We consider feasibility of the form factor interpolation method to solve problems of structural mechanics of plates connected with a triangular domain: to determine maximum deflection in transverse bending of plates by an uniformly distributed load, basic frequency of free oscillations, critical force under stability loss of plates in the case of their overall uniform compression. The boundary conditions of plates are homogeneous (either pivoting or rigid constraint). As geometric transformations that unite different subsets of triangles we use affinities of isosceles triangles. On the basis of isoperimetric properties of the form-factor of triangles we formulate isoperimetric theorems with respect to integral characteristics of triangular plates. We describe examples of constructing approximating functions for a limited subset of triangular plates.
展开▼
