A Novel Large Deformation Laminated Shell Element Model For Reinforced Concrete Shear Walls

The shear wall,the main lateral resistance component of high-rise building structure,is often in a complex stress state under large earthquakes,thus showing complex deformation behavior,even causing large displacement and large rotation and damage.The ideal shell element is the basis for accurately simulating the complex stress state of shear wall under large earthquakes,so it can be constructed accurately.It is necessary to simulate the shell model of shear wall with large displacement and large rotation.Nowadays,there are a lot of research results on flat shell elements.However,few flat shell elements can fully consider the problems of element compatibility,shear locking,film locking and geometric nonlinearity.Based on the generalized conforming element GQ12 with rotational degrees of freedom and the general plate element DKMQ,a new type of composite laminated shell element DKMGQ with 4 nodes and 24 degrees of freedom is constructed.The shell element is insensitive to grid distortion,universal in thickness and can consider large geometric deformation.The main research work of this paper is as follows:A new type of flat shell DKMGQ is developed,which is composed of GQ12 membrane and DKMQ plate.Based on the moving frame,the coordinate description of shell element theory is proposed,including the transformation between local coordinates,natural coordinates and global coordinates.Then the complete theoretical formulas of GQ12 membrane and DKMQ plate are given.On this basis,the total stiffness matrix of the new shell element DKMGQ is synthesized,and the total stiffness matrix based on the moving frame field is derived.The formulas for calculating the effective nodal load vector are given.Finally,the performances of the plate shells in this paper are verified by three classical examples of "plane stress","bending plate" and "shell structure".From the results of several classical examples,it can be seen that DKMGQ has high accuracy,is insensitive to grid distortion,has no shear locking and membrane.It has excellent performance such as locking and good convergence.Geometric Nonlinear Analysis of Elastic Plate Shell Based on DKMGQ Theory.Firstly,the generalized stress-strain relationship of DKMGQ shell under large displacement and large rotation in space is described,and the equilibrium equation of geometric nonlinearity based on displacement increment is given.On this basis,the concrete Green's strain matrix,equilibrium equation,tangent stiffness matrix and internal force vector of DKMGQ shell under complete Lagrangian TL formulation are derived.Secondly,the CR formulation of DKMGQ for large deformation problem is developed,and the nonadditive characteristics of large rotation are analyzed.Meanwhile,the method of updating angular displacement by multiplying the rotation matrix is given,which regards the large spatial rotation as a pseudo-vector.The method of calculating the pure deformation in the co-rotating coordinate system and the theoretical formulas of internal force and tangent stiffness are presented.Then the finite element method of geometrically nonlinear load control is described.Finally,numerical examples of bending and shearing of slender cantilever beams and torsional cantilever beams are used to verify the performance of DKMGQ shell considering geometric nonlinearity.Layered shell element theory based on elastic flat shell DKMGQ theory.The generalized constitutive matrix on the cross section of layered shell element is deduced to integrate the calculation formula of the overall stiffness of layered shell element;the tension-compression constitutive model of steel bar adopts ideal elastic-plastic constitutive model,and the two-dimensional constitutive model of concrete adopts diffuse crack model,on the basis of which the generalized constitutive transformation from material coordinate system under concrete cracking is deduced.Then,based on the assumption of plane cross-section,the formula for calculating the strain of each layer on the cross-section of the laminated shell is derived,and the stress is obtained according to the material constitutive law of the laminated shell,and then the internal force can be obtained by piecewise integration of the stress on the cross-section.The load control method is used to solve the non-linear problem,and Newton method is used to iterate and converge to the exact solution step by step in the incremental load step.Finally,the classical McNeice two-way plate example is used to verify the reliability of the DKMGQ in the hierarchical processing algorithm and the non-linear solution process.