TAILIEUCHUNG - About applying directly the alpha finite element method (αFEM) for solid mechanics using triangular and tetrahedral elements

This novel combination of the FEM and NS-FEM makes the best use of the upper bound property of the NS-FEM and the lower bound property of the standard FEM. This paper concentrates on applying directly the αFEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using α = for 2D problems and α = for 3D problems. | Vietnam Journal of Mechanics, VAST, Vol. 32, No. 4 (2010), pp. 235 – 246 ABOUT APPLYING DIRECTLY THE ALPHA FINITE ELEMENT METHOD (αFEM) FOR SOLID MECHANICS USING TRIANGULAR AND TETRAHEDRAL ELEMENTS Nguyen Thoi Trung1,2 , Nguyen Xuan Hung1,2 1 University of Science, VNU, HCM 2 Ton Duc Thang University, HCM Abstract. An alpha finite element method (αFEM) has been recently proposed to compute nearly exact solution in strain energy for solid mechanics problems using three-node triangular (αFEM-T3) and four-node tetrahedral (αFEM-T4) elements. In the αFEM, a scale factor α ∈ [0, 1] is used to combine the standard fully compatible model of the FEM with a quasi-equilibrium model of the node-based smoothed FEM (NS-FEM). This novel combination of the FEM and NS-FEM makes the best use of the upper bound property of the NS-FEM and the lower bound property of the standard FEM. This paper concentrates on applying directly the αFEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using α = for 2D problems and α = for 3D problems. 1. INTRODUCTION For many decades, the constant finite elements such as three-node triangle and fournode tetrahedron are popular and widely used in practice. The reason is that these elements can be easily formulated and implemented very effectively in the finite element programs using piecewise linear approximation. Further more, most FEM codes for adaptive analyses are based on triangular and tetrahedral elements, due to the simple fact that triangular and tetrahedral meshes can be automatically generated. However, these elements possess significant shortcomings, such as poor accuracy in stress solution, the overly stiff behavior and volumetric locking in the nearly incompressible cases. In the development of new finite element methods, the strain smoothing technique [1] has been applied to the FEM to formulate and develop four smoothed finite element methods (S-FEM) including a cell-based S-FEM

• Vật lý
• Vietnam Journal of Mechanics
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
• Languages Gibian and special operators
• The application FEM
• Betts miller janjic convective parameterization scheme
• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
• The gulf of Tonkin
• The kinetic energy distribution
• Duality in the analysis of responses to nonlinear systems
• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
• Aerodynamics of a wing in surface effect ship
• Theory and experiment
• Wing in surface effect ship
• The aerodynamic characteristics
• The Institute of Mechanics
• The error estimate
• The convergence rate for h
• p refinement
• The finite element analysis
• Three dimensional elastostatic mechanics problems
• Some initial experimental results
• Free water layer formation in horizontal pipes
• Water layer formation
• Hanoi Institute of Mechanics
• Bending vibration of beam elements under moving loads
• Considering vehicle braking forces
• Fluctuations of structures
• Beam elements according
• Continuous element for vibration analysis
• Thick shells of revolution
• Continous Element Method
• Finite element solutions
• Natural frequencies and harmonic responses
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• Buckling analysis of simply supported composite laminates subjected
• In plane compression load
• A novel mesh ffree method
• Alternative numerical technique
• Mesh free method
• A three story building
• Hedge algebras based fuzzy controller
• The structural system
• The El Centro earthquake
• Three story building against earthquake
• Laminar separation phenomenon combining with numerical calculations
• The turbulent separation
• The laminar separation
• Experimental study on mechanical properties
• Three phase polymer composite reinforced
• Glass fibers and titanium oxide particles
• Polymer composite reinforced
• Three phase composite
• Dynamic characteristics of elastically supported beam subjected
• A compressive axial force and a moving load
• The implicit Newmark method
• The Galerkin finite element method
• The axial force
• Eccentrically stiffened functionally graded plates and shallow shells
• Von Karman Donnell sense
• The formulation of governing equations
• The classical shell theory
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Evaluating structural safety based on fuzzy set theory
• Evaluating structural safety
• The fuzzy reliability
• Simple beam structure