The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details

This paper aims to present the details of mathematical derivation for static bending problem of isotropic sectorial plates that involve stress singularities at the vertex of the plates due to geometry and boundary conditions. Following the classical Kirchhoff's plate theory, the general complete solution of 4 th -order partial differential equation governing the plate-bending behaviors can be determined mathematically and expressed explicitly in the form of infinite series through the separation of variables method in terms of polar coordinates. Based on the principle of superposition the solution can be separated into two parts; namely, the particular solution and complementary solution in which the latter describes the local singular behaviors at its sharp vertex exactly. Some cases of circular, annular and sectorial plates with mixed circumferential edge conditions that remain undetermined analytically up to the present time are also suggested.Mathematics Subject Classification: 31A25, 74K20, 35Q74

This paper studies the behavior of uniformly loaded rectangular thin plates with a partial internal line support. The highlight of the problem is that the analytical formulation explicitly considers the moment singularities that occur at the tips of partial internal line supports. The proper finite Hankel transform is used to transform a pair of dual-series equations obtained from the mixed conditions along the partial internal line support to a single Fredholm integral equation. Numerical results concerning deflection, bending moment, resultant forces, and bending-stress intensity factors are given for a square plate. Some results are also compared with the case of a square plate without partial internal line support.

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.