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Research Papers

Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Oleg Dmitrochenko

Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finlandoleg.dmitrochenko

Aki Mikkola

Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finlandaki.mikkola@lut.f

Here, the cross product r1×r2 is represented using a concept of the skew-symmetric matrix r̃1 associated with vector r1.

The area element is dΔ=dp1dp2; that is why 2Δ is the Jacobian |(dp1dp2)/(Δi,Δj)| when Δk=1ΔiΔj, see Eqs. 1,5.

J. Comput. Nonlinear Dynam 3(4), 041012 (Sep 04, 2008) (8 pages) doi:10.1115/1.2960479 History: Received June 09, 2007; Revised November 26, 2007; Published September 04, 2008

In this paper, two triangular plate elements based on the absolute nodal coordinate formulation (ANCF) are introduced. Triangular elements employ the Kirchhoff plate theory and can, accordingly, be used in thin plate problems. As usual in ANCF, the introduced elements can exactly describe arbitrary rigid body motion when their mass matrices are constant. Previous plate developments in the absolute nodal coordinate formulation have focused on rectangular elements that are difficult to use when arbitrary meshes need to be described. The elements introduced in this study have overcome this problem and represent an important addition to the absolute nodal coordinate formulation. The two elements introduced are based on Specht’s and Morley’s shape functions, previously used in conventional finite element formulations. The numerical solutions of these elements are compared with previously proposed rectangular finite element and analytical results.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Triangular area and its coordinates

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Figure 2

Triangle element based on Specht’s shape functions

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Figure 3

A simple triangle element based on Morley’s shape functions

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Figure 4

Discontinuity of a mesh using Morley’s elements

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Figure 5

Discontinuity of two Morley’s elements

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Figure 6

Modeling of artificial discontinuity

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Figure 7

Mesh used for a test problem

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Figure 8

Free-falling plate-shaped pendulum

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Figure 9

Displacements of the tip of the plate pendulum

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Figure 10

Simulation of Dali’s soft clocks by triangles

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