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| An improved algorithm for nonlinear dynamic systems based on Wilson-θ and Newmark-β method |
| Received:June 10, 2016 Revised:December 20, 2016 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201704006 |
| KeyWord:Wilson-θ method Newmark-β method nonlinear dynamic system guess solution iterative correction |
| Author | Institution |
| 刘广 |
中山大学 力学系, 广州 |
| 刘济科 |
中山大学 力学系, 广州 |
| 陈衍茂 |
中山大学 力学系, 广州 |
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| Abstract: |
| When using Wilson-θ or Newmark-β method to solve nonlinear dynamic equations,usually,we rewrite the equations in the form of incremental equilibrium equations.The coefficient matrix has to be updated in each integral step according to the state variables.In essence,this procedure is to linearize the considered nonlinear system in a single time step.It is usually difficult,however,to handle some strongly nonlinear problems with multiple-degrees-of-freedom.By using an incremental process,in the paper a new fast algorithm was proposed based on Wilson-θ method or Newmark-β method.According to the obtained solution at one time point,we present an initial guessed solution at the next time instant.Then the guessed solution can converge to the true solution via iterative corrections.Numerical examples show that,using the presented fast algorithm together with Wilson-θ method or Newmark-β method,one can get highly accurate solutions.Moreover,the presented algorithm can provide us with a simple way to adjust the convergence as necessary.As the presented methods avoid linearization of the considered nonlinear dynamic systems,they are not only more applicable but also more computationally efficient. |
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