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Development of Nonlinear Triangular Planar Element Based on Co-rotational Framework

Co-rotational 이론 기반 비선형 삼각평면 유한요소의 개발

Cho Hae-Seong
,
Shin Sang-Joon†*
Department of Aerospace and Mechanical Engineering
Department of Aerospace and Mechanical Engineering

• 본 논문에 대한 토의를 2015년 10월 30일까지 학회로 보내주시면 2015년 12월호에 토론결과를 게재하겠습니다.

*Corresponding Author : ssjoon@snu.ac.kr
2015. pp. 485-490
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Abstract

구조의 기하학적 비선형해석을 위해 대표적으로 Total Lagrangian, Updated Lagrangian 정식화 기법이 있다. 이러한 고전적인 정식화 과정은 요소의 변형률을 가정하는 방법에 따라 그리고 요소의 절점 수에 따라 추가의 수학적 정식화 과정이 요구된다. 하지만 비교적 최근에 정립된 Co-roational(CR) 이론은 기 존재하는 보, 판, 쉘 요소에 독립적으로 요소 절점자유도에 따라 일정하게 적용하여 대변위, 작은 변형률을 갖는 구조의 기하비선형 해석을 가능케 한다. 본 논문에서는 회전자유도를 갖는 삼각평면요소에 대한 CR 기법을 정식화하였고 동적해석으로 확장하여 이를 상용프로그램과 검증하였다. 해석에 사용한 삼각평면요소는 OPtimal Triangular(OPT) 평면요소이다.

This paper presents development of a geometrically nonlinear triangular planar element including rotational degrees of freedom, based on the co-rotational(CR) formulation. The CR formulation is one of the efficient geometrically nonlinear formulations and it is based on the assumptions on small strain and large rotation. In this paper, modified CR formulation is suggested for the developemnt of a triangular planar element. The present development is validated regarding the static and time transient problems. The present results are compared with the results predicted by the previous researchers and those obtained by the existing commercial software.

키워드
기하학적 비선형 구조해석, Co-rotational 이론, 삼각평면요소
geometrically nonlinear structural analysis, co-rotational formulation, triangular planar element
References
1
D.J., Allman, 1984. A Compatible Triangular Element Including Vertex Rotations for Plane elasticity Problems. Compos. Struct., 19, pp.1-8.
10.1016/0045-7949(84)90197-4
2
D.J., Allman, 1988. A Quadrilateral Finite Element Including Vertex rotations for Plane Elasticity Problems. Int. J. Nummer. Meth. Eng., 18, pp.717-739.
10.1002/nme.1620260314
3
K-J., Bathe, E., Ramm and E.L., Wilson, 1975. Finite Element Formulations for Large Deformation Dynamic Analysis. Int. J. Nummer. Meth. Eng., 9, pp.353-386.
10.1002/nme.1620090207
4
J-M., Battini, 2007. A Modified Corotational Framework for Triangular Shell Elements. Comput. Meth. Appl. Mech. Eng., 196, pp.1905-1914.
10.1016/j.cma.2006.10.006
5
J-M., Battini, 2008. A Non-linear Corotational 4-node Plane Element. Mech. Res. Commun., 35, pp.408-413.
10.1016/j.mechrescom.2008.03.002
6
P.G., Bergan and C.A., Fellipa, 1985. A Triangular Membrane Element with Rotational Degrees of Freedom. Comput. Meth. Appl. Mech. Eng., 50, pp.25-60.
10.1016/0045-7825(85)90113-6
7
N., Carpenter, H., Stolarski and T., Belytschko, 1985. A Flat Triangular Shell Element with Improved Membrane Interpolation. Comput. Meth. Appl. Mech. Eng., 1, pp.161-168.
10.1002/cnm.1630010405
8
M.A., Crisfield, 1990. A Consistent Co-rotational Formulation for Non-linear, Three-dimenstional, Beam-elements. Comput. Meth. Appl. Mech. Eng., 81, pp.2969-2992.
10.1016/0045-7825(90)90106-V
9
Crisfield M.A. 1997Non-linear Finite Element Analysis of Solid and StructuresAdvanced Topics2Wiley, London
10
C.A., Felippa, 2003. A Study of Optimal Membrane Triangles with Drilling Freedoms. Comput. Meth. Appl. Mech. Eng.,, 192, pp.2125-2168.
10.1016/S0045-7825(03)00253-6
11
C.A., Felippa and B., Haugen, 2005. A Unified Formulation of Small-strain Coroational Finite Elements: I. Theory. Comput. Meth. Appl. Mech. Eng., 194, pp.2285-2335.
10.1016/j.cma.2004.07.035
12
Pai P.F. 2007 Highly Flexible Structures: ModelingComputation, and Experimentation AIAA, IncVA
10.2514/4.861925
13
C.C., Rankin and B., Nour-Omid, 1986. An Element Independent Co-rotational Procedure for the Treatment of Large Rotations. ASME J. Pressure Vessel Techn., 108, pp.165-174.
10.1115/1.3264765
14
J., Simo and F., Armero, 1993. Improved Version of Assumed Enhanced Strain Tri-linear Element for 3d Finite Deformation Problems. Comput. Meth. Appl. Mech. Eng., 110, pp.359-386.
10.1016/0045-7825(93)90215-J
15
R., Taylor, P., Beresford and E., Wilson, 1976. A Non-conforming Element for Stress Analysis. Int. J. Nummer. Meth. Eng., 10, pp.1211-1219.
10.1002/nme.1620100602
Information
  • Publisher :Computational Structural Engineering Institute of Korea
  • Publisher(Ko) :한국전산구조공학회
  • Journal Title :Journal of the Computational Structural Engineering Institute of Korea
  • Journal Title(Ko) :한국전산구조공학회 논문집
  • Volume : 28
  • No :5
  • Pages :485-490
  • Received Date : 2015-07-16
  • Revised Date : 2015-07-21
  • Accepted Date : 2015-07-22
  • DOI :https://doi.org/10.7734/COSEIK.2015.28.5.485
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