Application Of Generalized Displacement Principle To Solve The Bending Problem Of Rectangular Plates With Large Deflection

Entering the 21 st century,the whole fields have been developed rapidly.Time in aerospace engineering,port navigation engineering and modern architecture is used widely,such as the large deformation of plate and shell structure is applied to large span,or large span project.So the large deflection thin plate structure has important application value in in modern engineering,scientific research value in science and technology category.Due to the plate and shell structure's large deformation in the out-of-plane,and the solution of large deflection in thin plate bending more than the traditional method with higher order nonlinear differential equation.Thus,many problems have been brought to the structural design of Engineers.Thus this paper presents a new method to calculate the deformation of large deflection rectangular thin plate accurately and conveniently.The research based on a thin rectangular plate with small deflection,considering the impact of surface stress and deflection deformation of thin rectangular plate with large deflection,the basic differential equations,equilibrium equations and compatibility equations are deduced.This paper gives the basic solution of the rectangular plate as the basic system,using correct reciprocal method in actual system of generalized supported edge and quasi basic power system,generalized displacement solution is derived for the bending of rectangular plates.Combining with the coordinate equation,the deflection surface equation of a rectangular thin plate with one edges fixed and three edges simply supported,and three edges simply supported and side free deflection are deduced under uniform load.Application MATLAB platform to get the numerical solution of rectangular plate,and comparison with the ANSYS finite element simulation analysis results,proved that the modified work reciprocal method is feasibility to solve the bending problem of rectangular thin plates with large deflection under uniform distributed load,and the correctness of the deflection surface equation in this paper.As an application,one fixed side and three edges with simply supported reinforced concrete rectangular plate is analyzed.The results show that the method of reciprocal work not only has the value of scientific research theory,but also has certain engineering application value.Enrich the reciprocal method function,improve the reciprocal theory system,which provides a new method for solving the large deformation problem of rectangular plate,ease the engineering design limited of only rely on finite element simulation and analysis.