An adaptive local meshfree updated Lagrangian approach for large deformation analysis of metal forming

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

A Lagrangian approach to nonlinear modeling of anti-roll tanks

This paper presents two novel nonlinear models of u-shaped anti-roll tanks for ships, and their linearizations. In addition, a third simplified nonlinear model is presented. The models are derived using Lagrangian mechanics. This formulation not only simplifies the modeling process, but also allows one to obtain models that satisfy energy-related physical properties. The proposed nonlinear models and their linearizations are validated using model-scale experimental data. Unlike other models in the literature, the nonlinear models in this paper are valid for large roll amplitudes. Even at moderate roll angles, the nonlinear models have three orders of magnitude lower mean square error relative to experimental data than the linear models.

A novel manoeuvering model based on low-aspect-ratio lift theory and Lagrangian mechanics

This paper proposes a physically motivated reappraisal of manoeuvring models for ships and presents a new model developed from first principles by application of low aspect-ratio aerodynamic theory and Lagrangian mechanics. The coefficients of the model are shown to be related to physical processes, and validation is presented using the results from a planar motion mechanism dataset.

Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters

In estuaries and natural water channels, the estimate of velocity and dispersion coefficients is critical to the knowledge of scalar transport and mixing. This estimate is rarely available experimentally at sub-tidal time scale in shallow water channels where high frequency is required to capture its spatio-temporal variation. This study estimates Lagrangian integral scales and autocorrelation curves, which are key parameters for obtaining velocity fluctuations and dispersion coefficients, and their spatio-temporal variability from deployments of Lagrangian drifters sampled at 10 Hz for a 4-hour period. The power spectral densities of the velocities between 0.0001 and 0.8 Hz were well fitted with a slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange, and were similar to the Eulerian power spectral previously observed within the estuary. The result showed that large velocity fluctuations determine the magnitude of the integral time scale, TL. Overlapping of short segments improved the stability of the estimate of TL by taking advantage of the redundant data included in the autocorrelation function. The integral time scales were about 20 s and varied by up to a factor of 8. These results are essential inputs for spatial binning of velocities, Lagrangian stochastic modelling and single particle analysis of the tidal estuary.

A lagrangian formulation for statistical fluid registration

We defined a new statistical fluid registration method with Lagrangian mechanics. Although several authors have suggested that empirical statistics on brain variation should be incorporated into the registration problem, few algorithms have included this information and instead use regularizers that guarantee diffeomorphic mappings. Here we combine the advantages of a large-deformation fluid matching approach with empirical statistics on population variability in anatomy. We reformulated the Riemannian fluid algorithmdeveloped in [4], and used a Lagrangian framework to incorporate 0 th and 1st order statistics in the regularization process. 92 2D midline corpus callosum traces from a twin MRI database were fluidly registered using the non-statistical version of the algorithm (algorithm 0), giving initial vector fields and deformation tensors. Covariance matrices were computed for both distributions and incorporated either separately (algorithm 1 and algorithm 2) or together (algorithm 3) in the registration. We computed heritability maps and two vector and tensorbased distances to compare the power and the robustness of the algorithms.

A nonconservative Lagrangian framework for statistical fluid registration - SAFIRA

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented, where the deformation was regularized by penalizing deviations from a zero rate of strain. In, the terms regularizing the deformation included the covariance of the deformation matrices Σ and the vector fields (q). Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

An investigation of Nano-particle deposition in cylindrical tubes under Laminar condition using Lagrangian transport model

Aerosol deposition in cylindrical tubes is a subject of interest to researchers and engineers in many applications of aerosol physics and metrology. Investigation of nano-particles in different aspects such as lungs, upper airways, batteries and vehicle exhaust gases is vital due the smaller size, adverse health effect and higher trouble for trapping than the micro-particles. The Lagrangian particle tracking provides an effective method for simulating the deposition of nano-particles as well as micro-particles as it accounts for the particle inertia effect as well as the Brownian excitation. However, using the Lagrangian approach for simulating ultrafine particles has been limited due to computational cost and numerical difficulties. In this paper, the deposition of nano-particles in cylindrical tubes under laminar condition is studied using the Lagrangian particle tracking method. The commercial Fluent software is used to simulate the fluid flow in the pipes and to study the deposition and dispersion of nano-particles. Different particle diameters as well as different flow rates are examined. The point analysis in a uniform flow is performed for validating the Brownian motion. The results show good agreement between the calculated deposition efficiency and the analytic correlations in the literature. Furthermore, for the nano-particles with the diameter more than 40 nm, the calculated deposition efficiency by the Lagrangian method is less than the analytic correlations based on Eulerian method due to statistical error or the inertia effect.

Real-World Extensions To Scheduling Algorithms Based On Lagrangian Relaxation

Recently, efficient scheduling algorithms based on Lagrangian relaxation have been proposed for scheduling parallel machine systems and job shops. In this article, we develop real-world extensions to these scheduling methods. In the first part of the paper, we consider the problem of scheduling single operation jobs on parallel identical machines and extend the methodology to handle multiple classes of jobs, taking into account setup times and setup costs, The proposed methodology uses Lagrangian relaxation and simulated annealing in a hybrid framework, In the second part of the paper, we consider a Lagrangian relaxation based method for scheduling job shops and extend it to obtain a scheduling methodology for a real-world flexible manufacturing system with centralized material handling.

Large-chamber methane and nitrous oxide measurements are comparable to the backward Lagrangian stochastic method

Measurement of individual emission sources (e.g., animals or pen manure) within intensive livestock enterprises is necessary to test emission calculation protocols and to identify targets for decreased emissions. In this study, a vented, fabric-covered large chamber (4.5 × 4.5 m, 1.5 m high; encompassing greater spatial variability than a smaller chamber) in combination with on-line analysis (nitrous oxide [N2O] and methane [CH4] via Fourier Transform Infrared Spectroscopy; 1 analysis min-1) was tested as a means to isolate and measure emissions from beef feedlot pen manure sources. An exponential model relating chamber concentrations to ambient gas concentrations, air exchange (e.g., due to poor sealing with the surface; model linear when ≈ 0 m3 s-1), and chamber dimensions allowed data to be fitted with high confidence. Alternating manure source emission measurements using the large-chamber and the backward Lagrangian stochastic (bLS) technique (5-mo period; bLS validated via tracer gas release, recovery 94-104%) produced comparable N2O and CH4 emission values (no significant difference at P < 0.05). Greater precision of individual measurements was achieved via the large chamber than for the bLS (mean ± standard error of variance components: bLS half-hour measurements, 99.5 ± 325 mg CH4 s-1 and 9.26 ± 20.6 mg N2O s-1; large-chamber measurements, 99.6 ± 64.2 mg CH4 s-1 and 8.18 ± 0.3 mg N2O s-1). The large-chamber design is suitable for measurement of emissions from manure on pen surfaces, isolating these emissions from surrounding emission sources, including enteric emissions. © © American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America.

New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant. (C) 2012 Elsevier Inc. All rights reserved.

Motion segmentation using curve fitting on Lagrangian particle trajectories

In this paper we present a segmentation algorithm to extract foreground object motion in a moving camera scenario without any preprocessing step such as tracking selected features, video alignment, or foreground segmentation. By viewing it as a curve fitting problem on advected particle trajectories, we use RANSAC to find the polynomial that best fits the camera motion and identify all trajectories that correspond to the camera motion. The remaining trajectories are those due to the foreground motion. By using the superposition principle, we subtract the motion due to camera from foreground trajectories and obtain the true object-induced trajectories. We show that our method performs on par with state-of-the-art technique, with an execution time speed-up of 10x-40x. We compare the results on real-world datasets such as UCF-ARG, UCF Sports and Liris-HARL. We further show that it can be used toper-form video alignment.

A Lagrangian lattice Boltzmann method for Euler equations

A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.