GPU-acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods

2013 ◽  
Vol 258 ◽  
pp. 63-80 ◽  
Author(s):  
A. Karatarakis ◽  
P. Metsis ◽  
M. Papadrakakis
Keyword(s):  
Stiffness Matrix ◽  
Meshless Methods ◽  
Gpu Acceleration ◽  
Matrix Calculation

scholarly journals Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Emir Gülümser ◽  
Uğur Güdükbay ◽  
Sinan Filiz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Nonlinear Fem ◽  
Calculation Technique ◽  
Stiffness Matrices ◽  
Matrix Calculation ◽  
Element Method

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.

scholarly journals New Formula for Geometric Stiffness Matrix Calculation

2016 ◽  
Vol 04 (04) ◽  
pp. 733-748 ◽  
Author(s):  
I. Němec ◽  
M. Trcala ◽  
I. Ševčík ◽  
H. Štekbauer
Keyword(s):  
Stiffness Matrix ◽  
Geometric Stiffness ◽  
New Formula ◽  
Matrix Calculation

Transverse Natural Vibrations of a Cracked Beam Loaded with a Constant Axial Force

1993 ◽  
Vol 115 (4) ◽  
pp. 524-528 ◽  
Author(s):  
M. Krawczuk ◽  
W. M. Ostachowicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Numerical Calculations ◽  
Open Crack ◽  
Natural Vibrations ◽  
Cracked Beam ◽  
Matrix Calculation

The influence of transverse, one-edge open cracks on the natural frequencies of the cantilever beam subjected to vertical loads is analyzed. A finite element method (FE) is used for modelling the beam. A part of the cracked beam is modelled by beam finite elements with an open crack. Parts of the beam without a crack are modelled by standard beam finite elements. An algorithm of a linear stiffness matrix and a geometrical stiffness matrix calculation for a cracked element is presented. The results of numerical calculations obtained for the presented model are compared with the results of analytical calculations given in the literature and also with the results of numerical calculations obtained for a model with geometrical stiffness matrix of uncracked elements.

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