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This is a classical example, first presented by Simo and Tarnow (1994), and widely used to demonstrate the ability of the proposed formulations in solving problems with large motion (displacements and rotations) for long-term computations.
Simo & Tarnow citation:
Simo, J. and Tarnow, N. 1994. New energy and momentum conserving algorithm for the non-linear dynamics of shells.
International Journal for Numerical Methods in Engineering, Vol. 37(15): pp 2527 – 2549
This and the next image are from:
Felipe Schaedler de Almeida and Armando Miguel Awruch (Civil Engineering, Federal University of Rio Grande do Sul, Porto Alegre, Brazil),
“Corotational nonlinear dynamic analysis of laminated composite shells”, Finite Elements Analysis Design, 2011, 47: 1131–1145, 11th Pan-American Congress of Applied Mechanics – PACAM XI, January 4-8, 2010, Foz do Iguacu, PR, Brazil
ABSTRACT: The dynamic analysis of laminated composite shell structures is performed using a simple displacement-based 18-degree-of-freedom triangular flat shell element, obtained by the superposition of a membrane element and a plate element. The membrane element is based on the assumed natural deviatoric strain formulation (ANDES), having corner drilling degrees of freedom and optimal in-plane bending response. The plate element employs the Timoshenko’s laminated composite beam function to define the deflections and rotations on the element boundaries. This formulation provides first-order shear flexibility to the element and naturally avoids shear-locking problems as thin shells are analyzed. The geometrically nonlinear behavior of the structures is achieved by the element independent corotational formulation (EICR) together with a consistent treatment of finite rotations. An energy conserving procedure for the time-integration of the nonlinear dynamic equations is also included. Finally, two examples are presented to show that the algorithm is able to solve highly nonlinear dynamic problems.
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