Topics: Beam, plate, and shell elements II

• Formulation of isoparametric (degenerate) beam elements for large displacements and rotations
• A rectangular cross-section beam element of variable thickness; coordinate and displacement interpolations
• Use of the nodal director vectors
• The stress-strain law
• Introduction of warping displacements
• Example analysis: 180 degrees, large displacement twisting of a ring
• Example analysis: Torsion of an elastic-plastic cross-section
• Recommendations for the use of isoparametric beam and shell elements
• The phenomena of shear and membrane locking as observed for certain elements
• Study of solutions of straight and curved cantilevers modeled using various elements
• An effective 4-node shell element (the MITC4 element) for analysis of general shells
• The patch test, theoretical and practical considerations
• Example analysis: Solution of a three-dimensional spherical shell
• Example analysis: Solution of an open box
• Example analysis: Solution of a square plate, including use of distorted elements
• Example analysis: Solution of a 30-degree skew plate
• Example analysis: Large displacement solution of a cantilever
• Example analysis: Collapse analysis of an I-beam in torsion
• Example analysis: Collapse analysis of a cylindrical shell

Instructor: Klaus-Jürgen Bathe