Abstract
Finite element methods for solving biharmonic boundary value problems are considered. The particular problem discussed is that of a clamped thin plate. This problem is reformulated in a weak form in the Sobolev space \({\text{W}}_2^2 \). Techniques for setting up conforming trial functions for the weak problem are described, and these functions are utilized in a Galerkin technique to produce finite element solutions. The shortcomings of various trial function formulations are discussed, and a macro-element approach to local mesh refinement using rectangular elements is given.
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Whiteman, J.R. (1975). Conforming Finite Element Methods for the Clamped Plate Problem. In: Albrecht, J., Collatz, L. (eds) Finite Elemente und Differenzenverfahren. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 28. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5861-8_10
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DOI: https://doi.org/10.1007/978-3-0348-5861-8_10
Publisher Name: Birkhäuser, Basel
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