Transverse bending and free vibrations of elastic isotropic plates in the form of isosceles triangles

Abstract

This paper considers elastic isotropic plates in the form of isosceles triangles with combined boundary conditions (a combination of hinged support and rigid restraint conditions along the sides of the contour). Calculations were performed using FEM to determine the integral physical characteristics in the considered problems F (the maximum deflection of uniformly loaded plates w0 and the fundamental frequency of oscillations in the unloaded state ω). On the basis of the obtained numerical results, approximating functions have been constructed: "maximum deflection - form factor of plates", "basic frequency of oscillations - form factor of plates", the structure of which corresponds to the structure of similar formulas obtained when presenting known exact solutions in the corresponding problems of technical theory of plates in isoperimetric form. Based on the properties of the form factor of plates, these approximating functions limit the whole set of considered integral physical quantities and therefore can be used as reference solutions for the calculation of triangular plates of arbitrary form applying the method of interpolation by form factor (MIFF). We consider an example of calculation of a plate in the form of a rectangular triangle with hinged support of the sides.