Energy Method of Static Analysis of Stiffened Plates on Elastic Foundation

Abstract

This paper is devoted to derive the calculating formula of the deformation and the internal force of stiffened plate on elastic foundation, which is beneficial for the engineering design. Nowadays, we generally use the finite element method to solve the deformations and internal forces of stiffened plates on elastic foundation under loads, which the calculate setting is complex and the amount of calculation is large. In this paper the calculating deformation formula of this construction on elastic foundation under loads is derived by means of energy method. Calculating the potential energy of the foundation plate, that of the foundation beams, that of the loads on the stiffened plate and that of the foundation reactions forces, separately, and substituting them into the minimum condition of total potential energy while the structure is equilibrium, the calculating deformation formulas of this construction is obtained. The internal forces of foundation plate can be obtained according to formulas of mechanics of elasticity. The internal forces of foundation beams can be obtained according to the differential relationships among the deformation, bending moment and shearing force of the beam. Using the formulas in this paper, the deformations and the internal forces of stiffened plate on elastic foundation can be calculated out easily. Comparing with the finite element method, the amount of computation can be reduced greatly by using these formulas in this paper.