scholarly journals Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jungho Park ◽  
Ilwook Park ◽  
Usik Lee
Keyword(s):  
Transverse Vibration ◽  
Splitting Method ◽  
Element Model ◽  
Spectral Element ◽  
Arbitrary Boundary ◽  
Modeling And Analysis ◽  
One Dimensional ◽  
Proposed Model ◽  
Standard Finite Element Method ◽  
Element Method

Although the spectral element method (SEM) has been well recognized as an exact continuum element method, its application has been limited mostly to one-dimensional (1D) structures, or plates that can be transformed into 1D-like problems by assuming the displacements in one direction of the plate in terms of known functions. We propose a spectral element model for the transverse vibration of a finite membrane subjected to arbitrary boundary conditions. The proposed model is developed by using the boundary splitting method and the waveguide FEM-based spectral super element method in combination. The performance of the proposed spectral element model is numerically validated by comparison with exact solutions and solutions using the standard finite element method (FEM).

scholarly journals Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Ilwook Park ◽  
Usik Lee ◽  
Donghyun Park
Keyword(s):  
Frequency Domain ◽  
Computational Efficiency ◽  
Element Model ◽  
Spectral Element ◽  
Thin Plates ◽  
Plate Element ◽  
Kantorovich Method ◽  
Arbitrary Boundary ◽  
Finite Plate ◽  
Element Method

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

scholarly journals On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

2008 ◽  
Vol 15 (3-4) ◽  
pp. 425-434 ◽  
Author(s):  
N.B.F. Campos ◽  
J.R.F. Arruda
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Low Frequency ◽  
Element Model ◽  
Spectral Element ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Thin Plates ◽  
Arbitrary Boundary ◽  
Element Method

Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.

scholarly journals Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Ilwook Park ◽  
Taehyun Kim ◽  
Usik Lee
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Element Model ◽  
Spectral Element ◽  
Plate Element ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Plate Elements ◽  
Rectangular Plate Element

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

scholarly journals Three-Dimensional Simulation of Scalp Soft Tissue Expansion Using Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Qiu Guan ◽  
Xiaochen Du ◽  
Yan Shao ◽  
Lili Lin ◽  
Shengyong Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissue ◽  
Three Dimensional ◽  
Tissue Expansion ◽  
Element Model ◽  
Size Number ◽  
Proposed Model ◽  
Dimensional Simulation ◽  
Element Method

Scalp soft tissue expansion is one of the key medical techniques to generate new skin tissue for correcting various abnormalities and defects of skin in plastic surgery. Therefore, it is very important to work out the appropriate approach to evaluate the increase of expanded scalp area and to predict the shape, size, number, and placement of the expander. A novel method using finite element model is proposed to solve large deformation of scalp expansion in this paper. And the procedure to implement the scalp tissue expansion with finite element method is also described in detail. The three-dimensional simulation results show that the proposed method is effective, and the analysis of simulation experiment shows that the volume and area of the expansion scalp can be accurately calculated and the quantity, location, and size of the expander can also be predicted successfully with the proposed model.

The Least Squares Spectral Element Method for the Navier-Stokes and Cahn-Hilliard Equations

2015 ◽  
Author(s):  
Keunsoo Park ◽  
Carlos A. Dorao ◽  
Ezequiel M. Chiapero ◽  
Maria Fernandino
Keyword(s):  
Least Squares ◽  
Spectral Element Method ◽  
Element Model ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Order Continuity ◽  
Manufactured Solution ◽  
The Finite Element Model ◽  
Element Method

The least squares spectral element method (LS-SEM) offers many advantages in the implementation of the finite element model compared with the traditional weak Galerkin method. In this article, the LS-SEM is used to solve the Navier-Stokes (NS) and the Cahn-Hilliard (CH) equations. The NS equation is solved with both C0 and C1 basis functions and their performance is compared in terms of accuracy. A two-dimensional steady-state solver is verified with the case of Kovasznay flow and validated for the cavity flow, and a two-dimensional unsteady solver is verified by a transient manufactured solution case. The phenomenon of phase separation in binary system is described by the CH equation. Due to the fourth-order characteristics of the CH equation, only a high order continuity approximation is used by employing C1 basis function for both space and time domain. The obtained solutions are in accordance with previous results from the literature and show the fundamental characteristics of the NS and CH equations. The results in this study give the possibility of developing a solver for the coupled NS and CH equations.

Hybrid Dynamic Modeling and Analysis of High-speed Thin-rimmed Gears

2021 ◽  
pp. 1-23
Author(s):  
Changzhao Liu ◽  
Yu Zhao ◽  
Yong Wang ◽  
Tie Zhang ◽  
Hanjie Jia
Keyword(s):  
Finite Element ◽  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Modeling And Analysis ◽  
Lumped Parameter ◽  
Proposed Model ◽  
Angular Displacements

Abstract In this study, a hybrid dynamic model of high-speed thin-rimmed gears is developed. In this model, the translational and angular displacements (including the rigid and vibration displacements) with a total of six degrees of freedom (DOFs) are selected as the generalized coordinates for each gear, and the meshing force distributions along the contact line and between the teeth are considered. Thus, the model can be implemented under stationary and non-stationary conditions. The condensed finite element models are developed with the centrifugal and inertia forces for gear bodies. This paper proposes a novel method to couple the lumped parameter model and condensed finite element model for the hybrid dynamic model system, which considers the variation of the meshing tooth during the gear operation, namely, the variations of the acting point of meshing force. Based on the model, the dynamic analysis of high-speed thin-rimmed gears is conducted under stationary speed and acceleration processes. The effects of the flexible gear body, high speed, and tooth errors on the system dynamics and tooth load distribution are investigated. The analysis results are also compared with the current reference and pure finite element method to validate the proposed model.

An Equivalent-Acoustic Finite Element Method for Modeling Sound Absorbing Materials in the Automobile Passenger Compartment

2008 ◽  
Author(s):  
Donald J. Nefske ◽  
Shung H. Sung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Element Model ◽  
Acoustic Method ◽  
Passenger Compartment ◽  
One Dimensional ◽  
Absorbing Materials ◽  
Absorbing Material ◽  
Element Method

An equivalent-acoustic finite element method is developed for modeling sound absorbing materials, such as seats and interior trim in an automobile passenger compartment. The equivalent-acoustic method represents the sound absorbing material using acoustic finite elements with frequency-dependent material properties determined from the measured acoustic impedance of sound absorbing material samples. Solution of the equivalent-acoustic model within the Nastran computer capability, and coupling of the model with an acoustic finite element model of an enclosure, such as the passenger compartment, are developed. The accuracy of the equivalent-acoustic method is assessed for modeling a sound absorbing material in a one-dimensional impedance tube, a foam layer in a rectangular box enclosure, and the seats in an automobile passenger compartment.

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