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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
XFEM
Full Text:
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