**JAM 2008 Abstract**

**Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory
**

Peter J. Ryan, George G. Adams, Nicol E. McGruer

Summary

In beam theory, constraints can be classified as fixed/pinned depending on whether the rotational stiffness of the support is much greater/less
than the rotational stiffness of the free standing portion. For intermediate values of the rotational stiffness of the support, the boundary conditions
must account for the finite rotational stiffness of the constraint.
In many applications, particularly in MEMS and nanomechanics, the constraints exist only on one side of the beam. In such cases it
may appear at first that the same conditions on the constraint stiffness hold. However, it is the purpose of this paper to demonstrate
that even if the beam is perfectly bonded on one side only to a completely rigid constraining surface, the proper model for the boundary
conditions for the beam still needs to account for beam deformation in the bonded region. The use of a modified beam theory, which
accounts for bending, shear, and extensional deformation in the bonded region, is required in order to model this behavior. Examples
are given for cantilever, bridge, and guided structures subjected to either transverse loads or residual stresses. The results show significant
differences from the ideal bond case. Comparisons made to a three-dimensional finite element analysis show good agreement.
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