Geometric nonlinear analysis of space shell structures using generalized conforming flat shell elements – for space shell structures. (English) Zbl 0912.73065
Summary: We derive an updated Lagrangian formulation of the generalized conforming flat shell element with drilling degrees of freedom based on the incremental equation of virtual work for a three-dimensional continuum, aiming at a purely geometric nonlinear analysis of space structures. While solving the nonlinear equations, the Euler-Newton method and modified Euler-Newton method are used in static analyses, and the modified arc-length method and Newton arc-length method are used for post-buckling problems. We give numerical examples to demonstrate the effectiveness of the proposed approach.
Keywords:
updated Lagrangian formulation; incremental equation of virtual work; Euler-Newton method; modified Euler-Newton method; modified arc-length method; Newton arc-length method; post-buckling problemsReferences:
| [1] | Yuqiu, Generalized conforming triangular flat shell element, Eng. Mech. 10 (4) pp 1– (1993) |
| [2] | Washizu, Variational Methods in Elasticity and Plasticity (1984) |
| [3] | Yin, Conforming triangular membrane element with vertex rotational freedom from generalized conforming condition, Eng. Mech. 10 (2) pp 31– (1993) |
| [4] | Yuqiu, Generalized conforming plate bending elements using point and line compatibility conditions, Comput. Struct. 54 (4) pp 717– (1995) · Zbl 0871.73069 · doi:10.1016/0045-7949(94)00362-7 |
| [5] | Bathe, Computing Methods in Applied Sciences and Engineering (1982) |
| [6] | Jiaju, Large-displacement/rotation and large strain plastic finite element analysis of general shell structure, Int. J. Press. Vessels Pip. 40 pp 1– (1989) · doi:10.1016/0308-0161(89)90121-X |
| [7] | Bergen, Solution techniques for non-linear finite element problems, Int. j. numer. methods eng. 12 pp 1677– (1978) · Zbl 0392.73081 · doi:10.1002/nme.1620121106 |
| [8] | Crisfield, A faster incremental iterative solution procedure that handles ”snap-through”, Comput. Struct. 13 pp 55– (1981) · Zbl 0479.73031 · doi:10.1016/0045-7949(81)90108-5 |
| [9] | Simo, On a stress resultant geometrically exact model, Part 3, Computational aspects of the non-linear theory, Comput. Methods Appl. Mech. Eng. 79 pp 21– (1990) · Zbl 0746.73015 · doi:10.1016/0045-7825(90)90094-3 |
| [10] | Peng, A consistent co-rotational formulation for shells using the constant stress/constant moment triangle, Int. j. numer. methods eng. 35 pp 1829– (1992) · Zbl 0767.73076 · doi:10.1002/nme.1620350907 |
| [11] | Argyris, Finite element method the natural approach, Comput. Methods Appl. Mech. Eng. 17 (18) pp 1– (1979) · Zbl 0407.73058 · doi:10.1016/0045-7825(79)90083-5 |
| [12] | Simo, Three-dimensional finite-strain rod model, Part II: Computational aspects, Comput. Methods Appl. Mech. Eng. 58 pp 79– (1986) · Zbl 0608.73070 · doi:10.1016/0045-7825(86)90079-4 |
| [13] | Gruttmann, Hangover theory and numeric of thin elastic shells with finite rotations, Ing.-Arch. 59 pp 54– (1989) · doi:10.1007/BF00536631 |
| [14] | Bathe, A simple and effective element for analysis of general shell structures, Comput. Struct. 13 pp 673– (1981) · Zbl 0455.73075 · doi:10.1016/0045-7949(81)90029-8 |
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