Finite element modeling of linear elastodynamics problems with explicit time-integration methods and linear elements with the reduced dispersion error

2014 ◽  
Vol 271 ◽  
pp. 86-108 ◽  
Author(s):  
A. Idesman ◽  
D. Pham
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Time Integration ◽  
Integration Methods ◽  
Explicit Time Integration ◽  
Dispersion Error ◽  
Element Modeling ◽  
Linear Elastodynamics ◽  
Linear Elements ◽  
Time Integration Methods

FINITE ELEMENT MODELING OF ONE-DIMENSIONAL BOUSSINESQ EQUATIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 207-235 ◽  
Author(s):  
PARVIZ GHADIMI ◽  
MOHAMMAD HADI JABBARI ◽  
ARSHAM REISINEZHAD
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Auxiliary Equation ◽  
Numerical Techniques ◽  
Third Order ◽  
One Dimensional ◽  
Element Modeling ◽  
The Third

Finite element modeling of one-dimensional Beji and Nadaoka Boussinesq equation is presented. The continuous equations are spatially discretized using standard Galerkin method. Since the extended Boussinesq equations contain high-order derivatives, two different numerical techniques are proposed in this paper in order to simplify the discretization task of the third-order terms. In the first technique, an auxiliary equation is introduced to eliminate the third-order derivatives of the momentum equation while non-overlapping elements with linear interpolating functions are employed to account for the dependent variables. However, in the second method, overlapping elements with quadratic interpolating functions are applied for discretizing the governing equations. Time integration is performed using the Adams–Bashforth–Moulton predictor–corrector method. By considering the truncation error and theoretical analysis for both of the numerical techniques, accuracy and stability of the adopted finite element schemes have been studied. Finally, a computer code is developed based on the proposed schemes. To show the validity as well as the practicality of the developed code, five different test cases are presented, and the results are compared with some analytical solutions and experimental data. Favorable agreements have been achieved in all cases.

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