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Temporal stabilization of the node-based smoothed finite element method and solution bound of linear elastostatics and vibration problems. (English) Zbl 1398.74431
Summary: 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.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74K25 Shells
Software:
Mfree2D
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References:
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