A co-rotational element/time-integration strategy for non-linear dynamics. (English) Zbl 0804.70002
Summary: New procedures are proposed for implicit dynamic analysis using the finite element method. The main aim is to give stable solutions with significant rigid-body motions, in particular rotations. In contrast to most conventional approaches, the time-integration strategy is closely linked to the ‘element technologies’ with the latter involving a form of co-rotational procedure. For the undamped situation, one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied (i.e. with gravity loading).
MSC:
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
| 70E15 | Free motion of a rigid body |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
References:
| [1] | Stewart, Nature 355 pp 16– (1992) |
| [2] | ’An overview of semidiscretisation and time integration procedures’, in and (eds.), Computational Methods for Transient Analysis, Elsevier, Science, North-Holland, 1983, pp. 1-65. |
| [3] | Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1982. |
| [4] | and , The Finite Element Method, Vol 2, 4th edn, McGraw-Hill, Maidenhead, U. K., 1991. |
| [5] | and , ’An improved energy conserving implicit time, integration algorithm for nonlinear dynamic structural analysis’, Proc. 4th Int. Conf. on Struct. Mech. in Reactor Tech., San Francisco, August 1977. |
| [6] | Hughes, J. Appl. Mech. ASME 45 pp 366– (1978) · Zbl 0392.73075 · doi:10.1115/1.3424303 |
| [7] | Simo, Int. j. numer. methods eng. 31 pp 19– (1991) |
| [8] | Simo, Int. j. numer. methods eng. 34 pp 1117– (1992) |
| [9] | Hilber, Int. j. earthquake eng. struct. dyn. 5 pp 283– (1977) |
| [10] | Zienkiewicz, J. earthquake eng. struct. dyn. 8 pp 31– (1980) |
| [11] | Simo, Angnew Math. Phys. 43 pp 757– (1992) |
| [12] | and , ’An energy conserving co-rotational procedure for non-linear dynamics with finite elements’, in et al. (eds.), Proc. NATO Advanced Study Institute on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, Vol. II, IDMEC, Troia, Portugal, July 1993, pp. 197-214. |
| [13] | Peng, Int. j. numer. methods eng. 35 pp 1829– (1992) |
| [14] | Finite Element Procedures for Solid and Structures–Nonlinear Analysis, MIT Centre for Advanced Engineering Studies, 1986. |
| [15] | and , ’Dynamic finite element analysis applied to a simple model exhibiting dynamic instability’, Eng. Comput., to be published. · Zbl 0822.70003 |
| [16] | ’Dynamic Stability of suddenly loaded structures’, M. Sc. Thesis, Dept. of Aeronautics, Imperial College, London, 1992. |
| [17] | Non-linear Finite Element Analysis of Solids and Structures, Vol. 1, Wiley, Chichester, 1991. |
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