A convolution type semi-analytical GD method for structural transient response

The GDM (General differential method) is a numerical method solving partial differential equations based on Taylor series. The principle and coefficients are reduced in this paper. By using convolution, the original governing equation is transformed into a new equation that is a complete initial-value problem containing initial conditions. The equation is mathematically equivalent to Gutrin's variational principle but does not involve the use of functional and complicated calculations required in the variational principle. The dynamic response is obtained by solving this new governing equation using GDM in space domain and analytical series in time domain. Numerical results concerning the dynamic response of a beam are presented in this paper, showing that the proposed method is accurate and computationally efficient.