{ 2:::::;:::;::; 1 (9.1)

... due to this activity. In Fig. 9.3 an actual distortion of elements based on the cubic and quadratic ..... a1 + a2. Nixi + a3 Niyi + a4. Nizi. (9.25). If we take ai = a1 + a2xi + a3yi + a4zi and compare ... With no distortion both ele- ments give exact ...
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Mapped elements and numerical integration - 'infinite' and 'singularity' elements 9.1 Introduction In the previous chapter we have shown how some general families of finite elements can be obtained for Co interpolations. A progressively increasing number of nodes and hence improved accuracy characterizes each new member of the family and presumably the number of such elements required to obtain an adequate solution decreases rapidly. To ensure that a small number of elements can represent a relatively complex form of the type that is liable to occur in real, rather than academic, problems, simple rectangles and triangles no longer suffice. This chapter is therefore concerned with the subject of distorting such simple forms into others of more arbitrary shape. Elements of the basic one-, two-, or three-dimensional types will be 'mapped' into distorted forms in the manner indicated in Figs 9.1 and 9.2. In these figures it is shown that the