B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation
Yanhong Liu, Yong‐Sheng Shi, Dinghe Li, Guanghui Qing · Mechanics of Advanced Materials and Structures · 2011
Based on the modified Hellinger-Reissner (H-R) variational principle for the elastic material, the formulation of B-spline wavelet on the interval (BSWI) element of the Hamilton canonical equation was derived through the use of the interpolation scaling function of BSWI. To demonstrate the excellent predictive capability of the formulation, numerical studies were conducted on a thick plate and a three-layer plate with various common boundary conditions. The basic steps from which the formulation of the BSWI element of the Hamilton canonical equation was derived can also be extended to deduce the expressions of other wavelet elements in the Hamiltonian system, such as Daubechies orthogonal wavelet, biorthogonal wavelet based on lifting scheme, and so on.