Thin-plate stress analysis solved by combining FEM functions and approximations of class C⁰

Abstract

The method for constructing functions with finite support is used, which combines the properties of FEM functions and approximations in the form of series with unknown coefficients. To illustrate the properties of the approximating function constructed, we present the results of the solution of the 2D theory of elasticity for a thin plate, shown on figure 1,b. The thickness of the plate is h. One facet of the plate (at x = −a) is fixed and the other one (at x = − a) unfixed; the remaining two are under shear stresses τ and an evenly distributed load θ. The solution of the problem of determining the stress and strain in the plate can be obtained from the steady-state condition of the Lagrange functional by using the functions of class C0 of the high-degree approximation for scientific calculations. The calculations show that the obtained solution has high accuracy, even in cases when the length of the rectangular domain is considerably greater than its width.