Highly efficient FE simulations by means of simplified corotational formulation
DOI:
https://doi.org/10.31181/oresta2003074mKeywords:
Structural analysis, Co-rotational FEM, Geometric nonlinearity, Solid, ShellAbstract
Finite Element Method (FEM) has deservedly gained the reputation of the most powerful numerical method in the field of structural analysis. It offers tools to perform various kinds of simulations in this field, ranging from static linear to nonlinear dynamic analyses. In recent years, a particular challenge is development of FE formulations that enable highly efficient simulations, aiming at real-time dynamic simulations as a final objective while keeping high simulation fidelity such as nonlinear effects. The authors of this paper propose a simplified corotational FE formulation as a possible solution to this challenge. The basic idea is to keep the linear behavior of each element in the FE assemblage, but to extract the rigid-body motion on the element level and include it in the formulation to cover geometric nonlinearities. This paper elaborates the idea and demonstrates it on static cases with three different finite element types. The objective is to check the achievable accuracy based on such a simplified geometrically nonlinear FE formulation. In the considered examples, the difference between the results obtained with the present formulation and those by rigorous formulations is less than 3% although fairly large deformations are induced.
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References
Argyris, J. (1982). An excursion into large rotations. Computer Methods in Applied Mechanics and Engineering, 32(1-3), 85-155.
Bathe, K. J. (1996). Finite element procedures. New York : Prentice Hall.
Bathe, K. J., & Bolourchis, S. (1979). Large displacement analysis of three-dimensional beam structures. International Journal of Numerical Methods in Engineering 14(7), 961-986.
Belytschko, T., & Hsieh, B. J. (1979). Application of higher order corotational stretch theories to nonlinear finite element analysis. Computers & Structures, 11, 175–182.
Crisfield, M. A. (1990). A consistent corotational formulation for nonlinear three-dimensional beam element. Comp. Meths. Appl. Mech. Engrg., 81, 131–150.
Crisfield, M. A. (1997). Nonlinear finite element analysis of solids and structures. Vol. 2: Advanced Topics. Chichester: Wiley.
Crisfield, M. A., & Moita, G. F. (1996). A unified co-rotational for solids, shells and beams. Int. J. Solids Struc., 33, 2969–2992.
Felippa, C., & Haugen, B. (2005). A unified formulation of small-strain corotational finite elements: I. Theory. Computer Methods in Applied Mechanics and Engineering, 194(21-24), 2285-2335.
Felippa, C., & Militello, C. (1992). Membrane triangles with corner drilling freedoms – II The ANDES element. Finite Elem. Anal. Des., 12(3–4), 189–201.
Horrigmoe, G., & Bergan, P. G. (1978). Instability analysis of free-form shells by flat finite elements. Comp. Meths. Appl. Mech. Engrg., 16, 11–35.
Li, S., Zhang, J. & Cui, X. (2019). Nonlinear dynamic analysis of shell structures by the formulation based on a discrete shear gap. Acta Mechanica (230), 3571–3591.
Marinkovic, D., Rama, G., & Zehn, M. (2019). Abaqus implementation of a corotational piezoelectric 3-node shell element with drilling degree of freedom. Facta Universitatis, series: Mechanical Engineering, 17(2), 269-283.
Marinkovic, D., & Zehn, M. (2018). Corotational finite element formulation for virtual-reality based surgery simulators. Physical Mesomechanics, 21(1), 15-23.
Marinkovic, D., & Zehn, M. (2019). Survey of finite element method-based real-time simulations. Applied Sciences, 9(14), art. no. 2775.
Marinkovic, D., Zehn, M., & Rama, G. (2018). Towards real-time simulation of deformable structures by means of co-rotational finite element formulation. Meccanica, 53(11-12), 3123-3136.
Nguyen, V. A., Zehn, M., & Marinkovic, D. (2016). An efficient co-rotational FEM formulation using a projector matrix. Facta Universitatis, series: Mechanical Engineering, 14(2), 227-240.
Nygard, M. K., & Bergan, P. G. (1989). Advances in treating large rotations for nonlinear problems. In A. K. Noor, & J. T. Oden (Eds.), State-of the Art Surveys on Computational Mechanics (pp. 305–332). New York: ASME.
Rama, G., Marinkovic, D., & Zehn, M. (2018). Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures. Journal of Intelligent Material Systems and Structures, 29(3), 345-357.
Rama, G., Marinkovic, D., & Zehn, M. (2018a). A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(7), art. no. 356.
Rama, G., Marinkovic, D., & Zehn, M. (2018b). High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates. Composites Part B: Engineering, 151, 118-126.
Rankin, C. C., & Brogan, F. A. (1986). An element-independent corotational procedure for the treatment of large rotations, ASME J. Pressure Vessel Technology, 108, 165–174.
Turner, M. J., Clough, R. W., Martin, H. C., & Topp, L. J. (1956). Stiffness and deflection analysis of complex structures, J. Aeronaut. Sci., 23, 805-824.
Zehn, M.W., Marinkovic, D. (2019). Chances of real-time simulation in FE analyses with conventional hardware. Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications - Proceedings of the 7th International Conference on Structural Engineering, Mechanics and Computation, 2019, Cape Town, South Africa, pp. 531-536.
