면내회전자유도를 갖는 4절점 곡면 쉘요소
A Four-node General Shell Element with Drilling DOFs
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초록
이 연구에서는 감절점쉘요소의 개념에 근거한 새로운 4절점 곡면 쉘요소를 제시하였다. 회전장이 독립변수로 도입된 범함수에 의하여 면내회전자유도를 도입함으로써 개발된 쉘요소에서는 절점당 6자유도를 갖도록 하였다. 아울러 쉘요소의 면내거동 개선을위하여 4개의 비적합변위형에 의한 비적합변위를 면내방향의 변위성분에 추가하였으며, 면외거동 개선을 위하여 대체전단변형률장이 적용되었다. 이 연구에서의 비적합변위형의 수치적 구현에 있어서 일정한 변형률상태를 표현할 수 있도록 하기 위하여 비적합변위형의 직접수정법이 적용되었다. 이렇게 정식화된 쉘요소 강성행렬의 수치적분에 있어서는 부피적분을 위하여 9점 적분법이 사용되었다. 개발된쉘요소는 바람직하지 못한 영에너지모드를 갖지 않으며, 일정한 변형률 상태를 표현할 수 있음을 확인하였다. 개발된 4절점 곡면 쉘 요소에 대한 다양한 수치예제를 통한 검증 결과, 전반적으로 양호한 거동을 보여주고 있음을 확인하였다.
Abstract
In this study, a new 4-node general shell element with 6 DOFs per node is presented. Drilling rotational degrees of freedom are introduced by the variational principle with an independent rotation field. In formulation of the element,substitute transverse shear strain fields are used to avoid shear locking, while four nonconforming modes are applied in the in-plane displacement fields as a remedy for membrane locking. In addition, a direct modification method for nonconforming modes is employed in the numerical implementation of nonconforming modes to represent constant strain states. A 9-points integration rule is adopted for volume integration in the computation of the element stiffness matrix. With the combined use of these techniques, the developed shell element has no spurious zero energy modes, and can represent a constant strain state. Several numerical tests are carried out to evaluate the performance of the new element developed. The test results show that the behavior of the elements is satisfactory.
참고문헌 (40)
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- 白種均, "대체 변형률장에 의한 효율적인 4절점 쉘 유한요소의 개발", 박사, pp.1994
- 이태열, "직접 수정된 비적합 변위모드를 가진 평면쉘요소의개발 및 쉘 구조물 해석", 박사, pp.2002
- Hughes, T.J.R., "On drilling degrees of freedom", Comput. Methods Appl. Mech. Engrg., 72, pp.105~121 (1989)
- Iura, M., "Formulation of a membrane finite element with drilling degrees of freedom", Computational Mechanics, 9, pp.417~428 (1992)
- Cook, R. D., "Concepts and applications of finite element analysis, 3rd edition" (1989), John Wiley & Sons
- Choi, C. K., "A direct modification method for strains due to non-conforming modes", Structural Enigineering and Mechanics, 11(3), pp.325~340 (2001)
- Choi, C. K., "Direct modification for non-conforming elements with drilling DOF", Int. J. for Numerical Methods in Engineering, 55, pp.1463~1476 (2002)
- 최창근, "개선된 비적합 변위형과 대체전단변형율장을 이용한 4절점 평판 휨 요소", 대한토목학회 논문집, 21(2-A), pp.279~286 (2001)
- Bathe, K.J., "A continuum mechanics based four-node shell element for general nonlinear analysis", Engineering Computation, 1, pp.77~88 (1984)
- MacNeal, R.H., "A proposed standard set of problems to test finite element accuracy", Finite Elements in Analysis and Design, 1, pp.3~20 (1985)
- Hinton, E., "A family of quadrilateral Mindlin plate elements with substitute shear strain fields", Computers and Structures, 23, pp.409~431 (1986)
- Groenwold, A.A., "An efficient 4-node 24 DOF thick shell finite element with 5-point quadrature", Engrg. Compt, 12, pp.723~747 (1995)
- Taylor, R.L., "Finite elment analysis of linear shell problem, In Proc. of Mathmatics of Finite Elements and Application VI" (1987), Academic Press
- Simo, J. C., "On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspect", Comput. Methods Appl. Mech. Engrg., 73, pp.53~92 (1989)
- Choi, C.K., "Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes", Comput. Methods Appl. Mech. Engrg., 192, pp.1961~1971 (2003)
- Belytchko, T., "Physical stabilization of the 4-node shell element with one point quadrature", Comput. Methods Appl. Mech. Engrg, 113, pp.321~350 (1994)
- U.S. Nuclear Regulatory Commission, "Standard Review Plan 3.7.2 Revision 3, NUREG-0800", ~ (2007)
- 김재민, "Seismic response analysis of soil-structure interactive system using a coupled three-dimensional FE-IE method", NUCLEAR ENGINEERING AND DESIGN, 240(8), pp.1949~1966, ELSEVIER SCIENCE SA
- Lysmer, J., "A System for Analysis of Soil-Structure Interaction User’s Manual" (1988), University of California, Berkeley
- 최창근, "회전자유도를 갖는 비적합 8-절점입체요소의 개선", 한국전산구조공학회 논문집, 13(4), pp.475~484 (2000)
- 白種均, "대체 변형률장에 의한 효율적인 4절점 쉘 유한요소의 개발", 박사, pp.1994
- 이태열, "직접 수정된 비적합 변위모드를 가진 평면쉘요소의개발 및 쉘 구조물 해석", 박사, pp.2002
- Hughes, T.J.R., "On drilling degrees of freedom", Comput. Methods Appl. Mech. Engrg., 72, pp.105~121 (1989)
- Iura, M., "Formulation of a membrane finite element with drilling degrees of freedom", Computational Mechanics, 9, pp.417~428 (1992)
- Cook, R. D., "Concepts and applications of finite element analysis, 3rd edition" (1989), John Wiley & Sons
- Choi, C. K., "A direct modification method for strains due to non-conforming modes", Structural Enigineering and Mechanics, 11(3), pp.325~340 (2001)
- Choi, C. K., "Direct modification for non-conforming elements with drilling DOF", Int. J. for Numerical Methods in Engineering, 55, pp.1463~1476 (2002)
- 최창근, "개선된 비적합 변위형과 대체전단변형율장을 이용한 4절점 평판 휨 요소", 대한토목학회 논문집, 21(2A), pp.279~286 (2001)
- Bathe, K.J., "A continuum mechanics based four-node shell element for general nonlinear analysis", Engineering Computation, 1, pp.77~88 (1984)
- MacNeal, R.H., "A proposed standard set of problems to test finite element accuracy", Finite Elements in Analysis and Design, 1, pp.3~20 (1985)
- Hinton, E., "A family of quadrilateral Mindlin plate elements with substitute shear strain fields", Computers and Structures, 23, pp.409~431 (1986)
- Groenwold, A.A., "An efficient 4-node 24 DOF thick shell finite element with 5-point quadrature", Engrg. Compt, 12, pp.723~747 (1995)
- Taylor, R.L., "Finite elment analysis of linear shell problem, In Proc. of Mathmatics of Finite Elements and Application VI", pp.191~203 (1987), Academic Press
- Simo, J. C., "On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspect", Comput. Methods Appl. Mech. Engrg., 73, pp.53~92 (1989)
- Choi, C.K., "Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes", Comput. Methods Appl. Mech. Engrg., 192, pp.1961~1971 (2003)
- Belytchko, T., "Physical stabilization of the 4-node shell element with one point quadrature", Comput. Methods Appl. Mech. Engrg., 113, pp.321~350 (1994)
- U.S. Nuclear Regulatory Commission, "Standard Review Plan 3.7.2 Revision 3, NUREG-0800", ~ (2007)
- 김재민, "Seismic response analysis of soil-structure interactive system using a coupled three-dimensional FE-IE method", NUCLEAR ENGINEERING AND DESIGN, 240(8), pp.1949~1966, ELSEVIER SCIENCE SA
- Lysmer, J., "A System for Analysis of Soil-Structure Interaction User’s Manual" (1988), University of California