Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications

The problem of solving complex engineering problems has always been a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods has increased exponentially in the last few years, due to modern computers in the field of structural mechanics. Moreover, a wide range of numerical methods have been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications

Splines for damage and fracture in solids

This thesis addresses different aspects of numerical fracture mechanics and spline technology for analysis. An energy-based arc-length control for physically non-linear problems is proposed. It switches between an internal energy-based and a dissipation-based arc-length method. The arc-length control allows to trace an equilibrium path with multiple snap-through and/or snap-back phenomena and only requires two parameters. Phase field models for brittle and cohesive fracture are numerically assessed. The impact of different parameters and boundary conditions on the phase field model for brittle fracture is investigated. It is demonstrated that Γ-convergence is not attained numerically for the phase field model for brittle fracture and that the phase field model for cohesive fracture does not pass a two-dimensional patch test when using an unstructured mesh. The properties of the Bézier extraction operator for T-splines are exploited for the determination of linear dependencies, partition of unity properties, nesting behaviour and local refinement. Unstructured T-spline meshes with extraordinary points are modified such that the blending functions fulfil the partition of unity property and possess a higher continuity. Bézier extraction for Powell-Sabin B-splines is introduced. Different spline technologies are compared when solving Kirchhoff-Love plate theory on a disc with simply supported and clamped boundary conditions. Powell-Sabin B-splines are utilised for smeared and discrete approaches to fracture. Due to the higher continuity of Powell-Sabin B-splines, the implicit fourth order gradient damage model for quasi-brittle materials can be solved and stresses can be computed directly at the crack tip when considering the cohesive zone method

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field

Interactive Medical Image Registration With Multigrid Methods and Bounded Biharmonic Functions

Interactive image registration is important in some medical applications since automatic image registration is often slow and sometimes error-prone. We consider interactive registration methods that incorporate user-specified local transforms around control handles. The deformation between handles is interpolated by some smooth functions, minimizing some variational energies. Besides smoothness, we expect the impact of a control handle to be local. Therefore we choose bounded biharmonic weight functions to blend local transforms, a cutting-edge technique in computer graphics. However, medical images are usually huge, and this technique takes a lot of time that makes itself impracticable for interactive image registration. To expedite this process, we use a multigrid active set method to solve bounded biharmonic functions (BBF). The multigrid approach is for two scenarios, refining the active set from coarse to fine resolutions, and solving the linear systems constrained by working active sets. We\u27ve implemented both weighted Jacobi method and successive over-relaxation (SOR) in the multigrid solver. Since the problem has box constraints, we cannot directly use regular updates in Jacobi and SOR methods. Instead, we choose a descent step size and clamp the update to satisfy the box constraints. We explore the ways to choose step sizes and discuss their relation to the spectral radii of the iteration matrices. The relaxation factors, which are closely related to step sizes, are estimated by analyzing the eigenvalues of the bilaplacian matrices. We give a proof about the termination of our algorithm and provide some theoretical error bounds. Another minor problem we address is to register big images on GPU with limited memory. We\u27ve implemented an image registration algorithm with virtual image slices on GPU. An image slice is treated similarly to a page in virtual memory. We execute a wavefront of subtasks together to reduce the number of data transfers. Our main contribution is a fast multigrid method for interactive medical image registration that uses bounded biharmonic functions to blend local transforms. We report a novel multigrid approach to refine active set quickly and use clamped updates based on weighted Jacobi and SOR. This multigrid method can be used to efficiently solve other quadratic programs that have active sets distributed over continuous regions

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results

Discrete-Event Control and Optimization of Container Terminal Operations

This thesis discusses the dynamical modeling of complex container terminal operations. In the current literature, the systems are usually modeled in static way using linear programming techniques. This setting does not completely capture the dynamic aspects in the operations, where information about external factors such as ships and trucks arrivals or departures and also the availability of terminal's equipment can always change. We propose dynamical modeling of container terminal operations using discrete-event systems (DES) modeling framework. The basic framework in this thesis is the DES modeling for berth and quay crane allocation problem (BCAP) where the systems are not only dynamic, but also asynchronous. We propose a novel berth and QC allocation method, namely the model predictive allocation (MPA) which is based on model predictive control principle and rolling horizon implementation. The DES models with asynchronous event transition is mathematically analyzed to show the efficacy of our method. We study an optimal input allocation problem for a class of discrete-event systems with dynamic input sequence (DESDIS). We show that in particular, the control input can be obtained by the minimization/maximization of the present input sequence only. We have shown that the proposed approach performed better than the existing method used in the studied terminal and state-of-the-art methods in the literature

Integrated Development and Parallelization of Automated Dicentric Chromosome Identification Software to Expedite Biodosimetry Analysis

Manual cytogenetic biodosimetry lacks the ability to handle mass casualty events. We present an automated dicentric chromosome identification (ADCI) software utilizing parallel computing technology. A parallelization strategy combining data and task parallelism, as well as optimization of I/O operations, has been designed, implemented, and incorporated in ADCI. Experiments on an eight-core desktop show that our algorithm can expedite the process of ADCI by at least four folds. Experiments on Symmetric Computing, SHARCNET, Blue Gene/Q multi-processor computers demonstrate the capability of parallelized ADCI to process thousands of samples for cytogenetic biodosimetry in a few hours. This increase in speed underscores the effectiveness of parallelization in accelerating ADCI. Our software will be an important tool to handle the magnitude of mass casualty ionizing radiation events by expediting accurate detection of dicentric chromosomes

Main rotor-tail rotor intraction and its implications for helicopter directional control

Aerodynamic interference between the main and tail rotor can have a strong negative influence on the flight mechanics of a conventional helicopter. Significant unsteadiness in the tail rotor loading is encountered under certain flight conditions, but the character of the unsteadiness can depend on the direction of rotation of the tail rotor. Numerical simulations, using Brown's vorticity transport model, of the aerodynamic interaction between the main and tail rotors of a helicopter are presented for a range of forward and lateral flight trajectories. Distinct differences are predicted in the behavior of the system in left and right sideward flight that are consistent with flight experience that the greatest fluctuations in loading or control input are required in left sideways flight (for a counterclockwise rotating main rotor). These fluctuations are generally more extreme for a system with tail rotor rotating top-forward than top-aft. Differences are also exposed in the character of the lateral excitation of the system as forward flight speed is varied. The observed behavior appears to originate in the disruption of the tail rotor wake that is induced by its entrainment into the wake of the main rotor. The extent of the disruption is dependent on flight condition, and the unsteadiness of the process depends on the direction of rotation of the tail rotor. In intermediate-speed forward flight and right sideward flight, the free stream delays the entrainment of the tail rotor wake far enough downstream for the perturbations to the rotor loading to be slight. Conversely, in left sideward and quartering flight, the free stream confines the entrainment process close to the rotors, where it causes significant unsteadiness in the loads produced by the system

Numerical Simulations

This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation