MICRO-FINITE ELEMENT MODELING OF WRINKLE FORMATION FOR CELL LOCOMOTION APPLICATIONS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350019 ◽  
Author(s):  
HADI MOHAMMADI ◽  
WALTER HERZOG ◽  
KIBRET MEQUANINT
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Numerical Procedure ◽  
Elastic Membrane ◽  
Membrane Thickness ◽  
Thin Membrane ◽  
The Finite Element Method ◽  
A Cell ◽  
Equivalent Nodal Forces

We developed a generic numerical procedure using the finite element method (FEM) for modeling wrinkles on an elastic thin membrane. The geometric characterization of wrinkles formed in an elastic membrane, which is caused by a crawling cell, may help in understanding the forces acting between a cell and its compliant substrate. In this study, the equivalent nodal forces, obtained from the virtual changes in the element internal energy, were differentiated to calculate the stiffness matrix. Micro-wrinkles can be computed as a function of membrane thickness which affects the stiffness matrix. This model may be used for applications in cell mechanobiology.

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

scholarly journals A characterization of supersmoothness of multivariate splines

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
Michael S. Floater ◽  
Kaibo Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Order ◽  
Maximal Order ◽  
Spline Functions ◽  
Multivariate Splines ◽  
The Finite Element Method ◽  
Polynomial Splines ◽  
Element Method

Abstract We consider spline functions over simplicial meshes in $\mathbb {R}^{n}$ ℝ n . We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of smoothness at a vertex, a property known as supersmoothness, which plays a role in the construction of multivariate splines and in the finite element method. In this paper, we characterize supersmoothness in terms of the degeneracy of spaces of polynomial splines over the cell of simplices sharing the vertex, and use it to determine the maximal order of supersmoothness of various cell configurations.

A Maxwell's Second Equation Approach to the Finite Element Method Applied to Magnetic Field Determination

1987 ◽  
Vol 24 (3) ◽  
pp. 259-272 ◽  
Author(s):  
José Roberto Cardoso
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Undergraduate Students ◽  
Engineering Students ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Cad Cam ◽  
New Formulation ◽  
The Galerkin Method ◽  
Element Method

The burst of modern computing systems like CAD/CAM has given rise to the use of the finite element method (FEM), which is, at present, the most used numerical procedure in the determination of fields in continuous media. Undergraduate students find difficulty in understanding the usual way of demonstrating FEM by variational analysis or the Galerkin method. This paper introduces a new formulation of FEM, based on a direct application of Maxwell's second equation, which can be easily understood by undergraduate engineering students.

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.

Rigorous characterization of surface plasmon modes by using the finite element method

2011 ◽  
Author(s):  
B. M. A. Rahman ◽  
H. Tanvir ◽  
N. Kejalakshmy ◽  
A. Quadir ◽  
K. T. V. Grattan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Surface Plasmon ◽  
The Finite Element Method ◽  
Plasmon Modes ◽  
Element Method

Characterization of metal-clad TE/TM mode splitters using the finite element method

1997 ◽  
Vol 15 (12) ◽  
pp. 2264-2269 ◽  
Author(s):  
M. Rajarajan ◽  
C. Themistos ◽  
B.M.A. Rahman ◽  
K.T.V. Grattan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Tm Mode ◽  
Element Method

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.

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