Numerical experiments in quantum physics: Finite‐element method

1988 ◽  
Vol 56 (5) ◽  
pp. 444-448 ◽  
Author(s):  
Debra J. Searles ◽  
Ellak I. von Nagy‐Felsobuki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Quantum Physics ◽  
Element Method

Approximation of the Vibration Modes of a Plate and Shells Coupled With a Fluid

2006 ◽  
Vol 73 (6) ◽  
pp. 1005-1010 ◽  
Author(s):  
E. Hernández
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compressible Fluid ◽  
Numerical Experiments ◽  
Vibration Modes ◽  
Solid Interface ◽  
Thin Structure ◽  
Fluid Equations ◽  
Element Method

We consider a method to compute the vibration modes of an elastic thin structure (shell or plate) in contact with a compressible fluid. For the structure, the classical Naghdi equations, based on the Reissner–Mindlin hypothesis, are considered and its approximation using the mixed interpolation of tensorial component 4 finite element method. The fluid equations are discretized by using Raviart–Thomas elements, and a non-conforming coupling is used on the fluid-solid interface. Numerical experiments are reported, assessing the efficiency of this coupled scheme.

scholarly journals A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Enxi Zheng ◽  
Fuming Ma ◽  
Yujie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Numerical Experiments ◽  
Bessel Functions ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Rectangular Cavity ◽  
Total Field ◽  
Element Method

This paper is concerned with the scattering problem of a rectangular cavity. We solve this problem by a least-squares nonpolynomial finite element method. In the method, we use Fourier-Bessel functions to capture the behaviors of the total field around corners. And the scattered field towards infinity is represented by a combination of half-space Green functions. Then we analyze the convergence and give an error estimate of the method. By coupling the least-squares nonpolynomial finite element method and the Newton method, we proposed an algorithm for the inverse scattering problem. Numerical experiments are presented to show the effectiveness of our method.

scholarly journals A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Ali R. Soheili ◽  
J. Naghipoor ◽  
S. A. Ahmadian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Burger Equation ◽  
Time Dependent ◽  
Piecewise Polynomial ◽  
Two Space Dimensions ◽  
Time Dependent Problems ◽  
Element Method ◽  
Moving Finite Element

A gradient weighted moving finite element method (GWMFE) based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation.

scholarly journals Modeling a Dynamic Response at Resonant Vibrations of an Elongated Plate with an Integral Damping Coating

2020 ◽  
pp. 74-86
Author(s):  
V N Paimushin ◽  
V A Firsov ◽  
V M Shishkin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Dynamic Response ◽  
Viscoelastic Properties ◽  
Numerical Experiments ◽  
Vibration Frequencies ◽  
Damping Properties ◽  
Reinforcing Layer ◽  
Element Method

Classical methods of surface damping using free and constraining damping layers are discussed. The structure of a perspective integrated version of a damping coating is presented. This integral damping coating consists of two layers of a material with pronounced viscoelastic properties, between which there is a thin reinforcing layer of a high modulus material. A generalization of the Thompson-Kelvin-Voigt model is given for the description of viscoelastic properties of the material under tension-compression in the case of a complex stress state. A finite-element method was developed to determine the dynamic response of an elongated plate with the integral damping coating. This method is based on a four-layer finite element with 14 degrees of freedom: the main material is within the Kirchhoff-Love's model, the damping layers are in a flat stress state, the reinforcing layer perceives tension and compression. This model allows us to take into account the effect of transverse compression of the damping layers of the plate, which significantly increases its damping properties at high vibration frequencies. The stiffness matrices, the damping matrices, and the mass matrices of the constituent layers aim at obtaining similar complete matrices of a finite element. A system of resolving equations was obtained on the basis of the Lagrange equations of the second kind with respect to the vector of nodal displacements of the finite element model of the plate with an arbitrary dynamic load. In the case of a harmonic load with a frequency that coincides with one of the frequencies of free vibrations of the plate, a transition to a modal equation with respect to the normal coordinate corresponding to the given frequency is possible. Numerical experiments were carried out to test the developed finite element method using the example of a hingedly supported elongated plate with an integral damping coating. The numerical experiments showed a qualitative change in the composition of stresses in the damping layers of the plate at high vibration frequencies, which significantly affects its damping properties.

The Numerical Simulation of Workpiece Clamping

2014 ◽  
Vol 474 ◽  
pp. 218-223 ◽  
Author(s):  
Jarmila Oravcová
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Simulation Models ◽  
Contact Points ◽  
Reaction Forces ◽  
The Creation ◽  
Made In ◽  
Element Method

The paper deals with the effects of clamping forces on the workpiece during clamping fixture. It describes an experiment using numerical simulation. With numerical experiments we wanted to find out displacement of basic points of the model and changes in the reaction forces in contact points. In the experiment it was considered with initial inaccuracies of contact points. Verification of their effect was made on simulation models of workpieces, which were made in software ANSYS. The creation of the model was used finite element method.

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