Georges M. Fadel

Proceedings of the ASME Design Engineering Technical Conference

The meta-material design of the shear layer of a non-pneumatic wheel was completed using topology optimization. In order to reduce the hysteretic rolling loss, an elastic material is used and the shear layer microstructure is defined to achieve high compliance comparable to that offered by the elastomeric materials. To simulate the meta-material properties of the shear layer, the volume averaging analysis, instead of more popular homogenization methods, is used as the relative size of the shear layer places realistic manufacturing constraints on the size of unit cells used to generate the meta-material. In this design scenario the properties predicted by the homogenization methods are not accurate since the homogenization scaling assumptions are violated. A number of optimal designs are shown to have meta-material properties similar to those of the linear elastic properties of elastomers, making them good meta-material candidates for the shear layer of the non-pneumatic wheel.Copyright

Shear compliant hexagonal meso-structures having high shear strength and high shear strain

A shear layer for a shear band that is used in a tire is provided that has multiple cells or units having an auxetic configuration and that are constructed from aluminum or titanium alloys. The cells may have an angle of −10°.

Three-Dimensional Packing by a Heuristic-based Sequential Genetic Algorithm

This paper presents a hybrid Genetic Algorithm for three-dimensional packing optimization. It is applicable to a class of packing problems where the final number of packed items is unknown. Examples include the bin packing problem and the luggage capacity problem where the compactness or packing efficiency must be maximized by selecting an appropriate subset of items from a predefined set and packing them in a predefined container. Many algorithms, which are reviewed in this paper, have been developed in various engineering fields for specific applications. Packing algorithms can be categorized into two types according to the definition of the design variables. In the first type, the design variables are the spatial coordinates of the packed items. In this case, a constraint specifying zero collision between items must be considered and evaluated for each trial set of design variables. In the second type, the design variables correspond to the sequential order in which the items are considered for packing. In this case, the location of an item is unknown until it is successfully packed inside the container based on a sequence. The advantage of the latter approach is that the zero-collision constraint is implicitly defined in the packing procedure, thereby reducing the need for collision detection and the overall computation effort. The present algorithm is of the second type. The algorithm was developed in two phases. In the first phase, the algorithm was extensively studied and improved using a simplified packing problem where the container and all items are modeled as rectangular prisms with discrete 90-degree rotations. This phase allowed the identification of appropriate values for the problem-dependent genetic parameters such as crossover and mutation rates. In the second phase, sets of heuristic rules were implemented and tested. The use of appropriate heuristics led to an increase in computational efficiency without significant loss in optimality. This paper describes the algorithm and its multiple variants defined by the heuristic rules imbedded in the packing strategy. Several heuristics and packing strategies are presented and the issues related to computational efficiency are discussed. The algorithm is demonstrated on several test problems.

Using non-simply connected unit cells in the multiscale analysis and design of meta-materials

A method to discretize materials into lattices using non-simply connected, rectangular unit cells such that the corners of the unit cells do not necessarily meet is proposed as an alternative to discretizing with non-square, parallelogram unit cells. When analyzing non-simply connected lattices, the methods commonly used to evaluate linear elastic properties, homogenization and volume averaging, are shown to require only minor changes in their nite element implementations. The linear elastic properties of honeycomb structures, decomposed into non-simply connected lattices, are shown to demonstrate the same convergence characteristics illustrated in the literature for periodic materials with simply connected unit cells. Additionally, these mechanical properties agree with those predicted by established analytical formulae. Finally, topology optimization examples are used to demonstrate the potential application of the proposed methods to meta-material design. Notably, an auxetic honeycomb structure is obtained as a local minimum to a simple optimization problem.