scholarly journals Finite element modelling of moving loads on structures

2021 ◽  
Author(s):  
Gareth Forbes
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Moving Load ◽  
Equations Of Motion ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Structure Development ◽  
Simply Supported ◽  
Ansys Apdl ◽  
Element Method

This paper provides a breif description of the moving load problem (force or mass) across a structure. Development of a matlab script to solve the analytical equations of motion is provided. The method of implementation to solve this type of structural dynamics, using the Finite Element Method is then described with a matlab script for a simply supported beam provided. Additionally, a script and method for implementing the Finite Element Method using ANSYS APDL is also given.

Finite Element Models for Flexible Cosserat Solids

2020 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Minghe Shan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Displacement Vector ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Discrete Equations ◽  
Computation Efficiency ◽  
Elasticity Problems ◽  
Element Method

Abstract The application of the finite element method to the modeling of Cosserat solids is investigated in detail. In two- and three-dimensional elasticity problems, the nodal unknowns are the components of the displacement vector, which form a linear field. In contrast, when dealing with Cosserat solids, the nodal unknowns form the special Euclidean group SE(3), a nonlinear manifold. This observation has numerous implications on the implementation of the finite element method and raises numerous questions: (1) What is the most suitable representation of this nonlinear manifold? (2) How is it interpolated over one element? (3) How is the associated strain field interpolated? (4) What is the most efficient way to obtain the discrete equations of motion? All these questions are, of course intertwined. This paper shows that reliable schemes are available for the interpolation of the motion and curvature fields. The interpolated fields depend on relative nodal motions only, and hence, are both objective and tensorial. Because these schemes depend on relative nodal motions only, only local parameterization is required, thereby avoiding the occurrence of singularities. For Cosserat solids, it is preferable to perform the discretization operation first, followed by the variation operation. This approach leads to considerable computation efficiency and simplicity.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

Finite Element Analysis of Vibration of Toroidal Field Coils Coupled With Laplace Transform

1982 ◽  
Vol 49 (3) ◽  
pp. 594-600 ◽  
Author(s):  
K. Miya ◽  
M. Uesaka ◽  
F. C. Moon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Laplace Transform ◽  
Equations Of Motion ◽  
Toroidal Field ◽  
Inverse Laplace Transform ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Original Domain ◽  
Element Method

A numerical analysis of a vibration of toroidal field coils in a magnetic fusion reactor is shown here on the basis of the finite element method coupled with Laplace transform. Lagrangian consisting of kinetic, elastic strain, and magnetic energies was utilized to deduce equations of motion of the coils. The equations were solved numerically by applying the Laplace transform to a formulation with respect to time and the finite element method to one with respect to space. The Fast Fourier Transform algorithm was utilized for a calculation of the inverse Laplace transform to obtain a nodal vector of the coil’s displacement in the original domain. Numerical results reasonably explain a dependency of the coil current on a frequency of the coil.

Active Vibration Quenching Using Inverse Dynamics

1995 ◽  
Author(s):  
Thomas A. Trautt ◽  
Eduardo Bayo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Frequency Domain ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Input Function ◽  
Degree Of Freedom ◽  
The Finite Element Method ◽  
Simply Supported ◽  
Active Vibration

Abstract An inverse dynamics algorithm is derived for active vibration quenching of structures. The algorithm uses frequency domain technicques to compute an input function needed to produce a desired response at a particular degree of freedom. The desired response is a transition from the initial vibrating condition to a non-vibrating condition. The algorithm can also be used to modify the input function to correct for system disturbances while the input function is already being applied to the system. The algorithm is demostrated in a simulation of a simply supported beam controlled by a torque actuator at one end of the beam. The finite element method is used to discretize the equations of motion of the beam.

scholarly journals Vibration Analysis of Collecting Electrodes by means of the Hybrid Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
I. Adamiec-Wójcik ◽  
J. Awrejcewicz ◽  
A. Nowak ◽  
S. Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electrostatic Precipitator ◽  
Equations Of Motion ◽  
The Body ◽  
The Finite Element Method ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Rigid Finite Element Method ◽  
Element Method

The paper presents a hybrid finite element method of shell modeling in order to model collecting electrodes of electrostatic precipitators. The method uses the finite element method to reflect elastic features and the rigid finite element method in order to model mass features of the body. A model of dust removal systems of an electrostatic precipitator is presented. The system consists of two beams which are modeled by means of the rigid finite element method and a system of collecting shells modeled by means of the hybrid finite element method. The paper discusses both the procedure of deriving the equations of motion and the results of numerical simulations carried out in order to analyze vibrations of the whole system. Experimental verification of the model is also presented.

scholarly journals Analysis of vibration of beams with regularly located openings

2021 ◽  
pp. 22-28
Author(s):  
А.И. Притыкин
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Comparative Analysis ◽  
Natural Frequencies ◽  
The Finite Element Method ◽  
Program Complex ◽  
Simply Supported ◽  
Analytical Relations ◽  
Element Method

В справочной литературе содержатся расчетные зависимости для частот свободных колебаний балок со сплошной стенкой, но отсутствуют данные по собственным колебаниям перфорированных балок. В то же время в судостроении и строительной практике широко распространены балки с перфорированной стенкой, содержащей вырезы круглой, овальной и прямоугольной формы. В статье проведен анализ влияния вырезов на частоту свободных колебаний перфорированных свободно опертых балок. При этом первоначально рассматривались балки со сплошной стенкой, а затем балки таких же размеров с вырезами. Для удобства практических вычислений известная зависимость была трансформирована к виду, позволяющему оценить частоту колебаний только по соотношению площадей полки и стенки и габаритным размерам балки без необходимости определения ее момента инерции и погонной массы. Аналогичные зависимости были получены и для перфорированных балок с круглыми и прямоугольными вырезами, в которых дополнительными факторами являлись параметры перфорации: относительная высота вырезов и относительная ширина перемычек. При отсутствии вырезов формулы для перфорированных балоксводятся к формуле для балки со сплошной стенкой.Сравнительный анализ частот проводился путем расчета по аналитическим зависимостям и методом конечных элементов с использованием программного комплекса ANSYS. На основе проведенного анализа сделан вывод, что наличие регулярно расположенных вырезов с высотой, не превышающей рекомендации Морского Регистра РФ, в зависимости от параметров перфорации приводит к разному повышению частот собственных колебаний однопролетных балок, хотя степень их повышения невелика. Предложенные аналитические зависимости для балок разного конструктивного оформления удовлетворительно согласуются с результатами расчетов МКЭ. In manual on the ship structural mechanics the analytical relations for determination of the natural frequencies of the beams with solid web are given, but there are no data about proper vibration of perforated beams. At the same time in shipbuilding and in structural industry the perforated beams with circular, rectangular and oval openings are widely used. In this article the analysis of influence of openings on the natural frequencies of the simply supported perforated beams is performed. Initially it was considered beams with solid web and then beams of the same dimensions with openings. For commodity of practical calculations, the well-known relation was transformed to the form allowing to appreciate frequency of vibration only with knowledge of ratio of areas of shelves and web without necessity of finding their moment of inertia and running mass of beam. Similar relations were obtained for perforated beams with circular and rectangular openings, in which additional arguments were such parameters of perforation as related depth of openings and related width of web-posts. In case of absence of openings, the formulas for perforated beams are reduced to formula for beam with solid web. Comparative analysis was performed by calculations according to analytical relations and with the finite element method using the program complex ANSYS. On base of performed analysis it was made conclusion that existence of regularly located openings with depth not extending recommendations of Russian Maritime Register, in dependence on parameters of perforation brings to different increasing of natural frequencies of vibration of one span beams, although degree of this increasing is not high. Suggested analytical relations for beams of different constructive design are in a good correlation with results obtained by the finite element method.

A Comparison of Computed Deflections of Symmetric Angle-Ply Laminate Plates by the Ritz Method and the Finite Element Method

2014 ◽  
Author(s):  
Kenneth Carroll ◽  
Ernesto Gutierrez-Miravete
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Composite Laminates ◽  
Ritz Method ◽  
The Finite Element Method ◽  
Symbolic Manipulation ◽  
Transverse Loading ◽  
Simply Supported ◽  
Element Method

When a simply supported composite plate is subjected to a lateral load, the presence of the twist coupling stiffnesses in the governing differential equations of equilibrium does not allow the determination of an exact solution for the deflection and numerical methods must be used. This paper describes a comparison of computed approximations to the deflection of composite laminates subjected to transverse loading obtained using the Ritz method and the finite element method. The Ritz method is implemented with the symbolic manipulation program Maple and ANSYS is used to perform the finite element calculations. Reliable results are obtained using both methods.

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