Search results for "Rigid body"
showing 7 items of 17 documents
A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time
2004
The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
Parallel Collision Queries on the GPU
2013
We present parallel algorithms to accelerate collision tests of rigid body objects for a high number of independent transformations as they occur in sampling-based motion planning and path validation problems. We compare various GPU approaches with a different level of parallelism against each other and against a parallel CPU implementation. Our algorithms require no sophisticated load balancing schemes. They make no assumption on the distribution of the input transformations and require no pre-processing. Yet, we can perform up to 1 million collision tests per second with our best GPU implementation in our benchmarks. This is about 2.5X faster than our reference multi-core CPU implementati…
Expansive Voronoi Tree: A Motion Planner for Assembly Sequence Planning
2021
One major challenge in Assembly Sequence Planning (ASP) for complex real-world CAD-scenarios is to find an appropriate disassembly path for each assembled part. Complex real-world scenes are characterized by a large installation space. There each part has many different possible disassembly paths that differ in length and clearance. However, due to tight packing in the installation space, these paths can contain narrow passages. Therefore a motion planner is needed that is able to globally search for a reasonable path and to locally overcome narrow passages. Moreover, since motion planning requests are executed in the ASP context over and over again for many parts, both for those that can b…
Saliency Features for 3D CAD-Data in the Context of Sampling-Based Motion Planning
2021
In this paper, we consider disassembly scenarios for real-world 3D CAD-data, where each component is defined by a triangle mesh. For a fast construction of collision-free disassembly paths, common approaches use sampling-based rigid body motion planning which is well studied in the literature. One fact that has so far received little attention is that in industrial disassembly scenarios components are often attached to each other with flexible fastening elements like clips. In the planning process, the fastening elements show the following characteristics: 1) They can cause complex non-linear disassembly paths. 2) They are often deformable. 3) They are usually modeled in a relaxed state and…
The tennis racket effect in a three-dimensional rigid body
2017
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Differen…
Optimal control of spin-systems: Applications to Nuclear Magnetic Resonance and Quantum Information
2016
The goal of this thesis is to apply the optimal control theory to Nuclear Magnetic Resonance and Quantum Information. In a first step, we introduce the different topics and the dynamics of the analyzed systems. We give the necessary tools to use the Pontryagin Maximum Principle, and also an optimization algorithm, namely GRAPE. The first work is an application of the PMP to the control of a three-spin chain with unequal couplings. We continue with the study of a classical problem called "the tennis racket effect", which is a non-linear phenomenon occuring during the free rotation of a three-dimensional rigid body. We use the results in the following chapter to determine some control laws fo…