Beam and frame finite elements model slender structural members whose response includes bending, shear, axial deformation, moments, and rotations.
How They Work
The Euler-Bernoulli beam element uses transverse displacement and rotation degrees of freedom at each node. Its displacement field is cubic so that both displacement and slope can be matched at nodes. The resulting stiffness relates nodal transverse forces and bending moments to nodal deflections and rotations.
For short or deep beams, transverse shear deformation can become significant, motivating Timoshenko beam theory. Frame elements then combine axial bar behavior with beam bending behavior and use coordinate transformation matrices so arbitrarily oriented members can be assembled into plane frames, grids, and spatial frames.
Why It Matters
Beam and frame elements sit between simple axial trusses and full continuum or shell models. They are efficient for bridges, buildings, machine frames, and grid structures when member-level idealization is appropriate.
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