A Lookup-Table-Based Approach for Spatial Analysis of Contact Problems

The aim of this work is to present an efficient methodology to deal with general 3D-contact problems. This approach embraces three steps: geometrical definition of 3D surfaces, detection of the candidate contact points, and evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and ease in handling freeform shapes. This task is carried during preprocessing, which is performed before starting the multibody analysis. The preprocessing procedure can be condensed into four steps: a regular and representative collection of surface points is extracted from the 3D-parametric surface; for each point the tangent vectors to the u and v directions of the parametric surface and the normal vector are computed; the geometrical information on each point is saved in a lookup table, including the parametric point coordinates, the corresponding Cartesian coordinates, and the components of the normal, tangent, and bitangent vectors; the lookup table is rearranged such that the u-v mapping is converted into a 2D matrix being this surface data saved as a direct access file. For the detection of the contact points, the relative distance between the candidate contact points is computed and used to check if the bodies are in contact. The actual contact points are selected as those that correspond to the maximum relative indentation. The contact forces are determined as functions of the indentation or pseudopenetration, impact velocity, and geometric and material properties of the contacting surfaces. In general, lookup tables are used to reduce the computation time in dynamic simulations. However, the application of these schemes involves an increase of memory needs. Within the proposed approach, the amount of memory used is significantly reduced as a result of a partial upload into memory of the lookup table. A slider-crank mechanism with a cup on the top of the slider and a marble ball are used as a demonstrative example. A contact pair is considered between a cup and a marble ball, the contact forces for which are computed using a dissipative contact model.