Keywords: co-rotational approach, vectorial rotational variable, layered model, material nonlinearity, mixed interpolation of tensorial components, discrete shear gap.

A six-node curved co-rotational shell element with layered model is presented. Since the vectorial rotational variables [1,2] are employed in this shell element, the moment corresponding to this new defined rotational variable and the relationship between the vectorial rotational variables and rotational angles are shown in this work. The present element has several features:

• the rotational variables are commutative as the translational variables, so that the stiffness matrix of this element is symmetric;
• the updating of the rotational variables are simplified, so that the spin matrix for the updating of the convention rotational variables is unnecessary;
• a layered model is employed in this element so that it can be used in material nonlinear analyses, such as reinforced concrete structures, functionally graded material structures, and other elasto-plastic material structures.

The technique of mixed interpolation of tensorial components [3] and discrete shear gap [4] are adopted in this element to circumvent the membrane locking and the shear locking, respectively. The forward Euler algorithm with sub-increment technique [5] is used for elasto-plastic analyses. Owen's concrete model [6] is adopted in the present shell element for the current version so that this element can be used for reinforced concrete slabs.

Five sets of numerical examples are shown to verify the effectiveness and robustness of this element in the shell structures with different geometry (initially flat plate, initially curved in one direction roof, initially curved in two directions shell) and different material constitutions (linear elastic material, functionally graded material, reinforced concrete and elasto-plastic material).

1

Z.X. Li, L. Vu-Quoc, "An efficient co-rotational formulation for curved triangular shell element", International Journal for Numerical Methods in Engineering, 72(9), 1029-1062, 2007. doi:10.1002/nme.2064

2

Z.X. Li, B.A. Izzuddin, L. Vu-Quoc, "A 9-node co-rotational quadrilateral shell element", Computational Mechanics, 42(6), 873-884, 2008. doi:10.1007/s00466-008-0289-8

3

P.S. Lee, K.J. Bathe, "Development of MITC isotropic triangular shell finite elements", Computers & Structures, 82(11-12), 945-962, 2004. doi:10.1016/j.compstruc.2004.02.004

4

K.U. Bletzinger, M. Bischoff, E. Ramm, "A unified approach for shear-locking-free triangular and rectangular shell finite elements", Computers & Structures, 75(3), 321-334, 2000. doi:10.1016/S0045-7949(99)00140-6

5

D.R.J. Owen, E. Hinton, "Finite element in plasticity, theory and practice", Pineridge Press Limited, Swansea, United Kingdom, 1980.

6

D.R.J. Owen, J.A. Figueiras, "Ultimate load analysis of reinforced concrete plates and shells including geometric nonlinear effects", in E. Hinton, D.R.J. Owen, (Editors), "Finite element software for plates and shells", Pineridge Press, Swansea, United Kingdom, 327-396, 1984.

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