239 research outputs found
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Structure Preserving and Scalable Simulation of Colliding Systems
Predictive computational tools to study granular materials are important in fields ranging from the geosciences and civil engineering to computer graphics. The simulation of granular materials, however, presents many challenges. The behavior of a granular medium is fundamentally multi-scale, with pair-wise interactions between discrete granules able to influence the continuum-scale evolution of a bulk material. Computational techniques for studying granular materials must therefore contend with this multi-scale nature.
This research first addresses both the question of how to accurately model interactions between grains and the question of how to achieve multi-scale simulations of granular materials. We propose a novel rigid body contact model and a time integration technique that, for the first time, are able to simultaneously capture five key features of rigid body impact. We further validate this new model and time integration method by reproducing computationally challenging phenomena from granular physics.
We next propose a technique to couple discrete and continuum models of granular materials to one another. This hybrid model reveals a family of possible discretizations suitable for simulation. We derive an explicit integration technique from this framework that is able to capture phenomena previously reserved for discrete treatments, including frictional jamming, while treating bulk regions of the material with a continuum model. To effectively handle the large plastic deformations inherent in the evolution of a granular medium, we further propose a method to dynamically update which regions are treated with a discrete model and which regions are treated with a continuum model. We demonstrate that hybrid simulations of a dynamically evolving granular material are possible and practical, and lay the foundation for further algorithmic development in this space.
Finally, as the the tools used in computational science and engineering become progressively more complex, the ability to effectively train students in the field becomes increasingly important. We address the question of how to train students from a computer science background in numerical computation techniques by proposing a new system to automatically vet and identify problems in numerical simulations. This system has been deployed at the undergraduate and graduate level in a course on physical simulation at Columbia University, and has increased both student retention and student satisfaction with the course
6D Frictional Contact for Rigid Bodies
International audienceWe present a new approach to modeling contact between rigid objects that augments an individual Coulomb friction point-contact model with rolling and spinning friction constraints. Starting from the intersection volume, we compute a contact normal from the volume gradient. We compute a contact position from the first moment of the intersection volume, and approximate the extent of the contact patch from the second moment of the intersection volume. By incorporating knowledge of the contact patch into a point contact Coulomb friction formulation, we produce a 6D constraint that provides appropriate limits on torques to accommodate displacement of the center of pressure within the contact patch, while also providing a rotational torque due to dry friction to resist spinning. A collection of examples demonstrate the power and benefits of this simple formulation
ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
We present a differentiable dynamics solver that is able to handle frictional
contact for rigid and deformable objects within a unified framework. Through a
principled mollification of normal and tangential contact forces, our method
circumvents the main difficulties inherent to the non-smooth nature of
frictional contact. We combine this new contact model with fully-implicit time
integration to obtain a robust and efficient dynamics solver that is
analytically differentiable. In conjunction with adjoint sensitivity analysis,
our formulation enables gradient-based optimization with adaptive trade-offs
between simulation accuracy and smoothness of objective function landscapes. We
thoroughly analyse our approach on a set of simulation examples involving rigid
bodies, visco-elastic materials, and coupled multi-body systems. We furthermore
showcase applications of our differentiable simulator to parameter estimation
for deformable objects, motion planning for robotic manipulation, trajectory
optimization for compliant walking robots, as well as efficient self-supervised
learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor
Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control
The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques
Solving Coupled Differential Equation Groups Using PINO-CDE
As a fundamental mathmatical tool in many engineering disciplines, coupled
differential equation groups are being widely used to model complex structures
containing multiple physical quantities. Engineers constantly adjust structural
parameters at the design stage, which requires a highly efficient solver. The
rise of deep learning technologies has offered new perspectives on this task.
Unfortunately, existing black-box models suffer from poor accuracy and
robustness, while the advanced methodologies of single-output operator
regression cannot deal with multiple quantities simultaneously. To address
these challenges, we propose PINO-CDE, a deep learning framework for solving
coupled differential equation groups (CDEs) along with an equation
normalization algorithm for performance enhancing. Based on the theory of
physics-informed neural operator (PINO), PINO-CDE uses a single network for all
quantities in a CDEs, instead of training dozens, or even hundreds of networks
as in the existing literature. We demonstrate the flexibility and feasibility
of PINO-CDE for one toy example and two engineering applications: vehicle-track
coupled dynamics (VTCD) and reliability assessment for a four-storey building
(uncertainty propagation). The performance of VTCD indicates that PINO-CDE
outperforms existing software and deep learning-based methods in terms of
efficiency and precision, respectively. For the uncertainty propagation task,
PINO-CDE provides higher-resolution results in less than a quarter of the time
incurred when using the probability density evolution method (PDEM). This
framework integrates engineering dynamics and deep learning technologies and
may reveal a new concept for CDEs solving and uncertainty propagation
Development of a Multi-Physics model of a Civil Aircraft for Ground Manoeuvres using Modelica
Aircraft systems have become progressively more mechatronic and the interactions between
these systems are complex in nature. The objective of the approach followed in
this work is to provide means to navigate through the complexity of these systems. In
particular the project aims to develop a modelling paradigm that supports model reuse.
In this thesis the capabilities of an object-oriented language, Modelica, are investigated
in developing reusable library components. The component-models derived are acasual
parametric objects. These have been reused in developing a complex model of a large
civilian aircraft and its associated hydro-mechanical steering systems.
Modelica’s acasuality and object-oriented nature are features that help in the development
of library components. By following the systematic approach described in this
work when developing such model-components, the components at different levels of
granularity can be reused and this may aid will lead to agility in the analyses of the
design process
Efficient Collision Detection for Brittle Fracture
International audienceIn complex scenes with many objects, collision detection plays a key role in the simulation performance. This is particularly true for fracture simulation, where multiple new objects are dynamically created. In this paper, we present novel algorithms and data structures for collision detection in real-time brittle fracture simulations. We build on a combination of well-known efficient data structures, namely distance fields and sphere trees, making our algorithm easy to integrate on existing simulation engines. We propose novel methods to construct these data structures, such that they can be efficiently updated upon fracture events and integrated in a simple yet effective self-adapting contact selection algorithm. Altogether, we drastically reduce the cost of both collision detection and collision response. We have evaluated our global solution for collision detection on challenging scenarios, achieving high frame rates suited for hard real-time applications such as video games or haptics. Our solution opens promising perspectives for complex brittle fracture simulations involving many dynamically created objects
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