The saw-tooth method is currently extended in three-dimensions. Only the linear saw-tooth (now applied in two directions over each panel) has been completed. The singular integrals of constant elements are evaluated analytically by using the expressions of Hong et al [11]. All other integrations, including the direct and singular integrations of linear saw-teeth, are handled numerically. Details on the 3-D formulation and results will be given in []. To show the applicability of the saw-tooth correction method into three dimensions we only include in this paper results for a 3-D beam with square section, as shown in Figure 16. The predicted maximum deflection (.374m) is in excellent agreement to that predicted by beam theory (.375m).
Figure 16: Deflected shape for a 3-D
beam (length is 1m and section is .1 m rectangle) under uniform loading
predicted by the linear saw-tooth correction method. The deflections have been
magnified by a factor of 10. The used discretization is also shown.