Lecture 20: Beam, Plate, and Shell Elements II

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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