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)
Readings
Section 6.5
Examples
Problems 6.20, 6.21
References
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.
