An Improved Semi-Implicit Method for Structural Dynamics Analysis

1982 ◽  
Vol 49 (3) ◽  
pp. 589-593 ◽  
Author(s):  
K. C. Park
Keyword(s):  
Structural Dynamics ◽  
Truncation Error ◽  
Time Integration ◽  
Implicit Method ◽  
Dynamics Analysis ◽  
Accuracy Improvement ◽  
Implicit Algorithm ◽  
Solution Matrix ◽  
Difference Solution

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

A review of automatic time-stepping strategies on numerical time integration for structural dynamics analysis

2014 ◽  
Vol 80 ◽  
pp. 118-136 ◽  
Author(s):  
Diogo Folador Rossi ◽  
Walnório Graça Ferreira ◽  
Webe João Mansur ◽  
Adenilcia Fernanda Grobério Calenzani
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Dynamics Analysis ◽  
Time Stepping ◽  
Numerical Time Integration

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Structural Dynamics Analysis of “Shenguang-III” Target System

2007 ◽  
pp. 281-281
Author(s):  
Shaorong Yu ◽  
Jun Wang ◽  
Xueqian Chen ◽  
Shifu Xiao ◽  
Bing Xu ◽  
...  
Keyword(s):  
Structural Dynamics ◽  
Target System ◽  
Dynamics Analysis

Computational Aspects of Time Integration Procedures in Structural Dynamics—Part 2: Error Propagation

1978 ◽  
Vol 45 (3) ◽  
pp. 603-611 ◽  
Author(s):  
K. C. Park ◽  
C. A. Felippa
Keyword(s):  
Structural Dynamics ◽  
Error Propagation ◽  
Error Control ◽  
Time Integration ◽  
Trapezoidal Rule ◽  
Computational Error ◽  
Asymptotic Error ◽  
Average Acceleration ◽  
Computational Aspects ◽  
Acceleration Method

The propagation of computational error in the direct time integration of the equations of structural dynamics is investigated. Asymptotic error propagation equations corresponding to the computational paths presented in Part 1 are derived and verified by means of numerical experiments. It is shown that there exists an implementation form that achieves optimum error control when used in conjunction with one-derivative methods. No such form is found for two-derivative methods. A numerical beating phenomenon is observed for certain implementations of the average acceleration method and the trapezoidal rule, which from an error propagation standpoint, is highly undesirable.

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