LQG Control and Robustness Study for a Prestressed Membrane With Bimorph Actuators

2014 ◽  
Author(s):  
Ipar Ferhat ◽  
Cornel Sultan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Nominal System ◽  
Order Form ◽  
Lqg Control ◽  
Bimorph Actuators ◽  
Element Method

Linear Quadratic Gaussian (LQG) control is developed for a prestressed square membrane with bimorph actuators attached to it. The membrane is modeled using the finite element method and the membrane is assumed to be clamped on all edges. After obtaining the mass, damping, stiffness and input matrices in second order form using the weak form Finite Element Method (FEM), the problem is represented in first order form to develop the LQG controller. To study the robustness of the system, the control and observer gain matrices developed for the nominal system are applied to systems obtained from the nominal system by modifying material properties and prestress.

A Lagrangian Uniform-Mesh Finite Element Method Applied to Problems Governed by Poisson’s Equation

2007 ◽  
Author(s):  
Linxia Gu ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Lagrangian Formulation ◽  
Uniform Mesh ◽  
Interpolation Function ◽  
Step Functions ◽  
Surface Integration ◽  
Interpolation Functions ◽  
Element Method

A method is presented for the solution of Poisson’s Equations using a Lagrangian formulation. The interpolation functions are the Lagrangian operation of those used in the classical finite element method, which automatically satisfy boundary conditions exactly even though there are no nodes on the boundaries of the domain. The integration is introduced in an implicit way by using approximated step functions. Classical surface integration terms used in the weak form are unnecessary due to the interpolation function in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplified the connection between the mesh and the solid structures, thus providing a very easy way to solve the problems without a conforming mesh.

A Gradient Weighted Finite Element Method (GW-FEM) for Static and Quasi-Static Electromagnetic Field Computation

2019 ◽  
Vol 17 (06) ◽  
pp. 1950017 ◽  
Author(s):  
Bingxian Tang ◽  
She Li ◽  
Xiangyang Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Weak Form ◽  
Electromagnetic Problems ◽  
Tetrahedral Elements ◽  
Field Computation ◽  
Analytical Results ◽  
Element Method

This paper presented a Gradient Weighted Finite Element Method (GW-FEM) for solving electromagnetic problems. First, the analysis domain is discretized into a set of triangular or tetrahedral elements which are easy to automatically generate. Then, Gradient Weighted influence domains are further constructed by the center element with all the adjacent elements. The Galerkin Weak form is evaluated based on these influence domains. The GW-FEM is employed here for the solution of static and quasi-static electromagnetic problems by using linear triangular or tetrahedral elements. All the properties of GW-FEM are proved theoretically and analyzed in detail. Consistency between four benchmark results is obtained by GW-FEM and analytical results verify the accuracy, stability, and potential of this method. It turns out that GW-FEM possesses potentials in the applications of electromagnetic problems.

Weak Form Quadrature Element Method and Its Applications in Science and Engineering: A State-of-the-Art Review

2017 ◽  
Vol 69 (3) ◽  
Author(s):  
Xinwei Wang ◽  
Zhangxian Yuan ◽  
Chunhua Jin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
State Of The Art ◽  
Past Research ◽  
Weak Form ◽  
Spectral Element ◽  
General Interest ◽  
Science And Engineering ◽  
Quadrature Element Method ◽  
Element Method

The weak form quadrature element method (QEM) combines the generality of the finite element method (FEM) with the accuracy of spectral techniques and thus has been projected by its proponents as a potential alternative to the conventional finite element method. The progression on the QEM and its applications is clear from past research, but this has been scattered over many papers. This paper presents a state-of-the-art review of the QEM employed to analyze a variety of problems in science and engineering, which should be of general interest to the community of the computational mechanics. The difference between the weak form quadrature element method (WQEM) and the time domain spectral element method (SEM) is clarified. The review is carried out with an emphasis to present static, buckling, free vibration, and dynamic analysis of structural members and structures by the QEM. A subroutine to compute abscissas and weights in Gauss–Lobatto–Legendre (GLL) quadrature is provided in the Appendix.

scholarly journals Full-Discrete Weak Galerkin Finite Element Method for Solving Diffusion-Convection Problem.

2017 ◽  
Vol 13 (4) ◽  
pp. 7733-7345
Author(s):  
Asmaa Hamdan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Derivative ◽  
Main Idea ◽  
Weak Form ◽  
Diffusion Problem ◽  
Weak Galerkin ◽  
Weak Derivatives ◽  
Diffusion Convection ◽  
Element Method

This paper applied and analyzes full discrete weak Galerkin (WG) finite element method for non steady two dimensional convection-diffusion problem on conforming polygon. We approximate the time derivative by backward finite difference method and the elliptic form by WG finite element method. The main idea of WG finite element methods is the use of weak functions and their corresponding discrete weak derivatives in standard weak form of the model problem. The theoretical evidence proved that the error estimate in  norm, the properties of the bilinear form, (v-elliptic and continuity), stability, and the energy conservation law.

A Two-Step Taylor Galerkin Smoothed Finite Element Method for Lagrangian Dynamic Problem

2015 ◽  
Vol 12 (04) ◽  
pp. 1540004 ◽  
Author(s):  
Xiang Yang Cui ◽  
Shu Chang ◽  
Guang Yao Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Two Dimensional ◽  
Mesh Distortion ◽  
Smoothed Finite Element Method ◽  
System Equations ◽  
The Stability ◽  
Lagrangian Dynamic ◽  
Element Method

In this paper, a two-step Taylor Galerkin smoothed finite element method (TG-SFEM) is presented to deal with the two-dimensional Lagrangian dynamic problems. In this method, the smoothed Galerkin weak form is employed to create discretized system equations, and the cell-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stability and the adaptation of elements aberrations presented in the two-step TG-SFEM are studied through detailed analyses of numerical examples. In the analysis of wave propagation, the proposed method can provide smoother displacement and stress than the common SFEM does, and energy fluctuations are found to be minimal. In the large deformation problems, the TG-SFEM can acclimatize itself to the mesh distortion effectively and stay bounded for long durations because the isoparametric elements are replaced, and area integration over each smoothing cells is recast into line integration along edges and no mapping is needed. Therefore, the stability, flexibility of elements distortion and the property of energy conservation of the TG-SFEM applied on two-dimensional solid problems are well represented and clarified.

Study of Numerical Problem Based on the Extended Finite Element Method

2012 ◽  
Vol 472-475 ◽  
pp. 1623-1626
Author(s):  
Di Zhang ◽  
Feng Wang ◽  
Hui Xu
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Extended Finite Element Method ◽  
Weak Form ◽  
Balance Equations ◽  
Extended Finite Element ◽  
Crack Problems ◽  
Element Method

The extended finite element method (XFEM) provides an effective tool for analyzing crack problems.The control equations and the weak form can be established through balance equations ,boundary condition, geometry equations,etc.After the establishment of stiffness matrix,the crack problems can be solved by XFEM conveniently.

scholarly journals An efficient finite element method and error analysis for eigenvalue problem of Schrödinger equation with an inverse square potential on spherical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yubing Sui ◽  
Donghao Zhang ◽  
Junying Cao ◽  
Jun Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Original Problem ◽  
Eigenvalue Problems ◽  
Weak Form ◽  
Spherical Coordinate ◽  
One Dimensional ◽  
Spherical Domain ◽  
Element Method

Abstract We provide an effective finite element method to solve the Schrödinger eigenvalue problem with an inverse potential on a spherical domain. To overcome the difficulties caused by the singularities of coefficients, we introduce spherical coordinate transformation and transfer the singularities from the interior of the domain to its boundary. Then by using orthogonal properties of spherical harmonic functions and variable separation technique we transform the original problem into a series of one-dimensional eigenvalue problems. We further introduce some suitable Sobolev spaces and derive the weak form and an efficient discrete scheme. Combining with the spectral theory of Babuška and Osborn for self-adjoint positive definite eigenvalue problems, we obtain error estimates of approximation eigenvalues and eigenvectors. Finally, we provide some numerical examples to show the efficiency and accuracy of the algorithm.

BUCKLING ANALYSIS OF PLANAR FRAMEWORKS USING THE QUADRATURE ELEMENT METHOD

2011 ◽  
Vol 11 (02) ◽  
pp. 363-378 ◽  
Author(s):  
H. ZHONG ◽  
R. ZHANG ◽  
H. YU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Sections ◽  
Computational Efficiency ◽  
Variational Formulation ◽  
Weak Form ◽  
Buckling Analysis ◽  
The Finite Element Method ◽  
Quadrature Element Method ◽  
Element Method

The recently proposed weak form quadrature element method (QEM) is applied to the buckling analysis of planar frameworks. This method starts with approximation of the integrands in the weak form description (variational formulation) of a problem. Neither the nodes nor the number of nodes in a quadrature element is fixed, being adjustable according to convergence need. Examples are presented and comparison with the results of the finite element method is made to demonstrate the effectiveness and computational efficiency of the QEM. It is shown that the QEM is suitable for buckling analysis of planar frameworks with either varying or constant cross sections.

Finite Element Method Simulation of 35# Steel Cathodic Protection Models in the Seawater

2009 ◽  
Vol 79-82 ◽  
pp. 1153-1156 ◽  
Author(s):  
Hu Yuan Sun ◽  
Wei Wang ◽  
Li Juan Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cathodic Protection ◽  
Simulated Data ◽  
Finite Element Method Simulation ◽  
Weak Form ◽  
Physical Models ◽  
Sacrificial Anode ◽  
35 Steel ◽  
Element Method

Physical models of cathodic protection (CP) for copper protected by 35# steel and for 35# steel protected by aluminum sacrificial anode respectively in seawater were built in this study. Weak form of Laplace equation was deduced to make finite element method (FEM) numerical calculation conveniently. Then, potential distribution of each physical model was computed by FEM following with measured experiments for validation. Typical FEM simulated data along X-axis and Y-axis of physical models agree well with measured experimental data. For 35# steel protected by aluminum sacrificial anode models, normal cathodic protection, over-protected (OP) and under-protected (UP) models were built, respectively. The results demonstrated that it should be feasible of CP for copper by 35# steel and for 35# steel by aluminum sacrificial anode respectively, and FEM could afford well forecast for CP design in engineering.

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