Keywords: object oriented programming, visualization, boundary element method.

The paper present an object-oriented application for visualization of boundary and domain data resulting from numerical analysis of elastic solid models by the boundary element method (BEM). The C++ classes that implement the visualization pipeline and rendering resources of the application are components of OSW -- Object Structural Workbench --, a toolkit for developing object-oriented modeling programs in science and engineering [1]. To implement the proposed application, several new classes for BEM visualization have been created and added into the OSW Class Library (OCL).

The idea behind the implementation is simple. In addition to discretization of the boundary of the solid into boundary elements, a volume mesh is used in order to provide the interpolation functions necessary to visualize domain data. The visualization pipeline begins with a pre-processing step in which the domain of the input solid model is discretized in a volume mesh made up of tetrahedral cells. Next, one applies a boundary element extractor filter to the volume mesh generated in the previous step. Such filter takes as input the tetrahedron mesh and generates as output the same input mesh, into which are added triangular boundary elements corresponding to the tetrahedron faces without neighborhood. The resulting dataset is made up of two kinds of elements: triangular boundary elements and tetrahedral internal cells, which share the same mesh nodes. Boundary and internal nodes are appropriately labeled. The next step is to solve the discretized model by using the object-oriented boundary element processor presented in [2]. After that, one knows the displacements and surface forces at mesh boundary nodes, as well as the displacements and stresses at mesh internal nodes. The triangle and tetrahedron interpolation functions can be used to approximate values at any point on and , respectively. From the analysis results, one can be use several filters to extract boundary and domain values and visualize them by employing scalar and vector techniques as color mapping, contouring, warping, and oriented glyphs. Domain values can be also viewed on implicitly defined surfaces that cut the solid model.

Figure 1 illustrates an elastic thick spherical shell with external and internal radius 80 cm and 60 cm, respectively, modulus of elasticity 1000 Pa, and Poisson's ratio 0.3, in which was applied an internal pressure equal to 1 Pa. The window at the left displays color map and isolines for boundary displacements in the direction of the Y-axis. At the right, one uses transparency to show color map, isolines, and conical glyphs for displacements at domain points on two perpendicular sections crossing the deformed solid.

The main advantage of the proposed implementation is that, once obtained the analysis results, both visualization networks execution and image rendering are carried out in real-time, even when it runs on common Pentium-based workstations. The main disadvantage is the necessity of a volume mesh, which should not be required in BEM analysis. Improvements on the next version include the elimination of the domain mesh ant the implementation of tensor visualization techniques, such as tensor ellipsoids and hyperstreamlines.

1

P.A. Pagliosa, J.B. Paiva, "OSW: A Toolkit for Object-oriented Structural Mode-ling", in Developments in Engineering Computational Technology, ed. B.H.V. Topping, Civil-Comp Press, 151-166, 2000.

2

P.A. Pagliosa, J.B. Paiva, "Object-oriented Boundary Element Programming: A First Approach", in Third International Conference on Engineering Computational Technology, Prague, ed. B.H.V. Topping, Civil-Comp Press, 25-26, 2002. doi:10.4203/ccp.76.9

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