47 research outputs found
Asynchronous Variational Contact Mechanics
An asynchronous, variational method for simulating elastica in complex
contact and impact scenarios is developed. Asynchronous Variational Integrators
(AVIs) are extended to handle contact forces by associating different time
steps to forces instead of to spatial elements. By discretizing a barrier
potential by an infinite sum of nested quadratic potentials, these extended
AVIs are used to resolve contact while obeying momentum- and
energy-conservation laws. A series of two- and three-dimensional examples
illustrate the robustness and good energy behavior of the method
Discrete Differential Geometry of Thin Materials for Computational Mechanics
Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation
Functional Generative Design: An Evolutionary Approach to 3D-Printing
Consumer-grade printers are widely available, but their ability to print
complex objects is limited. Therefore, new designs need to be discovered that
serve the same function, but are printable. A representative such problem is to
produce a working, reliable mechanical spring. The proposed methodology for
discovering solutions to this problem consists of three components: First, an
effective search space is learned through a variational autoencoder (VAE);
second, a surrogate model for functional designs is built; and third, a genetic
algorithm is used to simultaneously update the hyperparameters of the surrogate
and to optimize the designs using the updated surrogate. Using a car-launcher
mechanism as a test domain, spring designs were 3D-printed and evaluated to
update the surrogate model. Two experiments were then performed: First, the
initial set of designs for the surrogate-based optimizer was selected randomly
from the training set that was used for training the VAE model, which resulted
in an exploitative search behavior. On the other hand, in the second
experiment, the initial set was composed of more uniformly selected designs
from the same training set and a more explorative search behavior was observed.
Both of the experiments showed that the methodology generates interesting,
successful, and reliable spring geometries robust to the noise inherent in the
3D printing process. The methodology can be generalized to other functional
design problems, thus making consumer-grade 3D printing more versatile.Comment: 8 pages, 12 figures, GECCO'1