On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics

1975 ◽  
Vol 42 (4) ◽  
pp. 865-869 ◽  
Author(s):  
T. Belytschko ◽  
D. F. Schoeberle
Keyword(s):  
Structural Dynamics ◽  
Unconditional Stability ◽  
Nonlinear Material ◽  
Convergence Criterion ◽  
Sufficient Condition ◽  
Time Step ◽  
Discrete Energy ◽  
Numerical Examples ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural

In this paper an implicit Newmark β-method with iterations for nonlinear structural dynamics is described; the algorithm is identical to standard algorithms except that a new convergence criterion is employed. A discrete energy is defined and it is shown that this discrete energy is bounded regardless of the size of the time step; this is a sufficient condition for the unconditional stability of the algorithm for nonlinear material problems. Numerical examples are given for problems with both geometric and material nonlinearities.

Stability Analysis of an Extrapolated Force Correction Method for Nonlinear Structural Dynamics

1982 ◽  
Vol 49 (1) ◽  
pp. 203-205 ◽  
Author(s):  
D. M. Trujillo
Keyword(s):  
Stability Analysis ◽  
Structural Dynamics ◽  
Correction Method ◽  
Unconditional Stability ◽  
Numerical Examples ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural

In this paper, conditions for the unconditional stability of an extrapolated force correction method have been identified. The analysis assumed a nonlinear elastodynamic system for which energy is conserved. Some numerical examples are included to demonstrate the performance of the method.

A Dissipative Momentum-Conserving Time Integration Algorithm for Nonlinear Structural Dynamics

2021 ◽  
pp. 2150116
Author(s):  
Salvatore Lopez
Keyword(s):  
Angular Momentum ◽  
Structural Dynamics ◽  
Time Integration ◽  
Integration Scheme ◽  
Second Phase ◽  
Time Step ◽  
Integration Algorithm ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural ◽  
Solution Point

A second-order accurate single-step time integration method for nonlinear structural dynamics is developed. The method combines algorithmic dissipation of higher modes and conservation of linear and angular momentum and is composed of two phases. In the first phase, a solution point is computed by a basic integration scheme, the generalized-[Formula: see text] method being adopted due to its higher level of high-frequency dissipation. In the second phase, a correction is hypothesized as a linear combination of the solution in the basic step and the gradient of vector components of the incremental linear and angular momentum. By solving a system composed of six linear equations, the searched for corrected solution in the time step is then provided. The novelty in the presented integration scheme lies in the way of imposing the conservation of linear and angular momentum. In fact, this imposition is carried out as a correction of the computed solution point in the time step and not through an enlarged system of equations of motion. To perform tests on plane and spatial motion of three-dimensional structural models, a small strains — finite rotations corotational formulation is also described.

Algorithms for Nonlinear Structural Dynamics

1978 ◽  
Vol 104 (2) ◽  
pp. 263-280 ◽  
Author(s):  
Hojjat Adeli ◽  
James M. Gere ◽  
William Weaver
Keyword(s):  
Structural Dynamics ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural

Applications of hybrid time–frequency methods in nonlinear structural dynamics

2014 ◽  
Vol 68 ◽  
pp. 134-143 ◽  
Author(s):  
I. Politopoulos ◽  
Ph. Piteau ◽  
J. Antunes ◽  
L. Borsoi
Keyword(s):  
Structural Dynamics ◽  
Time Frequency ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural
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