Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThree-dimensional multi-mesh material point method for solving collision problems
124
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and Sulskycite{Bardenhagen2000,Bardenhagen2001}, Hu and Chencite{Hu_Chen2003}. An improved one for three-dimensional material point method is presented in this paper. The improved algorithm emphasizes the energy conservation of the system and faithfully recovers opposite acting forces between contacting bodies. Contrasted to the one by Bardenhagen, both the normal and tangential contacting forces are more appropriately applied to the contacting bodies via the contacting nodes of the background mesh; Contrasted to the one by Hu and Chen, not only the tangential velocities but also the normal ones are handled separately in respective individual mesh. This treatment ensures not only the contact/sliding/separation procedure but also the friction between contacting bodies are recovered. The presented contact algorithm is validated via numerical experiments including rolling simulation, impact of elastic spheres, impact of a Taylor bar and impact of plastic spheres. The numerical results show that the multi-mesh material point method with the improved contact algorithm is more suitable for solving collision problems.
rate research
Read More
Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter being controlled by what is called mixing. This note describes a new approach to handling trust-regions within these and other fixed-point problems. Rather than adjusting the trust-region based upon improvement, the prior steps are used to estimate what the parameters and trust-regions should be, effectively estimating the optimal Polyak step from the prior history. Detailed results are shown for eight structures using both the Good and Bad Multisecan
A monolithic coupling between the material point method (MPM) and the finite element method (FEM) is presented. The MPM formulation described is implicit, and the exchange of information between particles and background grid is minimized. The reduced information transfer from the particles to the grid improves the stability of the method. Once the residual is assembled, the system matrix is obtained by means of automatic differentiation. In such a way, no explicit computation is required and the implementation is considerably simplified. When MPM is coupled with FEM, the MPM background grid is attached to the FEM body and the coupling is monolithic. With this strategy, no MPM particle can penetrate a FEM element, and the need for computationally expensive contact search algorithms used by existing coupling procedures is eliminated. The coupled system can be assembled with a single assembly procedure carried out element by element in a FEM fashion. Numerical results are reported to display the performances and advantages of the methods here discussed.
The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (emph{e.g.} Newton-Raphson method). A sole solution is obtained whereas many exist. However the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user.Geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it.This triangularization is a geometric construction of solutions, called construction plan. We aim at finding several solutions close to the sketch on a one-dimensional path defined by a global parameter-homotopy using a construction plan. Some numerical instabilities may be encountered due to specific geometric configurations. We address this problem by changing on-the-fly the construction plan.Numerical results show that this hybrid method is efficient and robust.
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nystroms quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.
The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the challenge of reliable data interpretation, i.e. conversion from detected signal to descriptors specific to tip-surface interactions and subsequently to materials properties. Here, we implemented a Bayesian inference approach for the analysis of the image formation mechanisms in band excitation (BE) SPM. Compared to the point estimates in classical functional fit approaches, Bayesian inference allows for the incorporation of extant knowledge of materials and probe behavior in the form of corresponding prior distribution and return the information on the material functionality in the form of readily interpretable posterior distributions. We note that in application of Bayesian methods, special care should be made for proper setting on the problem as model selection vs. establishing practical parameter equivalence. We further explore the non-linear mechanical behaviors at topological defects in a classical ferroelectric material, PbTiO3. We observe the non-trivial evolution of Duffing resonance frequency and the nonlinearity of the sample surface, suggesting the presence of the hidden elements of domain structure. These observations suggest that the spectrum of anomalous behaviors at the ferroelectric domain walls can be significantly broader than previously believed and can extend to non-conventional mechanical properties in addition to static and microwave conductance.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
