scholarly journals The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fubiao Lin ◽  
Junying Cao ◽  
Zhixin Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Local Defect ◽  
Local Refinement ◽  
Element Discretization ◽  
One Dimensional ◽  
Correction Technique ◽  
Polar Coordinate ◽  
Multiscale Finite Element

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

Effective Shear Area in One Dimensional Ship Hull Finite Element Models to Predict Natural Frequencies of Vibration

2013 ◽  
Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Numerical Results ◽  
Computational Method ◽  
Scale Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Area

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

scholarly journals Hierarchical Beam Finite Elements Based Upon a Variables Separation Method

2016 ◽  
Vol 08 (02) ◽  
pp. 1650026 ◽  
Author(s):  
Gaetano Giunta ◽  
Salim Belouettar ◽  
Olivier Polit ◽  
Laurent Gallimard ◽  
Philippe Vidal ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Three Dimensional ◽  
Finite Element Solution ◽  
Stress Fields ◽  
Element Solution ◽  
One Dimensional ◽  
Kinematic Approximation ◽  
The Cross

A family of hierarchical one-dimensional beam finite elements developed within a variables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equivalent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.

Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Matthias Maier ◽  
Rolf Rannacher
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Elliptic Problems ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Multiscale Problems ◽  
Multiscale Finite Element ◽  
Heterogeneous Multiscale ◽  
Multiscale Finite Element Methods

AbstractThis paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for

Three-Dimensional Numerical Simulation of Thermomechanical Constitutive Model for Shape Memory Polymers With Application to Morphing Wing Skin

2013 ◽  
Author(s):  
Olaniyi A. Balogun ◽  
Changki Mo ◽  
A. K. Mazher ◽  
John C. Brigham
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Thermomechanical Behavior ◽  
One Dimensional ◽  
Simulation Results ◽  
Wing Skin

This paper presents three-dimensional numerical simulation of thermomechanical constitutive model for shape memory polymers. Shape memory polymers (SMPs) are a class of smart materials with high potential for application to automotive, aerostructures, and medical devices, which can benefit from its intrinsic shape changing properties. In particular, looking at its application to aerospace substructure such as morphing wings, thermomechanical behavior of the SMPs needs to be well established and predicted. In order to predict the thermomechanical behavior of SMPs structures, a one-dimensional rheological thermomechanical constitutive model was adopted and a numerical simulation of this model was developed using a commercial finite element analysis package ABAQUS. The particular one-dimensional model was selected due to its potential to represent the key material behaviors of SMP with a relatively low number of required material constants, which is practical for engineering industrial applications. The model was expanded to a three-dimensional isotropic model and then incorporated into the finite element method by means of an ABAQUS user-defined subroutine (UMAT). The methods of three-dimensional expansion and numerical implementation are presented in this work. A time evolution of the analysis was conducted by making use of the backward difference method, which was applied to all quantities within the model including the material properties. A comparison of the numerical simulation results was carried out with the available experimental data. Numerical simulation results clearly exhibit the thermomechanical properties of the material, which include shape fixity, shape recovery, and recovery stress. Finally, a preliminary set of predictions for an unmanned aerial vehicle (UAV) morphing wing skin are also presented.

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