Rigid impacts of three-dimensional rocking structures

Studies of rocking motion aim to explain the remarkable earthquake resistance of rocking structures. State-of-the-art assessment methods are mostly based on planar models, despite ongoing efforts to understand the significance of three-dimensionality. Impacts are essential components of rocking motion. We present experimental measurements of free-rocking blocks on a rigid surface, focusing on extreme sensitivity of impacts to geometric imperfections, unpredictability, and the emergence of three-dimensional motion via spontaneous symmetry breaking. These results inspire the development of new impact models of three-dimensional facet and edge impacts of polyhedral objects. Our model is a natural generalization of existing planar models based on the seminal work of George W. Housner. Model parameters are estimated empirically for rectangular blocks. Finally, new perspectives in earthquake assessment of rocking structures are discussed.

Rigid Impacts of Three-dimensional Rocking Structures

Studies of rocking motion aim to explain the remarkable earthquake resistence of rocking structures . State - of - the -art assessment methods are mostly based on planar models , despite ongoing efforts to understand the significance of three - dimensionality . Impacts are essential components of rocking motion . We present experimental measurements of free -rocking blocks , focusing on extreme sensitivity of impacts to geometric imperfections , unpredictability , and the emergence of three - dimensional motion via spontaneous symmetry breaking . These results inspire the development of new impact models of three dimensional facet and edge impacts of polyhedral objects . Our model is a natural generalization of existing planar models based on the seminal work of George W. Housner . Model parameters are estimated empirically for rectangular blocks . Finally , new perspectives in earthquake assessment of rocking structures are discussed .

Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

Thickness and clearance visualization based on distance field of 3D objects

This paper proposes a novel method for visualizing the thickness and clearance of 3D objects in a polyhedral representation. The proposed method uses the distance field of the objects in the visualization. A parallel algorithm is developed for constructing the distance field of polyhedral objects using the GPU. The distance between a voxel and the surface polygons of the model is computed many times in the distance field construction. Similar sets of polygons are usually selected as close polygons for close voxels. By using this spatial coherence, a parallel algorithm is designed to compute the distances between a cluster of close voxels and the polygons selected by the culling operation so that the fast shared memory mechanism of the GPU can be fully utilized. The thickness/clearance of the objects is visualized by distributing points on the visible surfaces of the objects and painting them with a unique color corresponding to the thickness/clearance values at those points. A modified ray casting method is developed for computing the thickness/clearance using the distance field of the objects. A system based on these algorithms can compute the distance field of complex objects within a few minutes for most cases. After the distance field construction, thickness/clearance visualization at a near interactive rate is achieved.