Journal ArticleDOI
Temporal stabilization of the node-based smoothed finite element method and solution bound of linear elastostatics and vibration problems
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TLDR
In this paper, a stabilization procedure for curing temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular element, where a stabilization term is added into the smoothed potential energy functional of the original NS-FEMS, consisting of squared-residual of equilibrium equation.Abstract:
A stabilization procedure for curing temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular element. A stabilization term is added into the smoothed potential energy functional of the original NS-FEM, consisting of squared-residual of equilibrium equation. A gradient smoothing operation on second order derivatives is applied to relax the requirement of shape function, so that the squared-residual can be evaluated using linear elements. Numerical examples demonstrate that stabilization parameter can “tune” NS-FEM from being “overly soft” to “overly stiff”, so that eigenvalue solutions can be stabilized. Numerical tests provide an empirical value range of stabilization parameter, within which the stabilized NS-FEM can still produce upper bound solutions in strain energy to the exact solution of force-driven elastostatics problems, as well as lower bound natural frequencies for free vibration problems.read more
Citations
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Journal ArticleDOI
Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments
Wei Zeng,Gui-Rong Liu +1 more
TL;DR: The smoothed finite element methods (S-FEM) as discussed by the authors are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the mesh free methods.
Journal ArticleDOI
A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes
Trung Nguyen-Thoi,Trung Nguyen-Thoi,H.C. Vu-Do,Timon Rabczuk,Hung Nguyen-Xuan,Hung Nguyen-Xuan +5 more
TL;DR: In this article, a node-based smoothed finite element method (NS-FEM) was proposed for the solid mechanics problems, which is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes.
Journal ArticleDOI
A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates
Hung Nguyen-Xuan,Hung Nguyen-Xuan,Timon Rabczuk,Nhon Nguyen-Thanh,Trung Nguyen-Thoi,Trung Nguyen-Thoi,Stéphane Bordas +6 more
TL;DR: In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates.
Journal ArticleDOI
A stable node-based smoothed finite element method for acoustic problems
TL;DR: In this paper, a stable node-based smoothed finite element method (SNS-FEM) is proposed for analyzing acoustic problems using linear triangular and tetrahedral elements that can be generated automatically for any complicated configurations.
Journal ArticleDOI
Steady and transient heat transfer analysis using a stable node-based smoothed finite element method
TL;DR: In this paper, a stable node-based smoothed finite element method (SNS-FEM) is formulated for steady and transient heat transfer problems using linear triangular and tetrahedron element.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Journal ArticleDOI
Theory of Elasticity (3rd ed.)
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Mesh Free Methods: Moving Beyond the Finite Element Method
TL;DR: In this paper, Galerkin et al. defined mesh-free methods for shape function construction, including the use of mesh-less local Petrov-Galerkin methods.
Journal ArticleDOI
A stabilized conforming nodal integration for Galerkin mesh-free methods
TL;DR: In this paper, a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integrations, where an integration constraint is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation.
Journal ArticleDOI
A Smoothed Finite Element Method for Mechanics Problems
TL;DR: It is found that a quadrilateral element divided into four smoothing cells can avoid spurious modes and gives stable results for integration over the element and the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost.