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A new hybrid finite element approach for three-dimensional elastic problems

Cao C., Qin Q. H., Yu A.

Archives of Mechanics

2012

Vol. 64, nr 3

261-261

A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.

Trefftz functions and application to 3D elasticity

Lee C. Y., Qin Q. H., Wang H.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 3/4

251-263

When solving complex boundary value problems, the primary advantage of the Trefftz method is that Tr-efftz functions a priori satisfy the governing differential equations. For the treatment of three-dimensional isotropic elasticity problems, it is proposed that the bi-harmonic solutions in Boussinesq's method can be expressed as half-space Fourier series to bypass the difficulties of integral ion. A total of 29 Trefftz terms for each component of the displacement vectors are derived from (he general solutions of the elasticity system. Numerical assessments on the proposed formulations arc performed through two examples (a cubic and a cylindrical body). Results arc compared with those from the method of fundamental solutions (MFS) and the commercial finite element method (FEM) software STRAND 7, suggesting that Trefftz functions can provide pseudo-stability, faster convergence and reduced error margins.