Bending analysis of secured rectangular panels with one free edge

Abstract

A computational model of the flat walls of various tanks, retaining walls, deck and structural ceilings with one free edge is presented as a rectangular plate, three edges of which are secured, and the fourth free (Fig. 1). The transverse load on the elements is frequently uniform or hydrostatic (in the latter case, it can be represented as the sum of a uniform load and inversely symmetric load). This problem has been examined in [1, 2], and its has no exact solution in closed form. Timoshenko [1] reduces the solution to an infinite system of algebraic equations in terms of the unknown coefficients of trigonometric series with respect to two coordinates. Smotrov [2] used the finite-difference method. Numerical results presented in [1] were obtained for the most part by this approximate method. The purpose of this paper is to acquire more reliable numerical results for the bending analysis of the indicated components of water-development works. The method of superposition of correcting functions will be used to solve the problem in question [3]. The transverse load q is assumed constant. The problem is resolved in dimenionless quantities. The deflection function sought should satisfy the differential bending equation