Theory Manual Version 3.4
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Subsubsection 4.2.2.4: Shell sandwiched between solid elements Up Subsection 4.2.2: Shells with front and back face nodal displacements Chapter 5: Constitutive Models

#### 4.2.2.5 Rigid-Shell Interface

When the node of a deformable shell belongs to a rigid body, we need to substitute the nodal degrees of freedom with the rigid body degrees of freedom. The positions of the shell front face and back face nodes are where is the current position of the rigid body center of mass and is its initial position; is the rotation tensor for the rigid body. We assume that and are connected to the same rigid body. From these relations it follows that virtual displacements are and incremental displacements are where is the skew-symmetric tensor whose dual vector is , such that for any vector . When nodes are flexible (when they do not belong to any rigid body), the virtual work has the general form where denotes any additional degree-of-freedom at that node. If node is rigid we get If node is rigid we get When node belongs to a rigid body, the expression for must be substituted with
Similarly, the linearized virtual work has the general form When node is rigid but node is not, If nodes and are both rigid, If node is not rigid and node is rigid,
Subsubsection 4.2.2.4: Shell sandwiched between solid elements Up Subsection 4.2.2: Shells with front and back face nodal displacements Chapter 5: Constitutive Models