Nonlinear Elasto-Plastic And Dynamic Analysis Method Of Flexible Spatial Steel Framed Structures

With the development of social economy and construction method,more flexible structures such as large-span,high-rise and floating structures are used.The geometric nonlinear characteristics subjected to ultimate loads and dynamic loads is becoming increasingly significant.Tracking the force equilibrium path of these flexible structures is critical for the design and analysis process.Therefore,the accuracy and efficiency of method in solving geometric nonlinear problems are highly demanded.The general geometric nonlinear analysis is based on the large deformation theory,and introduce the artificial assumption of the displacement interpolation function to derive the elastic stiffness matrix and the geometric stiffness matrix base on virtual work principle.Combined with proper incremental iteration algorithm,the structure response can be obtained.However most traditional methods use the geometric stiffness matrix to deal with the rigid body displacement of the element,so the accuracy of the geometric stiffness matrix is highly demanded.Many researchers introduce the higher-order displacement interpolation function to derive the matrix with complicated form,the physical meaning of which is not clear,and then the accuracy and efficiency of the calculation cannot be guaranteed.In view of the limitations in describing element displacement and deformation of the geometric nonlinear analysis method mentioned above,the rigid body rule is adopted to analyze the large displacement and large rotation of the structure in this paper.When the elements move from C₁ state to C₂,the displacements of members can be decomposed into rigid body displacement and natural deformation in incremental step.After experiencing rigid body displacement,the initial equilibrium force acting on the element remains value unchanged and only the direction changes.In common situation,the rigid body displacements accounts for the main part of incremental displacement.The rigid body rule can also be used to deal with the equilibrium forces experienced by the rigid body displacement,so that the corrector phase is accurate and greatly simplified.According to the concept of rigid element,the geometric stiffness matrix which passes the rigid body test is derived in this paper,It is concise in form.Thus the calculation efficiency will be highly improved while the geometric stiffness matrix is used in the predictor of incremental iteration process.The physical concept of nonlinear analysis process based on rigid body rule is clear and the calculation process is simple,which overcome the disadvantages of traditional methods.Based on the rigid body rule and the second-order refined plastic hinge model,the spatial elasto-plastic beam element and its stiffness matrix are constructed in this paper.A highly efficient and simple nonlinear incremental iteration method is developed to effectively analyze the coupling effect of material and geometric nonlinearity of flexible spatial steel frame structures such as finite rotation and second-order effect caused by section yield.In this method,the rigid-body rule is implanted into the incremental iteration method.Moreover,on the basis of static analysis method and direct integration method,the dynamic time history analysis method of frame structure is proposed.In each time step,the nodal force increments are obtained by the nonlinear analysis according to the rigid body rule.The numerical examples of the dynamic analysis of3-D framed structures show that the proposed method is highly efficient and accurate for simulating the dynamic nonlinear behavior of spatial framed structures undergoing the large displacements and rotations,and is applicable for engineering practice.Through analysis and verification of typical examples,the new type material-geometric nonlinear and dynamic nonlinear analysis method for flexible structures has obvious advantages of precision and efficiency with less elements number,which is suitable for engineering applications,and the universal applicability of the rigid body rule for complex nonlinear problems is proved.