Discrete-Continual Method On The Basis Of B-Splines For Solving The Problem Of Plate Bending
The well-known problem of bending a thin isotropic plate under static load is considered. To solve this problem, one of the possible wavelet-implementations of the discrete-continuum finite element method based on the use of B-splines is used. It should be mentioned, in particular, that the target of research is plates with constant physical and geometrical parameters along one direction (so-called “basic direction”). The article presents a continuous formulation of the corresponding problem with the main direction highlighted - we have a differential equation with operator coefficients with corresponding boundary conditions. Further, some issues related to the construction of normalized basis functions of a B-spline are considered, a discrete-continual formulation of the problem is presented (formed with the use of the technique of finite element approximation). Resultant system of ordinary differential equations with constant coefficients is given. The final part of the article describes an example of the numerical implementation of the proposed approach, as well as an example of analysis (numerical example).