한국지반공학회논문집 (Journal of the Korean Geotechnical Society)

한국지반공학회 (Korean Geotechnical Society)
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축대칭 쉘 요소의 유한요소 수식화와 지반공학적 활용

Numerical Formulation of Axisymmetric Shell Element and Its Application to Geotechnical Problems

  • 신호성 (울산대학교 건설환경공학부) ;
  • 김진욱 (울산대학교 건설환경공학부)
  • Shin, Hosung (Dept. of Civil & Environmental Engrg., Univ. of Ulsan) ;
  • Kim, Jin-Wook (Dept. of Civil & Environmental Engrg., Univ. of Ulsan)
  • 투고 : 2020.11.02
  • 심사 : 2020.11.30
  • 발행 : 2020.12.31
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초록

구조물에 대한 축대칭 쉘요소는 지반과 구조물의 상호작용에 대한 유한요소해석에서 효율성과 정확성을 높이게 된다. 본 논문에서는 Kirchhoff 이론에 근거한 축대칭 쉘요소의 힘평형 방정식과 모멘트 평형 방정식을 유도하였다. 축방향 변형에 대한 지배방정식은 등매개변수 형상함수를 이용한 Galerkin 수식화를 수행하고, 휨에 대한 지배방정식은 고차의 형상함수를 이용하였다. 개발된 축대칭 쉘요소는 지반과의 연계해석을 위하여 지반해석 유한요소 프로그램인 Geo-COUS에 결합하였다. 원형판과 액체 저장 탱크에 대한 예제해석을 통하여 개발된 요소의 정확성을 확인하였다. 그리고 축대칭 쉘요소에 대한 에너지 평형방정식을 제시하였다.

Use of axisymmetric shell element for the structure increases the efficiency and accuracy in finite element analysis of the interaction between the ground and the structure. This paper derived the force balance equation and the moment balance equation for an axisymmetric shell element based on Kirchhoff's theory. The governing equation for the axial deformation used the isoparametric shape function in the Galerkin formulation, and the governing equation for the shell bending used the higher-order shape function. The developed axisymmetric shell element was combined with Geo-COUS, a geotechnical finite element program for the coupled analysis with the ground. The accuracy of the developed element was confirmed through the example analyses of the circular plate and the liquid storage tank. And the energy balance equation for the axisymmetric shell element is presented.

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참고문헌

  1. Boisse, P. and Coffignal, G. (1999), "Error through the Constitutive Relation for Beam and C0 Plate Finite Elements: Static and Vibration Analyses", Computer Methods in Applied Mechanics and Engineering, Vol.176, No.1-4, pp.81-109. https://doi.org/10.1016/S0045-7825(98)00331-4
  2. Booker, J.R. and Small, J.C. (1983), "The Analysis of Liquid Storage Tanks on Deep Elastic Foundations", Int. J. Numer. Anal. Meth. Geomech., 7, pp.187-207. https://doi.org/10.1002/nag.1610070205
  3. Cheung, Y.K. and Zinkiewicz, O.C. (1965), "Plates and Tanks on Elastic Foundations - An Application of Finite Element Method", International Journal of Solids and Structures, Vol.1, No.4, pp. 451-461. https://doi.org/10.1016/0020-7683(65)90008-9
  4. Flugge, W. (1973), Stresses in shells, Springer, p.526.
  5. Grafton, P.E. and Strome, D.R. (1963), "Analysis of Axisymmetrical Shells by the Direct Stiffness Method", AIAA Journal, Vol.1, No.10, pp.2342-2347. https://doi.org/10.2514/3.2064
  6. Jones, R.E. and Strome, D.R. (1966), "Direct Stiffness Method Analysis of Shells of Revolution Utilizing Curved Elements", AIAA Journal, 4(9), pp.1519-1525. https://doi.org/10.2514/3.3729
  7. Kukreti, A.R. and Siddiqi, Z.A. (1997), "Analysis of Fluid Storage Tanks Including Foundation-superstructure Interaction Using Differential Quadrature Method", Applied Mathematical Modelling, Vol.21, No.4, pp.193-205. https://doi.org/10.1016/S0307-904X(97)00007-3
  8. Melerski, E.S. (1991), "Simple Elastic Analysis of Axisymmetric Cylindrical Storage Tanks", Journal of Structural Engineering, Vol.117, No.11, pp.3239-3260. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:11(3239)
  9. PLAXIS (2018), "Bending of axisymmetric plates".
  10. Prathap, G. and Ramesh, B.C. (1986), "A Field Consistent Three-noded Quadratic Curved Axisymmetric Shell Element", 23, pp. 711-724. https://doi.org/10.1002/nme.1620230413
  11. Raveendranath, P., Singh, G., and Pradhan, B. (1999), "A Two-node Curved Axisymmetric Shell Element based on Coupled Displacement Field", Int. J. Numer. Methods Eng., 45, pp.921-935. https://doi.org/10.1002/(SICI)1097-0207(19990710)45:7<921::AID-NME618>3.0.CO;2-I
  12. Shin, E.C., Kang, J.G., and Park, J.J. (2009), "Thermal Stability in Underground Structure with Ground Freezing", J. of the Korean Geotechnical Society, Vol.25, No.3, pp.65-74.
  13. Tessler, A. (1982), "An Efficient, Conforming Axisymmetric Shell Element Including Transverse Shear and Rotary Inertia", Computers & Structures, 15, pp.567-574. https://doi.org/10.1016/0045-7949(82)90008-6
  14. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of plates and shells, McGraw-Hill, p.580.
  15. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method: Solid mechanics, Butterworth-Heinemann, p.459.