scholarly journals A New Family of Explicit Time Integration Algorithms with Controllable Accuracy for Structural Dynamics

2017 ◽  
Author(s):  
Xiaoqiong Du ◽  
Yongliang Zhao ◽  
Xiaoliang Yan
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Explicit Time Integration ◽  
New Family ◽  
Integration Algorithms

A New Family of Higher-Order Time Integration Algorithms for the Analysis of Structural Dynamics

2017 ◽  
Vol 84 (7) ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Higher Order ◽  
Weighted Residual Method ◽  
New Family ◽  
Equal Degree ◽  
Fundamental Limitations ◽  
Mixed Formulations ◽  
Dependent Variables ◽  
Integration Algorithms

For the development of a new family of implicit higher-order time integration algorithms, mixed formulations that include three time-dependent variables (i.e., the displacement, velocity, and acceleration vectors) are developed. Equal degree Lagrange type interpolation functions in time are used to approximate the dependent variables in the mixed formulations, and the time finite element method and the modified weighted-residual method are applied to the velocity–displacement and velocity–acceleration relations of the mixed formulations. Weight parameters are introduced and optimized to achieve preferable attributes of the time integration algorithms. Specific problems of structural dynamics are used in the numerical examples to discuss some fundamental limitations of the well-known second-order accurate algorithms as well as to demonstrate advantages of using the developed higher-order algorithms.

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