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.

Studying Dynamics of a Cantilever Bar With Variable Bending Stiffness

“…When writing equation ( 2), the deflections of the contour nodes of the "linear"grid will also be "captured nodes (3,4,6); their values will be excluded from the boundary conditions at the ends of the bar (at nodes 5, 2):…”

“…Works [4,5] study the bending of elastic isotropic isosceles triangular plates with the following boundary conditions: hinged or rigid edges; they were calculated using the finite element method with the use of approximating functions. As an example, a calculation is given for the bending of a plate in the form of a right-angled triangle with hinged support along the contour.…”

Physical and Mechanical State of Cantilever Triangular Plates

“…In [4,5], the bending of elastic isotropic plates in the form of isosceles triangles with different boundary conditions (hinged or rigid edges) is considered. For their calculation, the finite element method with the construction of approximating functions was used, and an example was also given for calculating the bending of a plate in the form of a right-angled triangle with hinged support along the contour.…”

“…In [7][8][9][10], a method of interpolation by the shape coefficient based on affine transformations was proposed for calculating triangular plates with a hinged or rigid support along their perimeter, a bending stress-strain state is considered, including with free vibrations. The plate material can be either isotropic or orthotropic.…”