The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics

Computationally-useful methods of estimating the critical time step for linear triangular elements and for linear quadrilateral elements are given. Irregular nodal-point arrangements, position-dependent properties, and a variety of boundary conditions can be accommodated. The effects of boundary conditions and element shape on the critical time step are discussed. Numerical examples are presented to illustrate the effect of various boundary conditions and for comparison to the finite-difference method.

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A Simple Explicit–Implicit Time-Marching Technique for Wave Propagation Analysis

International Journal of Computational Methods ◽

10.1142/s0219876218500822 ◽

2018 ◽

Vol 16 (01) ◽

pp. 1850082 ◽

Cited By ~ 2

Author(s):

Delfim Soares

Keyword(s):

Wave Propagation ◽

Time Integration ◽

Critical Time ◽

Implicit Time ◽

Time Step ◽

Stiffness Matrices ◽

Time Integrators ◽

Propagation Analysis ◽

Time Marching ◽

Critical Time Step

A new explicit–implicit time integration technique is proposed here for wave propagation analysis. In the present formulation, the time integrators of the model are selected at the element level, allowing each element to be considered as explicit or implicit. In the implicit elements, controllable algorithm dissipation is provided, enabling an [Formula: see text]-stable formulation. In the explicit elements, null amplitude decay is considered, enabling maximal critical time-step values. The new methodology renders a very simple and effective time-marching algorithm. Here, just displacement–velocity relations are considered, and no computation of accelerations is required. Moreover, explicit/implicit analyses can be carried out just by the tuning of local effective matrices, inputting or not stiffness matrices into their computations. At the end of the paper, numerical results are presented, illustrating the performance and potentialities of the new method.

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Critical time-step for central difference integration schemes in discrete methods: Translational and rotational degrees of freedom

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2019.04.003 ◽

2019 ◽

Vol 353 ◽

pp. 158-182

Author(s):

A. Mimouna ◽

H.A. Tchelepi

Keyword(s):

Degrees Of Freedom ◽

Critical Time ◽

Time Step ◽

Central Difference ◽

Integration Schemes ◽

Rotational Degrees Of Freedom ◽

Discrete Methods ◽

Critical Time Step

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Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

Journal of Applied Mechanics ◽

10.1115/1.3424304 ◽

1978 ◽

Vol 45 (2) ◽

pp. 371-374 ◽

Cited By ~ 232

Author(s):

T. J. R. Hughes ◽

W. K. Liu

Keyword(s):

Finite Element ◽

Finite Elements ◽

Transient Analysis ◽

Critical Time ◽

Unconditional Stability ◽

Time Step ◽

Explicit Finite Element ◽

New Family ◽

Critical Time Step ◽

Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

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Critical time step for a bilinear laminated composite Mindlin shell element.

10.2172/919205 ◽

2004 ◽

Author(s):

Daniel Carl Hammerand

Keyword(s):

Critical Time ◽

Laminated Composite ◽

Shell Element ◽

Time Step ◽

Critical Time Step

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A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2007-0014 ◽

2007 ◽

Vol 7 (3) ◽

pp. 227-238 ◽

Cited By ~ 23

Author(s):

S.H. Razavi ◽

A. Abolmaali ◽

M. Ghassemieh

Keyword(s):

Fourth Order ◽

Initial Conditions ◽

Time Integration ◽

Critical Time ◽

Linear Acceleration ◽

Time Step ◽

Time Integration Method ◽

Acceleration Method ◽

The Stability ◽

Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

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