Nonlinear Analysis

Lecture 20: Beam, Plate, and Shell Elements II

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

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