Lecture 19: Beam, Plate, and Shell Elements I

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Topics: Beam, plate, and shell elements I

  • Brief review of major formulation approaches
  • The degeneration of a three-dimensional continuum to beam and shell behavior
  • Basic kinematic and static assumptions used
  • Formulation of isoparametric (degenerate) general shell elements of variable thickness for large displacements and rotations
  • Geometry and displacement interpolations
  • The nodal director vectors
  • Use of five or six nodal point degrees of freedom, theoretical considerations and practical use
  • The stress-strain law in shell analysis, transformations used at shell element integration points
  • Shell transition elements, modeling of transition zones between solids and shells, shell intersections

Instructor: Klaus-Jürgen Bathe

Related Resources

Study Guide (PDF)


Section 6.5


Problems 6.20, 6.21


Bathe, K. J., and S. Bolourchi. “A Geometric and Material Nonlinear Plate and Shell Element.Computers & Structures 11 (February 1980): 23-48.

Bathe, K. J., and S. Bolourchi. “Large Displacement Analysis of Three-Dimensional Beam Structures.International Journal for Numerical Methods in Engineering 14 (1979): 961-986.

Bathe, K. J., E. Dvorkin, and L. W. Ho. “Our Discrete Kirchhoff and Isoparametric Shell Elements for Nonlinear Analysis: An Assessment.Computers & Structures 16 (1983): 89-98.

Bathe, K. J., and L. W. Ho. “A Simple and Effective Element for Analysis of General Shell Structures.Computers & Structures 13 (October-December 1981): 673-681.

Dvorkin, E., and K. J. Bathe. “A Continuum Mechanics-Based Four-Node Shell Element for General Nonlinear Analysis.Engineering Computations 1 (1984): 77-88.

Bathe, K. J., and P. M. Wiener. “On Elastic-Plastic Analysis of I-Beams in Bending and Torsion.Computers & Structures 17 (1983): 711-718.

Bathe, K. J., and E. Dvorkin. “A Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation.International Journal for Numerical Methods in Engineering 21 (February 1985): 367-383.

Bathe, K. J., and E. Dvorkin. “A Formulation of General Shell Elements: The Use of Mixed Interpolation of Tensorial Components.International Journal for Numerical Methods in Engineering 22 (March 1986): 687-722.

Lee, P.S., and K. J. Bathe. “Development of MITC Isotropic Triangular Shell Finite Elements.Computers & Structures 82 (May 2004): 945-962.

Bathe, K. J., and P. S. Lee. “Measuring the Convergence Behavior of Shell Analysis Schemes.Computers & Structures 89 (February 2011): 285-301.

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