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Published in:
2014 | OriginalPaper | Chapter
4. Elements and Local Coordinates
Author : M. Reza Eslami
Published in: Finite Elements Methods in Mechanics
Publisher: Springer International Publishing
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Abstract
The presentation of the finite element method for the elastic membrane problem, a triangular element with straight sides and linear shape function to approximate the elevation of the elastic membrane due to lateral pressure, was employed. In this chapter, we correct ourself that there is no limitation as far as the geometry of the element and the order of approximation of the shape function is concerned. In one, two, and three dimensional problems elements with higher order geometries and approximating shape functions may be used to prepare a finite element model. Also, since it is always more efficient to employ the local coordinates for the integration purpose of the element stiffness and force matrices, the local and global coordinate systems are discussed and the Jacobian matrix is explained.