Partition Variational Principle And Its Application For Elastic-Plastic Bending Rectangular Plates And Circular Shaft Torsion

With the continuous development of social economy,the scale of China ’s construction industry and building science and technology are also gradually rising.In architectural design,it is not only required to meet the aesthetics of the building,but also to consider the unity of structural safety,economy and practicality.As common structural components in the construction industry and other fields,plates and shafts will undergo certain deformation under load.According to the characteristics of deformation,they are divided into linear elastic deformation and nonlinear plastic deformation.In real life,the linear relationship is often considered,and the deformation of the nonlinear relationship is neglected,which makes the calculation often fail to meet the accuracy requirements.Therefore,the research on the elastic-plastic deformation of plates and circular shafts is particularly important and has certain theoretical significance and application value.In this paper,based on the basic principle of rectangular plate,the Euler equation and partition criterion of ideal elastic-plastic bending rectangular plate are derived by using the elastic-plastic partition variational principle.According to the partition criterion of strain energy density,the total strain energy density of elastic zone and the total strain energy density of plastic zone are calculated.The interface between elastic zone and elastic-plastic zone is given,and the deflection surface equation of ideal material bending rectangular plate is derived.The deflection surface equation is applied to MATLAB numerical analysis software for programming calculation.At the same time,ANSYS finite element simulation software is used for modeling analysis,and the data results obtained by the two are plotted in charts for comparative analysis.According to the principle of minimum potential energy and the principle of minimum complementary energy,the Euler equation of linear strengthened pure bending rectangular plate is derived,and the deformation equation is solved.The elastoplastic problem of circular shaft torsion is solved by the elastoplastic partition variational principle,and the corresponding analytical solution is obtained.The research results show that the method of solving the deflection surface equation of the ideal material bending rectangular plate and the pure bending rectangular plate of the linear strengthening material and the analytical solution of the elastic-plastic torsion of the circular shaft under the uniform load is applicable.It is shown that this method can be used to solve the problem of elastic plastic deformation and provides a new method for further study of elastic plastic deformation of materials.