Abstract
In this paper, a formulation of a novel three-dimensional finite element is presented in the framework of the generalized finite element method based on the partition of unity method. The 8-node conventional linear element is enriched by the reduced quadratic polynomial terms, and it can reproduce the quadratic deformation mode with only corner nodes. The presented element is a compatible element, and it can avoid linear dependency, which is a well-known problem of generalized finite elements. Linear and nonlinear bending analyses of a cantilever beam are demonstrated. The proposed element provides superior solution convergence in comparison with that of the conventional second-order elements. It is also shown that a high-precision solution can be obtained when the mesh is strongly distorted.
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