An alternative alpha finite element method (A\(\alpha \)FEM) for free and forced structural vibration using triangular meshes. (English) Zbl 1423.74910
Summary: An alternative alpha finite element method (A\(\alpha \)FEM) using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two-dimensional solid mechanics problems. In the A\(\alpha \)FEM, the piecewise constant strain field of linear triangular FEM models is enhanced by additional strain terms with an adjustable parameter \(\alpha \) which results in an effectively softer stiffness formulation compared to a linear triangular element. The element is further extended to the free and forced vibration analyses of solids. Several numerical examples show that the A\(\alpha \)FEM achieves high reliability compared to other existing elements in the literature.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
Keywords:
numerical methods; finite element method (FEM); alpha finite element method (\(\alpha \)FEM); node-based smoothed finite element method (NS-FEM)Software:
XFEMReferences:
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