Reciprocal Method of Work for Solving the Bending of Rectangular Thin Plate on Elastic Foundation under the Combined Action of Lateral Loads and Forces in Middle Plane of the Plate

The reciprocal method of work is used to solve the bending problems of thin plate on elastic foundation under the combined action of lateral loads and forces in middle plane of the plate. The basic system is a simply supported thin plate on elastic foundation under combined action of lateral loads and forces in the middle plane of the plate. Two expressions of the deflection surface equation of the basic system are derived, the first is the double trigonometric function, and the second is the mixture of hyperbolic function and trigonometric function. The practical systems consist of thin plates on elastic foundation constrained by different boundary conditions. The deflection surface equation of the practical system is solved by using the reciprocal method of work between the practical system and the basic system. Compared with the finite element method with ANSYS software, the solution error is less than 5%, which satisfies the requirement of maximum error. This indicates that application of the reciprocal method of work is correct for solving the problem.