In the article the task of cross bending of elastic isotropic plates with simply supported and clamped edge from the action of evenly distributed load is described. It is suggested to use form factor interpolation technique to determine the value of maximum plate deflection; and the ratio of inner conformal radius to the outer as a geometric argument is proposed to be used instead of form factor. Such replacement allows the increase of the technique accuracy.
The article deals with the transverse bending problem of thin elastic orthotropic plates with combined boundary conditions. The form factor interpolation method is used for deformation calculations. Analytical expressions of maximum deflection surfaces are obtained. It is proposed to use these expressions as the reference solutions. The example of the solution to the problem of transverse bending plate in the form of a parallelogram is given.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.