Nonlinear Analysis Based On The Energy-conserving Time Integration Methods

A time integratuion algorithms is the key element of the hybiid test or the finiteelement analysis. But the stability and accuracy of the integratuion algorithms shouldbe considered. The energy approach can be used to judge the stability of a timeintegration used in the linear or nolinear analysis. So the stepwise integrationalgorithms peforming the equations of motion based on energy approach areunconditionally stable for linear or nolinear structures. Therefore, theenergy-conserving integration methold becomes more and more popular. However,the energy-conserving integration methods are just applied in the field of space flight.although the application in the field of civil engineering is rare. The application of theenergy-conserving integration methods in the large span space structure is studied inthis dissertation, and the main work and results are as follows:1. The energy-conserving time integration method and the average accelerationmethod are studied. The stability of these two integration methods are studiedwith the energy of the system. The theoretical analyses shows thatenergy-conserving time integration method is unconditionally stable, and theaverage acceleration method is conditionally stable because of its increment inenergy.2. In order to apply the energy-conserving time integration method to the field ofcivil engineering, this method is added to the OpenSees software platform as asubprogram, and a simple pendulum numerical example is used to prove thecorrectness and the effectiveness of this program. The energy-conserving timeintegration method, the average acceleration method and the TRBDF2method arestudied in this example. The energy approach is used to prove that theenergy-conserving time integration method with no increment in energy isunconditionally stable; the average acceleration method with some increment inenergy is conditionally stable and the TRBDF2method with negative increment inenergy is unconditionally stable.3. In order to study the application of the energy-conserving time integration methodin the large span space structure, some analysis in the plane truss structure, threedimensional truss structure and the roof of a gas station show that the subprogram added to the OpenSees software platform can be used to do dynamic analysis inboth two dimensional and three dimensional truss structure. The geometricnonlinearity and material nonlinearity in structure is studied to research hownonlinearity influences the numerical stability of an integration method. Theresults show that the average acceleration method turn to be conditionally stablewhen geometric nonlinearity is considered, and a smaller time step is needed tomake it stable. With the integration step increasing, the error of the averageacceleration method becomes bigger，while the material nonlinearity gettingincreasing, the error becomes smaller. The same phenomenon can be seen whilethe elastic buckling force is getting lower. A stability condition is proposed andproved to be effective. Relatively the energy-conserving time integration methodis unconditionally stable.