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Structural Engineering and Mechanics Volume 11, Number 2, February 2001 , pages 221-236 DOI: https://doi.org/10.12989/sem.2001.11.2.221 |
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A local point interpolation method for stress anlaysis of two-dimensional solids |
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G.R. Liu and Y.T. Gu(Singapore)
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| Abstract | ||
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A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids. | ||
| Key Words | ||
| meshless method; stress analysis; interpolation function; weak form; strong form. | ||
| Address | ||
| G.R. Liu and Y.T. Gu, Dept. of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 | ||