Modeling the Multiphysics Wrinkling Instability of Ionic Polymer Composite Plates for Artificial Muscle Applications

2016 ◽  
Author(s):  
John G. Michopoulos ◽  
Athanasios P. Iliopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polymer Composite ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Artificial Muscle ◽  
Composite Plates ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Ionic Polymer

In this paper we first present the derivation of the governing equations that describe the multiphysics behavior of Ionic Polymer Composite Plates (IPMC). This is done in a manner that accounts for their non-linear large deflection deformation under the influence of mechanical, electrical, thermal and multicomponent mass transport fields. We subsequently present numerical solutions of the system of these equations via the use of the finite element method for a case of a specific rectangular plate. Emphasis is given in identifying the multiphysics based wrinkling instability behavior that manifest near the corners of these plates due to multiphysics stimuli.

Dynamic Instability of Delaminated Composite Plates under Parametric Excitation

2006 ◽  
Vol 326-328 ◽  
pp. 1765-1768 ◽  
Author(s):  
Meng Kao Yeh ◽  
Kuei Chang Tung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Excitation ◽  
Composite Plate ◽  
Dynamic Instability ◽  
Composite Plates ◽  
Modal Parameters ◽  
The Finite Element Method ◽  
Electromagnetic Device ◽  
Instability Regions

The dynamic instability behavior of delaminated composite plates under transverse excitations was investigated experimentally and analytically. An electromagnetic device, acting like a spring with alternating stiffness, was used to parametrically excite the delaminated composite plates transversely. An analytical method, combined with the finite element method, was used to determine the instability regions of the delaminated composite plates based on the modal parameters of the composite plate and the position, the stiffness of the electromagnetic device. The delamination size and position of composite plates were varied to assess their effects on the excitation frequencies of simple and combination resonances in instability regions. The experimental results were found to agree with the analytical ones.

Linearization of the finite element method for gradient flows by Newton’s method

2020 ◽  
Author(s):  
Georgios Akrivis ◽  
Buyang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Solutions ◽  
Resolvent Estimate ◽  
Optimal Order ◽  
Gradient Flows ◽  
The Finite Element Method ◽  
Element Method

Abstract The implicit Euler scheme for nonlinear partial differential equations of gradient flows is linearized by Newton’s method, discretized in space by the finite element method. With two Newton iterations at each time level, almost optimal order convergence of the numerical solutions is established in both the $L^q(\varOmega )$ and $W^{1,q}(\varOmega )$ norms. The proof is based on techniques utilizing the resolvent estimate of elliptic operators on $L^q(\varOmega )$ and the maximal $L^p$-regularity of fully discrete finite element solutions on $W^{-1,q}(\varOmega )$.

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

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