An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes

Authors:
N. Nguyen-Thanh;Timon Rabczuk;H. Nguyen-Xuan;Stéphane P. A. Bordas
Affiliations:
Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99423 Weimar, Germany;Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99423 Weimar, Germany;Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore 117576, Singapore and Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science, VNU-HCM, ...;Department of Civil Engineering, University of Glasgow, Rankine building, G12 8LT, Scotland and Royal Academy of Engineering/Leverhulme Trust Senior Research Fellow ("Towards the next generation s ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
Cited 5

Efficient implementation of quadrilaterals with high coarse-mesh accuracy

Computer Methods in Applied Mechanics and Engineering
Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems

Computer Methods in Applied Mechanics and Engineering
Review: Meshless methods: A review and computer implementation aspects

Mathematics and Computers in Simulation
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems

Computers and Structures
A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes

Journal of Computational Physics
Strain smoothing in FEM and XFEM

Computers and Structures

An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates

Finite Elements in Analysis and Design
The multi-scale physical and numerical modeling of fracture phenomena in the MgCa0.8 alloy

Computers and Structures
An Edge-based Imbricate Finite Element Method (EI-FEM) with full and reduced integration

Computers and Structures
An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics

Computational Mechanics
An Imbricate Finite Element Method (I-FEM) using full, reduced, and smoothed integration

Computational Mechanics

Quantified Score

Hi-index	7.29

Visualization

Abstract

An alternative alpha finite element method (A@aFEM) 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@aFEM, the piecewise constant strain field of linear triangular FEM models is enhanced by additional strain terms with an adjustable parameter @a 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@aFEM achieves high reliability compared to other existing elements in the literature.