Abstract:

Part or all of the mesh can be eliminated by using the compact support, the orthogonality and other properties of the wavelet function and the meshless algorithm to enhance the computing capability and reduce the error. A meshless algorithm was proposed based on the wavelet basis function. The field function of the meshless algorithm was generated and the corresponding control equation was derived using the Daubechies wavelet as the basis function. Calculation showed that the solution of the proposed algorithm is in excellent agreement with the theoretical solution. Compared with the finite element method, the proposed method is characterized by reduced error and improved precision under the roughly same computing time. The calculation results proved that the wavelet based meshless algorithm effective.

Key words: solid mechanics, wavelet basis function, compact support property, orthonormality, meshless method, finite element method