Solution of boundary value problems of the theory of layered orthotropic plates using spline-functions (Q2754751)

A rectangular layered plate consists of orthotropic layers of variable in two directions thickness. There are no sliding between layers and separation of them. Bending of the plate is described by a fourth-order partial differential equation with variable coefficients calculated through mechanical characteristics of the layers. Solution of the problem is sought in the form \(w(x,y) = \sum_{i=0}^N w_i(x)\psi_i(y)\), where \(w_i(x)\) are unknown functions and \(\psi_i(y)\) \((N>6)\) are functions constructed using \(B\)-splines of the fifth degree and satisfying boundary conditions at the plate sides \(y=0\) and \(y=b\). After application of the spline collocation technique, a system of \((N+1)\) ordinary differential equations is derived. This system is reduced to normal form and is solved by a stable method of discrete orthogonalization. A numerical example for a three-layered clamped plate is considered.