Temporal spectral element method and its application in optimization of dynamic response

The temporal spectral element method is adopted to solve the dynamic differential equations.After the discrete dynamic response in time domain is deeply considered,the second order differential equations are transformed into first order ones by using Bubnov-Galerkin method and the transient responses can be calculated accurately and efficiently.The critical point and its adjacent GLL point method is developed to deal with the constraints related to the time.Furthermore,it is proposed that spectral element division and interpolation number are function of dynamic load variation.Two optimization examples of spring shock absorber and the five DOFs vehicle suspension system are given.The artificial design variable is introduced.A detailed analysis of the advantages and disadvantages for the proposed method is finished.Results show the correctness of the method,thus providing a reference for further study of dynamic response optimization.