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| Mixed natural neighbour Galerkin method for the strain gradient elasticity |
| Received:April 06, 2012 Revised:August 20, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201304015 |
| KeyWord:meshless method natural neighbour interpolation size effect strain gradient |
| Author | Institution |
| 王凯 |
济南工程职业技术学院 机电工程系,济南 |
| 周慎杰 |
山东大学 机械工程学院,济南 |
| 聂志峰 |
山东科技大学 机械电子工程学院,青岛 |
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| Abstract: |
| Based on the constrained variational principle,the mixed natural neighbour Galerkin method for 2D and 3D strain gradient elasticity is proposed.The displacements and the first-order gradients of displacements are chosen to be independent nodal degrees of freedom,and the geometrical constraints between them are enforced by using Lagrange multipliers,which enables the relaxation of the continuity and consistency requirements.All the nodal unknowns including the Lagrange multipliers are approximated by the non-Sibsonian interpolation,which is easy to evaluate and can simplify the imposition of essential boundary condition.The validity and accuracy of the proposed method are investigated through numerical examples.The results show that size effects are observed when the length of deformation field and the characteristic length of the material are comparable,and excellent agreements with analytical solutions are obtained. |