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.

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.

Steel Cofferdam Design and Calculation for High Pile Cap Construction

2011 ◽  
Vol 255-260 ◽  
pp. 1879-1884
Author(s):  
Gui Yun Xia ◽  
Mei Liang Yang ◽  
Chuan Xi Li ◽  
Shang Wu Lu
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Structural Strength ◽  
General Purpose ◽  
Structural Safety ◽  
Pearl River ◽  
Guangzhou City ◽  
Finite Element Software ◽  
Pile Cap ◽  
Calculating Model

Using the steel cofferdam of Xinzhao Pearl River Bridge in Guangzhou City as the engineering background, structural designing and size proposing of steel cofferdam are introduced briefly. To ensure structural safety, general purpose finite element software Ansys was used to analyze structural strength and stability. Load styles and boundary conditions were also discussed. 6 load cases with calculating model were presented.

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.

Quasi-Eulerian Finite Element Formulation for Fluid-Structure Interaction

1980 ◽  
Vol 102 (1) ◽  
pp. 62-69 ◽  
Author(s):  
T. Belytschko ◽  
J. M. Kennedy ◽  
D. F. Schoeberle
Keyword(s):  
Finite Element ◽  
Interaction Analysis ◽  
Fluid Structure Interaction ◽  
General Purpose ◽  
Element Formulation ◽  
Finite Element Program ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Eulerian Formulation ◽  
Element Program

A quasi-Eulerian formulation is developed for fluid-structure interaction analysis in which the fluid nodes are allowed to move independent of the material thus facilitating the treatment of problems with large structural motions. The governing equations are presented in general form and then specialized to two-dimensional plane and axisymmetric geometries. These elements have been incorporated in a general purpose transient finite element program and results are presented for two problems and compared to experimental results.

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