Research On Calculation Method Of Multi-Layer Shell Element Based On Inelasticity-Separated Method

As an important part of the structure,planar members such as shear wall and floor are widely used in the civil engineering field.Under the action of natural disasters such as earthquakes,structures tend to enter nonlinearities,so it is important to accurately and quickly describe the nonlinear behavior of these components.The multi-layer shell element is widely used for the numerical simulation of engineering structures because of its simple model and clear physical property.Based on the inelasticity-separated finite element method and the multilayer shell element theory,a efficient method to solve multi-layer shell element is proposed and applied to the numerical simulation of plate and wall components.The main research work of this article is as follows:By decomposing the section deformation(strain and curvature)of the multi-layer shell element into linear elastic deformation and nonlinear deformation and the nonlinear deformation field is established by using Gaussian integration in the middle of the element as the interpolation point,and further according to the principle of virtual work and conditions of internal force equilibrium at Gaussian integration,a governing equation for the multi-layer shell element with the IS FEM form is derived by treating the decomposed nonlinear deformation as additional degrees of freedom.The whole governing equation of structure is obtained by integrating the governing equations of the elements.The first term on the left side of the whole control equation is a 2×2 block matrix,in which the block matrix at the lower right corner represents the material nonlinearity information of the structure.The nonlinear stiffness matrix of the structure is isolated from the overall stiffness matrix.The Gaussian integration point of any element in each iteration step goes into nonlinearity such that the elements in the block matrix of the lower right corner are not zero.If the element that does not enter the nonlinearity and its corresponding position is zero,the row and column whose element is zero can be eliminated to form a small scale nonlinear stiffness matrix in order to avoid the decomposition of the overall tangent stiffness matrix of the structure,only the smaller scale of the nonlinear stiffness matrix needs to be decomposed in the process of solving the nonlinear response of the structure,thus improving the computational efficiency of the nonlinear analysis of the structure.In the nonlinear stage of local materials in the structure,most of the elements were generally in the linear elastic state,and only a small part of them were in the nonlinear state.The dimension of block matrix in the lower right corner was low.Therefore,Woodbury formula can be used to efficiently solve the overall governing equation of the structure.When material nonlinearity occurs in a large range of structures,the dimension of block matrix in the lower right corner is larger,even exceeding the dimension of the overall stiffness matrix.Therefore,Woodbury formula and combination approximation can be used to jointly solve the governing equation.Based on statistical analysis of time complexity function theory show that the multilayer shell element model is established,this paper analyses the method compared with the traditional variable stiffness finite element method has significant advantages in terms of nonlinear analysis efficiency.Finally,taking a beam,plate and wall member as an example,the calculation results of the proposed method and the analysis results of the traditional finite element method are compared and analyzed.The calculation result of this method is equivalent to the traditional method,but the method of this paper can greatly improve the computational efficiency of structural nonlinearity analysis.