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
Related Resources
Study Guide (PDF - 1.2MB)
Readings
Section 6.5
Examples
Problems 6.20, 6.21
References
Bathe, K. J., and A. Chaudhary. “On the Displacement Formulation of Torsion of Shafts with Rectangular Cross-Sections.” International Journal for Numerical Methods in Engineering 18 (October 1982): 1565-1568.
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 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.
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., C. A. Almeida, and L. W. Ho. “A Simple and Effective Pipe Elbow Element: Some Nonlinear Capabilities.” Computers & Structures 17 (1983): 659-667.
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.
