scholarly journals Dynamic Response of a Beam Due to an Accelerating Moving Mass Using Moving Finite Element Approximation

2011 ◽  
Vol 16 (1) ◽  
pp. 171-182 ◽  
Author(s):  
İsmail Esen
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Moving Mass ◽  
Moving Finite Element

Dynamic Response of an Overhead Crane Beam Due to a Moving Mass Using Moving Finite Element Approximation

2010 ◽  
Vol 450 ◽  
pp. 99-102 ◽  
Author(s):  
Ismail Gerdemeli ◽  
Ismail Esen ◽  
Derya Özer
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Mass Velocity ◽  
Beam Deflection ◽  
Element Approximation ◽  
Moving Mass ◽  
Overhead Crane ◽  
Mass Ratio ◽  
Beam System ◽  
Moving Finite Element

In this study, dynamic behaviour of a beam system of an overhead crane is investigated. A MATLAB code is developed for numerical analyses. The moving mass on the beam is modelled as a moving finite element to include inertial effects of mass. Dynamic response of the beam is obtained depending on the mass ratio between load and beam mass. Besides, a variety of mass velocities are considered. Analysis are carried out considering mass ratio (mass of the load/mass of the beam m/M) as 0.1, 0.2, 0.4, 0.6, 0.8 and 1 and mass velocities as 1, 2, 4, 8, and 12.5 m/s. Dynamic response of the beam depends on velocity and mass of moving load. As the position of the moving mass in the span changes, it alters the natural frequency of the beam system. Generally, if the mass velocity increases, maximum beam deflection occurs far from the beam midpoint. For some values of the velocity, the maximum response may occur before the beam midpoint. At very high speeds, the maximum beam deflection occurs near the beam endpoint. At very slow speeds, the maximum beam deflection occurs near the midpoint because the system reduces to a quasi-static solution. At the same mass ratio, load velocity increases, with the increment of the beam deflection. Both mass velocity and mass ratio affects the dynamic response of the beam but the effect of velocity is greater than the mass ratio.

An Angular Finite Element Method for the Solution of the Even-Parity Equation

2009 ◽  
Author(s):  
R. Becker ◽  
R. Koch ◽  
M. F. Modest ◽  
H.-J. Bauer
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Basis Functions ◽  
New Method ◽  
Discrete Ordinates ◽  
Test Case ◽  
Element Approximation ◽  
Promising Alternative ◽  
Element Discretization ◽  
Spatial Coordinates

The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.

Finite Element Approximation of the p-Laplacian

1993 ◽  
Vol 61 (204) ◽  
pp. 523 ◽  
Author(s):  
John W. Barrett ◽  
W. B. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation
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