ABSTRACT
In Chapter 7, methods were discussed for deriving the static stiffness and consistent mass matrices for line elements such as beam, bar and shaft elements. Two fundamental assumptions made in the derivation of these matrices were
• what stresses are significant in any particular problem • how the displacement in the member is related through shape functions to
the displacements at the ends of the member. A skeletal structure is assembled from clearly identifiable members (elements) connected at joints (nodes). A continuum such as a plate or a floor slab has no such identifiable members (elements) connected at joints (nodes). However, in order to extend the ideas developed in Chapter 7 to continuum structures, it is necessary to imagine that the structure is in fact assembled from a set of imaginary elements called finite elements connected only at imaginary joints called nodes. This process is known as spatial discretisation. Because of the fact that finite elements are imaginary, a structure could be discretised in various ways, using triangular, rectangular, quadrilateral finite elements with straight or curved boundaries. Some of the common shapes of elements used are shown in Fig. 8.1.
