A time-integration method for the viscoelastic-viscoplastic analyses of polymers and finite element implementation

2009 ◽  
Vol 79 (5) ◽  
pp. 550-575 ◽  
Author(s):  
Jeong Sik Kim ◽  
Anastasia H. Muliana
Keyword(s):  
Finite Element ◽  
Integration Method ◽  
Time Integration ◽  
Time Integration Method ◽  
Finite Element Implementation

A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments

1990 ◽  
Vol 57 (3) ◽  
pp. 553-561 ◽  
Author(s):  
I. Nishiguchi ◽  
T.-L. Sham ◽  
E. Krempl
Keyword(s):  
Finite Element ◽  
Finite Deformation ◽  
Numerical Experiments ◽  
Deformation Theory ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Time Integration Method ◽  
Finite Element Implementation ◽  
Finite Deformation Theory

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

scholarly journals Influence of Dynamic Analysis Methods on Seismic Response of a Buttress Dam

2014 ◽  
Vol 10 (3) ◽  
pp. 12-26 ◽  
Author(s):  
Cornel Ilinca ◽  
Răzvan Vârvorea ◽  
Adrian Popovici
Keyword(s):  
Finite Element ◽  
Spectral Analysis ◽  
Integration Method ◽  
Seismic Analysis ◽  
Time Integration ◽  
Hydrodynamic Effect ◽  
Analysis Method ◽  
Dam Foundation ◽  
Time Integration Method ◽  
Spectral Analysis Method

Abstract The seismic analysis of a buttress dam with 73.50 m height is performed by the spectral analysis method and the direct time integration method. An accelerogram with 0.1g maximum acceleration was applied horizontally, in the upstream - downstream direction, at the bottom of the dam-foundation finite element mesh. The hydrodynamic effect of the reservoir was considered according to the added mass procedure (Westergaard relation). ABAQUS software was used to make the analyses. The same type of finite element C3D20R was used for the mesh of the dam body and of the foundation. The comparison of the results is made on the displacements, the stress state and the sliding stability on the dam-foundation contact in the full reservoir hypothesis. The comprehensive analysis concluded that both methods had provided close results for the considered case study. The spectral analysis method revealed itself to be more conservative compared to the direct time integration method.

scholarly journals An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

2021 ◽  
Vol 11 (4) ◽  
pp. 1932
Author(s):  
Weixuan Wang ◽  
Qinyan Xing ◽  
Qinghao Yang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Weak Form ◽  
High Accuracy ◽  
Numerical Dissipation ◽  
Frequency Range ◽  
Time Integration Method ◽  
Numerical Damping

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

scholarly journals Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012145
Author(s):  
Ryuma Honda ◽  
Hiroki Suzuki ◽  
Shinsuke Mochizuki
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Implicit Time ◽  
Explicit Time Integration ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Time Integration Methods

Abstract This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

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