Mesh-based modeling towards engineering analysis

The engineering analysis is the stage of the product design process, where the engineer evaluates a digital prototype, by means of combining shapes and dimensions with materials through physical laws. Unfortunately, this stage only allows the engineer to assess, whether the digital prototype fulfill the requirements or not, but she/he does not have the opportunity to explore design variations, which could lead to improvements in the model. Such an exploration would provide interaction and therefore enrichment to the analysis, since different variations of the same model could be verified and optimized. This paper presents a mesh-based modeling concept for tetrahedral meshes, where CAD-like modifications can be applied to digital prototypes, keeping the quality of the tetrahedral elements and therefore the soundness of the following simulation. In order to keep the quality of the tetrahedral mesh during modifications such as face extrusion, blending change or feature dragging, the topology and the geometry of the tetrahedral mesh are locally adjusted. This adjustment is obtained by a combination of complex topological operations and smoothing techniques, improving the quality of 1-ring vertices and not only of single elements. This method finds an appropriate configuration of the local mesh, which provides a correct interpolation of the mesh nodes. This local configuration is found by evaluating a quality function, which optimizes the gradient of a vertex regarding the 1-ring vertex. The correct interpolation of the mesh nodes generates a low condition number of the simulating linear system, a well-conditioned problem and therefore accuracy in the solution. The proposed concept will allow engineers to interact during the analysis stage and explore different combinations and variations of a digital prototype, by means of modifying the domain and re-simulating its physical behavior. This interaction loop will generate faster optimizations, reducing the time to market of a product and providing engineers with a functionality to better understand how different features influence the solution of a problem.