Theoretical Research And Application Of Two-step Unconditionally Stable Non-iterative Displacement Method

The stepwise integration method is the most common method to solve dynamic equations.In this thesis,a two-step unconditionally stable non-iterative dissipative displacement algorithm is derived based on the principle of dimensional equilibrium.The algorithm has the noniterative properties of explicit integration method and the unconditionally stable properties of implicit integration method,and the accuracy is at least second order.The research contents and achievements of this thesis are as follows:(1)Select representative explicit and implicit numerical integration algorithms,and introduce their calculation iterative formula in detail.The numerical characteristics of the algorithm are analyzed from the aspects of spectral radius,period extension rate,amplitude attenuation rate and transcendence.The conclusion that the algorithm has second-order accuracy is obtained.The unconditional stability of the implicit algorithm is proved,and the numerical damping characteristics of other algorithms are explored.(2)Based on the principle of dimensional balance,a two-step unconditionally stable non iterative dissipative displacement algorithm is derived.The accuracy,stability and numerical dissipation characteristics of the algorithm are analyzed.It is found that the algorithm in this thesis is efficient and saves storage space.At the same time,the non iterative characteristic and unconditional stability of this algorithm are verified by theoretical analysis,and the conclusion that displacement and velocity have no amplitude transcendence is given.(3)Four different numerical examples show that the algorithm has the advantages of unconditional stability,controllable numerical damping dissipation,high computational efficiency and no overshoot of displacement and velocity,which reflects the important value of the numerical algorithm in this thesis.