Abstract
The triangular elements with quadratic and cubic shape functions in terms of the local area coordinates are presented and coordinate transformation law with the associated Jacobian matrix calculations are given in the chapter. As an application, the Field problem in two dimensions is considered and employing the quadratic triangular element, the stiffness and force matrices are calculated. The quadrilateral element is discussed in the following and the shape functions in the global and local coordinates are obtained. The field problem is reconsidered and the element matrices are calculated employing the bilinear quadrilateral element.
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Further Readings
Nejad-Malayeri AR, Mansour K (1999) Finite element solution of two-dimensional potential flow using linear, second, and third order shape functions, B.Sc. project, submitted to the Aeronautical and Aerospace Department, Amirkabir University of Technology, Spring
Segerlind LJ (1984) Applied finite element analysis. Wiley, New York
Bathe KJ, Wilson EL (1976) Numerical methods in finite element analysis. Prentice Hall Inc., New Jersey
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© 2014 Springer International Publishing Switzerland
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Eslami, M.R. (2014). Two-Dimensional Higher Order Elements. In: Finite Elements Methods in Mechanics. Solid Mechanics and Its Applications, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-08037-6_15
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DOI: https://doi.org/10.1007/978-3-319-08037-6_15
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-08037-6
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