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.

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.

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.

scholarly journals Behavior of Interfaces between Granular Soil and Structure: A State-of-the-art Review

2015 ◽  
Vol 9 (1) ◽  
pp. 213-223 ◽  
Author(s):  
Yao-Kun Li ◽  
Xiao-Lei Han ◽  
Jing Ji ◽  
Dong-Long Fu ◽  
Yan-Kun Qiu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Future Development ◽  
State Of The Art ◽  
Constitutive Relations ◽  
Granular Soil ◽  
Structural Components ◽  
The Finite Element Method ◽  
Numerical Techniques ◽  
Element Method

A state-of-the-art review of the behavior of interfaces between granular materials and solid structural components is presented. The review includes both the experimental and theoretical researches on the interfaces between soils and steel, as well as those between soils and concrete. Development of constitutive relations of such interfaces is also summarized. Furthermore, numerical techniques, both the Finite Element Method and the Discrete Element Method (DEM), to simulate the interface behaviors are stated. Aspects for future development in this area are also included.

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.

scholarly journals Analisis Pondasi Tiang Pancang Theematic Mall dan Hotel Majalaya Bandung

2020 ◽  
Vol 17 (2) ◽  
pp. 57-65
Author(s):  
Arip Yusup ◽  
Eko Walujodjati
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
State Of The Art ◽  
Pile Cap ◽  
Element Method

Salah satu pondasi dalam adalah pondasi tiang pancang, pondasi ini digunakan pada Proyek Theematic Mall dan Hotel Majalaya-Bandung. Penelitian ini bertujuan untuk menganalisis pondasi yang ada pada proyek tersebut. Analisis pembebanan yang diperhitungkan mengacu pada SNI 1727-2013. Perencanaan pembebanan mengunakan program analis struktur yang menghadirkan state of the art dalam teknologi tiga dimensi finite element method bagi struktur teknik dan untuk perhitungan pondasi mengunakan metode Begemann dan Borms dengan mengunakan data kekuatan bahan hasil uji tanah SPT dan CPT untuk tiang pancang, untuk kekuatan Pondasi pilecap mengunakan SNI-03-2847-2002. Berdasarkan dari hasil analisis dan data tanah didapatkan tahanan aksial *Pn=720,96 Kn dan tahanan lateral tiang pancang * Hn = 27,14 kn. Untuk tahanan geser tinjauan pondasi telapak/pile cap arah y Vc*  = 2274,3 kn, arah x Vc* =2173,5 kn dan tinjauan dua arah   Vnp= 12012 kn. Untuk perhitungan penulangan pile cap didapatkan hasil analisis yang lebih besar daripada yang dilapangan yaitu As= 18480 mm2 (analisis) dan As = 9575,89 mm2 (lapangan), dikarenakan pada hasil analisis perhitungan dilapangan didapatkan nilai tahanan aksial dan lateral lebih kecil daripada hasil analisis.

Complex Fractional-Spectral Method for Space Curved Struts: Theory and Application

1997 ◽  
Vol 12 (2) ◽  
pp. 59-67 ◽  
Author(s):  
A.M. Horr ◽  
L.C. Schmidt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Structural Systems ◽  
Temperature Dependent ◽  
Large Structures ◽  
Damping Characteristics ◽  
Stability And Accuracy ◽  
Element Method

Based on the theory of fractional calculus and the complex spectral theory of vibration, a new spectrally-formulated finite-element method of analysis is developed which is capable of making accurate predictions of the dynamic response of damped structures with curved struts. The frequency-dependent and temperature-dependent damping characteristics of structural materials can be modelled accurately using the fractional derivative model. The main features of the complex-spectral element method of analysis are presented in this paper. Although most structural systems can be analysed and designed by using the conventional finite element method, in order to guarantee stability and accuracy of the solution the number of elements used to model the structure may be very large. Hence, it appears that, for large structures, it may be more effective to use the spectral approach presented in this paper.

Fuzzy Finite Element Method in Diffusion Problems

2014 ◽  
pp. 309-328 ◽  
Author(s):  
S. Chakraverty ◽  
S. Nayak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Transfer Fluid ◽  
Uncertain Differential Equation ◽  
Science And Engineering ◽  
Physical Problems ◽  
Interval Finite Element Method ◽  
Real Practice ◽  
Diffusion Problems ◽  
Element Method

Diffusion is an important phenomenon in various fields of science and engineering. It may arise in a variety of problems viz. in heat transfer, fluid flow problem and atomic reactors etc. As such these diffusion equations are being solved throughout the globe by various methods. It has been seen from literature that researchers have investigated these problems when the material properties, geometry (domain) etc. are in crisp (exact) form which is easier to solve. But in real practice the parameters used in the modelled physical problems are not crisp because of the experimental error, mechanical defect, measurement error etc. In that case the problem has to be defined with uncertain parameters and this makes the problem complex. In this chapter related uncertain differential equation of various diffusion problems will be investigated using finite element method, which may be called fuzzy or interval finite element method.

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