A Weighted Residual Quadratic Acceleration Time Integration Method in Nonlinear Structural Dynamics

2010 ◽  
Author(s):  
A.A. Gholampour ◽  
M. Ghassemieh
Keyword(s):  
Structural Dynamics ◽  
Integration Method ◽  
Time Integration ◽  
Acceleration Time ◽  
Time Integration Method ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Structural

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.

scholarly journals A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics

2019 ◽  
Vol 9 (15) ◽  
pp. 3076
Author(s):  
Qinyan Xing ◽  
Qinghao Yang ◽  
Weixuan Wang
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Weak Form ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Structural Dynamic ◽  
Time Integration Method ◽  
Nonlinear Structural ◽  
Nonlinear Dynamic Equations ◽  
Step Algorithm

This paper presents a step-by-step time integration method for transient solutions of nonlinear structural dynamic problems. Taking the second-order nonlinear dynamic equations as the model problem, this self-starting one-step algorithm is constructed using the Galerkin finite element method (FEM) and Newton–Raphson iteration, in which it is recommended to adopt time elements of degree m = 1,2,3. Based on the mathematical and numerical analysis, it is found that the method can gain a convergence order of 2m for both displacement and velocity results when an ordinary Gauss integral is implemented. Meanwhile, with reduced Gauss integration, the method achieves unconditional stability. Furthermore, a feasible integration scheme with controllable numerical damping has been established by modifying the test function and introducing a special integral rule. Representative numerical examples show that the proposed method performs well in stability with controllable numerical dissipation, and its computational efficiency is superior as well.

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