Keywords: shell element, three-dimensional solid element, reinforced concrete, geometric nonlinearity, material nonlinearity, engineering practice..

A family of new three-dimensional isoparametric curvilinear shell elements is presented. Their kinematic behaviour resembles that of usual two-dimensional shells. All points through its thickness remain located on a line passing through the corresponding top and bottom nodes of the shell. However, their distance can change. They are modelled as three-dimensional objects with 4 to 9 nodes at the top surface and the same at the bottom surface. Three displacement degrees of freedom (DOFs) are allocated at each node of the element, so that for example a (9+9) node element has 54 DOFs. A similar two-dimensional shell element would feature 9 nodes located at the shell's mid-plane, each of them having 3 displacements plus 2 rotational DOFs, i.e. 45 DOFs in total. Although the additional DOFs may involve a small overhead in execution cost, it is mitigated by the easy use of the new shells, their three-dimensional visualization, simple connection to adjacent three-dimensional solid parts etc. The elements consider both geometrical and material nonlinearity and do not suffer from locking or any rank deficiency. An analysis of the calculated maximum displacement vs. the mesh density for the case of a shallow and deep square slab demonstrates the performance of the three-dimensional shell elements presented in this paper.

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