Plotting of contours in a natural way

Abstract

SUMMARYA simple and straightforward scheme for plotting contours is introduced. For any function the appropriate contours are traced on the paths of constant function values disclosing the information contained in the shape functions. The exactness of the contours matches that of the finite element analysis. Extreme value considerations must be carried out to decide whether contours appear in an element at all. Three co-ordinate systems are dealt with: the local, the global and the screen co-ordinate system, and the necessary mutual transformations. A short section deals with the treatment of contour discontinuities acrosy element borders which frequently occur with stresses and heat fluxes. Finally, some examples are shown.

Algorithms for Accurate and Fast Plotting of Contour Surfaces in 3D Using Hexahedral Elements

“…14a, the time taken for 68 elements is 0.3297 s while the direct approach takes 0.604396 s for generation and plotting of one contour surface. It can be seen that the execution time taken by the developed algorithm is nearly 50 % less as compared to that of the direct method [10,12].…”

“…These two objectives are conflicting in nature. Often in practical applications accuracy becomes one of the major issues and as observed earlier the direct method suggested by the researchers [10,12] is used for deriving contour surface. This method is computation intensive and does not provide contour surface in the form of explicit boundaries.…”

“…Since the basic approach of [9] is the same as that of [8], it also develops inaccuracies in contour locations. Stelzer and Welgel [10] suggest a direct method for tracing contour surfaces in 3D by converting the contour equation / (r, s, t) = C into r = w(s, t) (where /(r, s, t) is the interpolation function in local coordinates r, s and t), and then varying s and t in the interval [-1, 1] and restricting r between -1 and ?1. The contour surface is represented as a set of contour points in local coordinates which are mapped to global coordinates and finally converted into screen coordinates for display purpose.…”

Validation of finite element modelling through photoelastic fringe contours

“…Earlier research for processing of FE results was con®ned to plotting line contours. 6,7 In contrast to line contours, the fringe contours appear as broad bands. The thickness of the fringe is indicative of the gradient of the variable.…”

Development of photoelastic fringe plotting scheme from 3D FE results

“…There have been e orts to post process FE results of two-dimensional models to plot photoelastic contours. One way of plotting contours is to ÿnd the points within a 2D element for which the ÿeld variable corresponds to a given contour value [5][6][7]. This necessitates the use of solving non-linear equations in determining the co-ordinates of the points forming the contour.…”