Use of Hexahedral Element,PN5X1,in Problems with Curved Boundaries

Abstract

Finite element analysis is mainly developed to investigate the behaviour under load of structures with complex geometries, in which it is either difficult or impossible to obtain solutions using conventional methods. The solution of many practical problems, such as those of dam structures, rock mechanics, flanges, welds, crankshafts, and thick?walled pipe intersections, necessarily requires the finite element method. It is interesting to note that almost all practical problems involve curved boundaries. One way of obtaining a good approximation of the domain is by using a fine mesh. On the other hand, isoparametric finite elements can closely approximate curved boundaries. While approximating such boundaries, distortion of elements is natural. However, there are problems associated with distorted elements, such as locking due to large aspect ratios, distortion sensitivity, and several others. Thus, there is a real need to look at problems with curved boundaries using a fresh approach. We develop here a new technique for dealing with such problems by using hexahedral elements. We modify a 14?node hexahedral element, PN5X1, and then use it to analyse a variety of problems with curved boundaries. The main approach is based on a demonstration that conventional interpolation functions can also be used to extrapolate in the outside neighbourhood of the hexahedron. Hence, strain energy integration used to determine the stiffness matrix can be extended to both over?filled and under?filled hexahedra. Suitable ways to represent the over?filling and under?filling, and appropriate integration schemes, help us to extend PN5X1 to accommodate unmodified geometries of structural components. We also investigate the computational economy of the proposed method by trying simplified integration schemes and comparing the results with those obtained by other methods.