Abstract
In modern times the finite element method has become established as the universally accepted analysis method in structural design. The method leads to the construction of a discrete system of matrix equations to represent the mass and stiffness effects of a continuous structure. The matrices are usually banded and symmetric. No restriction is placed upon the geometrical complexity of the structure because the mass and stiffness matrices are assembled from the contributions of the individual finite elements with simple shapes. Thus, each finite element possesses a mathematical formula which is associated with a simple geometrical description, irrespective of the overall geometry of the structure. Accordingly, the structure is divided into discrete areas or volumes known as elements. Element boundaries are defined when nodal points are connected by a unique polynomial curve or surface. In the most popular (isoparametric, displacement type) elements, the same polynomial description is used to relate the internal, element displacements to the displacements of the nodes. This process is generally known as shape function interpolation. Since the boundary nodes are shared between neighbouring elements, the displacement field is usually continuous across the element boundaries. Figure 2.1 illustrates the geometric assembly of finite elements to form part of the mesh of a modelled structure.
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Friswell, M.I., Mottershead, J.E. (1995). Finite Element Modelling. In: Finite Element Model Updating in Structural Dynamics. Solid Mechanics and its Applications, vol 38. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8508-8_2
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DOI: https://doi.org/10.1007/978-94-015-8508-8_2
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