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Theory Manual Version 3.4
 Subsection 4.2.1: Shell with mid-surface nodal displacements Up Subsection 4.2.1: Shell with mid-surface nodal displacements Subsubsection 4.2.1.2: Quadrilateral shells 

4.2.1.1 Elastic Shell

For an elastic shell, the internal virtual work becomes where The linearization of the internal virtual work is The first of these integrals may be discretized as where The second integral in (4.2.1.1-3) becomes where Similar expressions may be derived for the external work and inertia forces.
In FEBio a 3-point Gaussian quadrature rule is used for the through-the-thickness integration. FEBio currently supports four- and eight-node quadrilateral and three- and six-node triangular shell elements.
 Subsection 4.2.1: Shell with mid-surface nodal displacements Up Subsection 4.2.1: Shell with mid-surface nodal displacements Subsubsection 4.2.1.2: Quadrilateral shells