Accurate and fast algorithms for contour plotting in 2D and 3D domains for finite element analysis FEA data

Abstract

Contour plotting is one of the basic operations performed in many engineering analyses where visual inspection of results is to be carried out. Such analyses produce a large amount of data which is cumbersome to interpret in its numerical form. The graphical representation of the numerical data in the form of contour lines in 2D and contour surfaces in 3D makes the analyses more informative and faster. Finite Element Analysis (FEA) is one of such analyses which produces voluminous data and whose graphical representation becomes a necessity. Contour plotting is one method which is used for graphical representation. It substitutes a large amount of numerical data into graphical patterns, which helps to perceive the physical consequences of a calculation. To users, not familiar with the details of FEA, it is possibly one of the best ways to perceive the analysis results. So, once the solver determines the element resultants, a post-processor in the form of contour plots is used to graphically display the domain response to the applied loads and boundary conditions. For a user, the accuracy of the analysis results depends on the accuracy of the graphical patterns which are displayed as contour lines or surfaces on the screen. Generally, higher order elements are used for accurate analysis, but are degenerated into linear elements for contour plotting to avoid complexity. This leads to loss of information in the graphical plotting. In some cases, to visualize the solutions effectively, approximations on finer meshes are required. In the present work, an attempt is made to develop accurate and fast algorithms for different meshes used for analysis in FEA. All the algorithms depend upon the contour equations developed using Shape Functions for these meshes. The simplest way to plot contours on 2D domain is to use linear interpolation over triangular elements. This method works well only if the accuracy of higher order is not required.