical model in structural dynamics. Because this partial differential equation has order four, analysis of vibration eigenfrequencies is much more complicated than that of a vibrating membrane, whose governing PDE has order two. As a matter of fact, for the simplest rectangular geometry the plate boundary value problems do not even allow the separation of the two space variables, thus one must resort to alternative approaches. Bolotin's method, published in 1961, offers such an asymptotic alternative. More recently, the three authors generalized Keller-Rubinow's wave method to the thin plate equation, constituting a different approach. In this paper, we establish that for various combinations of boundary conditions (clamped, hinged, roller-supported and free), after some conversion the wave method and Bolotin's method yield an identical set of transcendental equations for asymptotic values of the eigenfrequencies of a rectangular plate, thus confirming the equivalence of these two methods.

Mixed Boundary Value Problem of Plate with Crack

A semi‐infinite plate, of which a part on the boundary is rigidly stiffened and in which a crack initiates from an end of the stiffened edge as a problem of a mixed boundary value of thin plate bending, is analyzed. The problem is solved by a complex variable method which uses a rational mapping function. Two analytical methods are described: one method can apply to general loads and the other can apply when the free boundary, even partially, exists. These methods give a solution in a closed form for a shape represented by the rational mapping function. Uniform bending and torsion are considered as loads. Bending moment distributions before and after crack initiation, and the stress intensity factor are investigated for crack length, stiffened edge length, and the Poisson's ratio.

Elastic-plastic finite element analysis of plates

A general finite element displacement analysis capable of determining the complete elastic-plastic behavior of complex shaped, transversely loaded plates is presented. The approach is formulated in incremental form and is based on the tangent stiffness concept. A layered plate model is adopted to aid in the description of the elastic-plastic behavior of the plate, since the process of plastification in a plate is difficult to describe mathematically. The method is developed for an elastic, linearly-strain hardening material; but could easily be extended to treat a more general material behavior. A few example solutions are given, demonstrating the validity of the proposed numerical technique from which valuable solutions to complex elastic-plastic plate boundary value problems can be obtained.