Energy Consistent Integration Method And Its Applications To Hybrid Testing

Time step-by-step integration methods are effective tools for both numerical analysis and hybrid test in structural engineering.Unfortunately,traditional linearly-stable time integration methods may lose numerical stability in nonlinear analysis.To obtain a more effective and accurate result,it is necessary to study the nonlinear stability of time integration methods,as well as their applications in numerical simulation and hybrid test.In this dissertation,the nonlinear stability of incremental time integration methods,novel energy-consistent and dissipative methods,as well as their applications in numerical simulation and hybrid test are studied.1.To broaden the application of energy integration method,a general expression of energy-consistent method is proposed by contrastive analysis on different energy conserving methods.By the specialization of this general expression,the proposed form can help fomulate new integration methods,as well as decribe existing methods.Both accuracy and existence of solution are studied.Results show that the accuracy of nonlinear correction method for restoring force is second order,while other methodsare conditional second order because of their dependence on the characteristics of system and the existence of solution.A single-DOF structure with nonlinear elasticity and elastoplasticity has been simulated with the proposed energy-consistent method and the traditional average acceleration method,respectively.The numerical results show that the energy-consistent method has better numerical stability and energy consistency.2.This dissertation presents a nonlinear correction method for the truss element,and also provides the derivation of the equivalent stiffness.Nonlinear dynamic analysis of a single pendulum,a plane truss and a space grid structure are conducted using finite element program.It is shown that the nonlinear correction method for truss element has good numerical stability,while the implicit midpoint method and the average acceleration method are energy-inconsistent or even unstable.Based on the nonlinear correction method,an energy dissipation method is proposed to suppress the spurious high frequency response which is produced by finite element discretization.Both theoretical derivation and numerical results demonstrate that energy dissipation method can filter out the false high-frequency response of the structure,while little influence on low-frequency response.3.For structures with nonlinear damping,the implicit midpoint method is proved to be nonlinearly unconditional stable by using energy criterion.Furthermore,the numerical stability of implicit midpoint method for kinematic hardening model are studied.These analyses are first conducted on SDOF structure,and then extended to MDOF structure by using element assembling theory.Theoretical analysis and numerical simulation show that the implicit midpoint method is stable when being used to solve equation of motion with nonlinear damping and kinematic hardening model.4.A novel nonlinear correction method for beam element is proposed by introducing multiple parameters.Compared to traditional integration methods,the proposed method is shown to have better energy consistency.Considering the shortcomings of the existing linear correction method,an improved linear correction method is then proposed.In order to extend the application range of the improved method,the development process of its realization in open source finite element software OpenSees is also given.The comparative analysis shows that the improved linear correction method is still stable when the axial deformation of beam is large;while the average acceleration method and implicit midpoint method are energy-inconsistent or even divergent.5.A general applicable format of the energy-consistent method is proposed for hybrid test.The energy-consistent integration method is implemented in SDOF structure hybrid test.Test results show that the energy error of second order energy integration is almost zero,while the energy error of average acceleration method becomes larger with the time increasesing.The connection between beam-column simulation program and test system is realized,and then used for hybrid test of a full-scale steel frame.The energy error of the energy-consistent method is shown to be less than that of the average acceleration method.Considering the efficiency of iteration process,a new iteration format is proposed to avoid overshooting.The effectiveness of this format is validated by both numerical and test results.