Infinite Element Formulation to Simulate Magnetic Boundary Conditions for Magnetostrictive Materials

2010 ◽  
Author(s):  
J.L. Pérez-Aparicio ◽  
R. Palma
Keyword(s):  
Boundary Conditions ◽  
Element Formulation ◽  
Infinite Element ◽  
Magnetostrictive Materials

scholarly journals Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

2019 ◽  
Author(s):  
Liang Wang ◽  
Xue Zhang ◽  
Filippo Zaniboni ◽  
Eugenio Oñate ◽  
Stefano Tinti
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Element Formulation ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Landslide Modeling ◽  
Element Method

AbstractNotwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

scholarly journals Numerical Simulation of Reciprocating Flow Forced Convection in Two-Dimensional Channels

2003 ◽  
Vol 125 (3) ◽  
pp. 403-412 ◽  
Author(s):  
Cuneyt Sert ◽  
Ali Beskok
Keyword(s):  
Boundary Conditions ◽  
Forced Convection ◽  
Temperature Fields ◽  
Bottom Surface ◽  
Bulk Temperature ◽  
Element Formulation ◽  
Two Dimensional ◽  
Penetration Length ◽  
Time Accuracy ◽  
Reciprocating Flow

Numerical simulations of laminar, forced convection heat transfer for reciprocating, two-dimensional channel flows are performed as a function of the penetration length, Womersley (α) and Prandtl (Pr) numbers. The numerical algorithm is based on a spectral element formulation, which enables high-order spatial resolution with exponential decay of discretization errors, and second-order time-accuracy. Uniform heat flux and constant temperature boundary conditions are imposed on certain regions of the top surface, while the bottom surface is kept insulated. Periodicity of velocity and temperature fields is imposed on the side boundaries, while the flow is driven by an oscillating pressure gradient. These sets of boundary conditions enable time-periodic solution of the problem. Instantaneous and time-averaged surface and bulk temperature distributions, and Nusselt number variations are presented. For high α flows, the temperature field is significantly affected by the Richardson’s annular effect. Overall, forced convection increases by increasing the penetration length, α and Pr. Corresponding steady-flow simulations are performed by matching the volumetric flowrate. For the limited parameter space investigated in this paper, steady unidirectional forced convection is more effective than the reciprocating flow forced convection.

A Finite Element Solution for Fully Intrinsic Plate Theory

2014 ◽  
Author(s):  
Zahra Sotoudeh
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Plate Theory ◽  
General Purpose ◽  
Flexible Body ◽  
Element Formulation ◽  
Element Solution ◽  
Beam Equations ◽  
Linear Version ◽  
Rotation Parameters

The fully intrinsic equations for plates (and analogous ones for shells), although equally as elegant as the corresponding beam equations, have neither been used for general-purpose finite element nor multi-flexible-body analysis. The fully intrinsic equations for plates have the same advantages of fully intrinsic equations for beams. These equations are geometrically exact, the highest order of nonlinearities is only of second order, and they do not include rotation parameters. We present a finite element formulation for these equations, and then investigate different possible boundary conditions and loading situations on simplified linear version.

A four-node quadrilateral element for vibration and damping analysis of sandwich plates with viscoelastic core

2017 ◽  
Vol 21 (3) ◽  
pp. 1072-1118 ◽  
Author(s):  
Shanhong Ren ◽  
Guozhong Zhao
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Complex Eigenvalue ◽  
Constrained Layer Damping ◽  
Quadrilateral Element ◽  
Frequency Dependent ◽  
Viscoelastic Core ◽  
Rectangular Element

Constrained layer damping treatments have been widely used as an effective way for vibration control and noise reduction of thin-walled plates and shells. Despite extensive application in vibration and damping analysis of sandwich plates with viscoelastic core, the rectangular element is challenged by irregular structural forms in practical engineering. In this paper, a three-layer four-node quadrilateral element with seven degrees of freedom at each node is presented. Compared with classical rectangular element, the four-node quadrilateral element has stronger adaptability in complex structural forms and boundary conditions. Based on the layer-wise theory where the constrained layer and the base layer meet Kirchhoff theory and the viscoelastic layer satisfies first-order shear deformation theory, the finite element formulation of the sandwich plate with viscoelastic core is derived by the Hamilton principle in variational form and based on the generalization of the discrete Kirchhoff Quadrilateral plate element. The complex modulus model is employed to describe the viscoelastic core of sandwich plates, allowing for the material’s frequency dependent characteristics. The natural frequencies and associated modal loss factors are computed based on the complex eigenvalue problems. The frequency dependent characteristic of the viscoelastic core is considered and an iterative procedure is introduced to solve the nonlinear eigenvalue problem. At last, six verification numerical examples that include three sandwich beam-plates and three sandwich plates are provided to compare present method with experiment, analytical method, Galerkin method, finite element methods and commercial software (NASTRAN). The results show that the proposed finite element can accurately and efficiently simulate the sandwich plates treated with constrained layer damping with a variety of structural forms and boundary conditions.

A Combined Perfectly Matching Layer and Infinite Element Formulation for Unbounded Wave Problems in the Frequency Domain

2014 ◽  
Author(s):  
Joseph S. Pettigrew ◽  
Anthony J. Mulholland ◽  
Jeffrey L. Cipolla ◽  
John Mould ◽  
Robert Banks
Keyword(s):  
Frequency Domain ◽  
Marked Improvement ◽  
Test Problem ◽  
Near Field ◽  
Element Formulation ◽  
Infinite Element ◽  
Matching Layer ◽  
Modal Response ◽  
New Type ◽  
Wave Problems

In this paper, Berenger’s Perfectly Matching Layer (PML) and Bettess’ Infinite Element (IE) scheme are combined to create a new type of element for unbounded acoustic wave problems. An assessment of this new element formulation is made through its use in the calculation of the acoustic modal response of a spherical radiator in the frequency domain. The performance of the PML+IE approach is contrasted with the IE only methodology by comparing them to the exact solution of this test problem in terms of the surface inertia and resistance in the near field. The results are encouraging and the PML+IE approach shows a marked improvement in performance, particularly at lower frequencies.

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