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.

Meshless TL and UL approaches for large deformation analysis

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using the UL approach than using in the TL approach.

Controlling a submerged rigid body : a geometric analysis

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Controlled drift: an investigation into the controllability of underwater vehicles with minimal actuation

This paper is directed towards providing an answer to the question, ”Can you control the trajectory of a Lagrangian float?” Being a float that has minimal actuation (only buoyancy control), their horizontal trajectory is dictated through drifting with ocean currents. However, with the appropriate vertical actuation and utilising spatio-temporal variations in water speed and direction, we show here that broad controllabilty results can be met such as waypoint following to keep a float inside of a bay or out of a designated region. This paper extends theory experimen- tally evaluted on horizontally actuated Autonomous Underwater Vehicles (AUVs) for trajectory control utilising ocean forecast models and presents an initial investi- gation into the controllability of these minimally actuated drifting AUVs. Simulated results for offshore coastal and within highly dynamic tidal bays illustrate two tech- niques with the promise for an affirmative answer to the posed question above.

Controlling Minimally-Actuated Vehicles for Applications in Ocean Observation

Establishing a persistent presence in the ocean with an AUV to observe temporal variability of large-scale ocean processes requires a unique sensor platform. In this paper, we propose a strategy that utilizes ocean model predictions to increase the autonomy and control of Lagrangian or profiling floats for precisely this purpose. An A* planner is applied to a local controllability map generated from predictions of ocean currents to compute a path between prescribed waypoints that has the highest likelihood of successful execution. The control to follow the planned path is computed by use of a model predictive controller. This controller is designed to select the best depth for the vehicle to exploit ambient currents to reach the goal waypoint. Mission constraints are employed to simulate a practical data collection mission. Results are presented in simulation for a mission off the coast of Los Angeles, CA USA, and show surprising results in the ability of a Lagrangian float to reach a desired location.

Control and application of minimally-actuated underwater vehicles

Establishing a persistent presence in the ocean with an Autonomous Underwater Vehicle capable of observing temporal variability of large-scale ocean processes requires a unique sensor platform. In this paper, we examine the utility of Lagrangian profiling floats for such extended deployments. We propose a strategy that utilizes ocean model predictions to facilitate a basic level of autonomy to achieve general control of this minimally-actuated underwater vehicle. We extend experimentally validated techniques for utilising ocean current models to control under-actuated autonomous underwater vehicles by presenting this investigation into the application of these methods on profiling floats. With the appropriate vertical actuation, and utilising spatiotemporal variations in water speed and direction, we show that broad controllability results can be met. First, we apply an A* planner to a local controllability map generated from predictions of ocean currents. This computes a path between start and goal waypoints that has the highest likelihood of successful execution over a given duration. The computed depth plan is generated with a model predictive controller, and selects the depths for the vehicle so that ambient currents guide it toward the goal. Mission constraints are included to simulate and motivate a practical data collection mission. Results are presented in simulation for a mission off the coast of Los Angeles, CA USA, that show surprising results in the ability of a drifting vehicle to maintain a prescribed course and reach a desired location.

Response of a buried tunnel to surface blast using different numerical techniques

This paper presents a comparative study on the response of a buried tunnel to surface blast using the arbitrary Lagrangian-Eulerian (ALE) and smooth particle hydrodynamics (SPH) techniques. Since explosive tests with real physical models are extremely risky and expensive, the results of a centrifuge test were used to validate the numerical techniques. The numerical study shows that the ALE predictions were faster and closer to the experimental results than those from the SPH simulations which over predicted the strains. The findings of this research demonstrate the superiority of the ALE modelling techniques for the present study. They also provide a comprehensive understanding of the preferred ALE modelling techniques which can be used to investigate the surface blast response of underground tunnels.

Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. Because of this, conventional design procedures cannot capture the true behaviour of a composite frame throughout its full loading range, and so a procedure to account for those non-linearities is much needed. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. Different material non-linearity for different composite structural components such as T-beams, concrete-filled tubular (CFT) and steel-encased reinforced concrete (SRC) sections can be treated using a routine numerical procedure for their section properties in this plastic hinge approach. Simple and conservative initial and full yield surfaces for general composite sections are proposed in this paper. The refined plastic hinge approach models springs at the ends of the element which are activated when the surface defining the interaction of bending and axial force at first yield is reached; a transition from the first yield interaction surface to the fully plastic interaction surface is postulated based on a proposed refined spring stiffness, which formulates the load-displacement relation for material non-linearity under the interaction of bending and axial actions. This produces a benign method for a beam-column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined with a simple application of the method herein and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. Recourse is made to an updated Lagrangian formulation to consider geometric non-linear behaviour and to develop a non-linear solution strategy. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. By way of contrast, the plastic zone approach possesses the drawback of strain-based procedures which rely on determining plastic zones within a cross-section and which require lengthwise integration. Following development of the theory, its application is illustrated with a number of varied examples.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.