The Bending Plates On Elastic Foundation With Different Boundary Conditions Under The Concentrated Load

With the continuous development of society, public transportation, high-rise civil buildings and industrial buildings have been developed rapidly. Making the plate on elastic foundation is more and more widely application. It can be used such as road pavement, airstrip, foundation of the large structures and slipway projects. The bending problem of plates on elastic foundation has been one of the classic academic research topics in engineering field. Due to the complexity of it, it’s still difficult to find simple enough means to get an accurate analytical solution which not only meet the equilibrium differential equation but also meet the boundary conditions. Therefore, finding a new and system method to solve the bending problem of plates on elastic foundation is quite necessary.This paper applies reciprocal method to derived the deflection curve equation of four edges fixed, fixed on one opposite sides and the others are simply supported, fixed on one opposite sides and the others are free, fixed on one opposite sides and simply supported on one side and the other is free, two adjacent edges simple supported and the other two adjacent edges are free and angular point supported, two adjacent edges fixed and the other two adjacent edges are free and angular point supported rectangular thin plates on elastic foundation under a concentrated load. Using MATLAB programming solves numerical solution with various boundary conditions, and compares it with the ANSYS finite element simulation values. From the comparison of the results it can be seen that the accuracy of applying reciprocal method to solve the bending problems of thin plates on elastic foundation. This method is applied to analyze of practical engineering, which is simplified as two adjacent edges fixed and the other adjacent edges are free thin plate on elastic foundation. The result provides the guarantee for the engineering.