Dual-series equations formulation for static deformation of plates with a partial internal line support

Abstract

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

Dual series method for solving Helmholtz equation with mixed boundary conditions of the third kind

“…Much attention was received to investigate mixed problems with partly infinite boundaries can often be reduced to study dual integral equations [1][2][3][4][5][6],while for the finite regions the problems can often reduce to study dual series equations. Dual series equations related to Laplace equation in cylindrical, spherical and other coordinates involving potential theory, diffraction theory, elasticity theory and other applications can be found in [10][11][12] and other monographs. In this paper, we treated the dual series equations by defining Hankel integral transform of a function related to the unknown function satisfying the dual series equations, and then the inverse transformation produces ultimately the function sought for.…”

“…In this paper, we treated the dual series equations by defining Hankel integral transform of a function related to the unknown function satisfying the dual series equations, and then the inverse transformation produces ultimately the function sought for. In [9][10][11] Hankel integral transform method is used for investigation solutions for dual integral equations involving a Bessel function of the first kind of order zero as a kernel. The analysis of the dual series equations led to a Fredholm integral equation of the second kind which is solved numerically.…”

“…k  and some of the coefficients ,b ii a is zero, the dual equations (5) and (6) reduced to known solutions [10], [11]. Now to solve (5) and (6), let us to introduce the substitution…”

Numerical solution of the problems for plates on some complex partial internal supports

“…To the best of our knowledge a rigorous justification of DSC has not been established yet. Later, in 2007Later, in , 2008 Sompornjaroensuk and Kiattikomol [11,12] transformed the problem with one LPIS to dual series equations, which then by the Hankel transformation are reduced to the form of a Fredholm integral equation. It should be noted that the kernel and the right-hand side of the equation are represented in a series containing Hankel functions of both first and second kinds; therefore, the numerical treatment for this integral equation is very difficult.…”

Regularization method for solving dual series equations involving heat equation with mixed boundary conditions

“…Because of the application of the mixed equations in physical problems, which are based on the time independent and Helmholtz equation, several articles have been studied the solution of mixed problem which has a dual equations [9,6,4,3,5,8,7], [16], [15]. For instance, in this article, we consider a mixed problem of solid cylindrical with an infinite height and given radius R. In particular, inside the disk 0 < r < r 0 , the boundary conditions on the surface of cylindrical and outside the disk r 0 < r < R are given, and of first kind and second kind respectively, or vis versa.…”