Element Stiffness Matrix Integration in Image-Based Cartesian Grid Finite Element Method

2014 ◽  
pp. 304-315 ◽  
Author(s):  
Luca Giovannelli ◽  
Juan J. Ródenas ◽  
José M. Navarro-Jimenez ◽  
Manuel Tur
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Cartesian Grid ◽  
Element Stiffness Matrix ◽  
Element Method

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

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.

On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading

1983 ◽  
Vol 50 (1) ◽  
pp. 95-100 ◽  
Author(s):  
H. A. Mang ◽  
R. H. Gallagher
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Stiffness Matrix ◽  
Circular Cylindrical Shell ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Buckling Loads ◽  
Large Rotations ◽  
Element Method

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.

scholarly journals Circular Space Curve Frame (3D) with any Load and Spring Supports by Transfer Matrix Method and Finite Element Method

2019 ◽  
Vol 8 (12) ◽  
pp. 3981-3987
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Complex Problem ◽  
Fem Method ◽  
Circular Space ◽  
Element Method

In this paper, authors present a new numerical method, combining the Transfer Matrix Method and Finite Element Method (TMM - FEM), to analyze spatially circular curved bar, with general load and elastic support. Analysis space curved bar is complex problem because conventional methods will not simultaneously calculate the entire structure, or difficulty in establish the stiffness matrix, or the size of stiffness matrix is too large due to multiple elements. TMM - FEM method is proposed to promote the advantages of each method. Due to being directly generated from the parametric equations of the bar axis, the analytical results are accurate. Results are programed in Matlab and verified with SAP2000 programe.

scholarly journals EXAMPLE OF GRAGUAL TRANSFORMATION OF STIFFNESS MATRIX AND MAIN SET OF EQUATIONS AT ADDITIONAL FINITE ELEMENT METHOD

2020 ◽  
Vol 16 (2) ◽  
pp. 14-25
Author(s):  
Anna Ermakova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Limit State ◽  
Ultimate Limit State ◽  
Nonlinear Properties ◽  
Design Diagram ◽  
Ultimate Limit ◽  
Gradual Transformation ◽  
Element Method

The paper considers the example of gradual transformation of the stiffness matrix and the main set of equations at Additional Finite Element Method (AFEM). It is corresponded to the increase of load and the ideal failure model of structure. AFEM uses the additional design diagrams and additional finite elements (AFE) for this operation. This process is illustrated by the transformation of design diagram of bended concrete console from the beginning of its loading to the collapse. The structure reveals four physical nonlinear properties before the ultimate limit state. Every nonlinear property appears under the action of corresponded load. The stiffness matrix and the set of equations are changed under influence of the value of load and the presence of observed nonlinear properties at this moment.

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