Alexandros I. Ginnis

An isogeometric BEM for exterior potential-flow problems in the plane

In this paper, the isogeometric concept introduced by Hughes, in the context of Finite Element Method, is applied to Boundary Element Method (BEM), for solving an exterior planar Neumann problem. The developed isogeometric-BEM concept is based on NURBS, for representing the exact body geometry and employs the same basis for representing the potential and/or the density of the single layer. In order to examine the accuracy of the scheme, numerical results for the case of a circle and a free-form body are presented and compared against analytical solutions. This enables performing a numerical error analysis, verifying the superior convergence rate of the isogeometric BEM versus low-order BEM. When starting from the initial NURBS representation of the geometry and then using knot insertion for refinement of the NURBS basis, the achieved rate of convergence is O(DoF-4). This rate may be further improved by using a degree-elevated initial NURBS representation of the geometry (kh-refinement).

Sectional-curvature preserving skinning surfaces

Abstract In this work we develop a method for constructing sectional-curvature preserving (scp) C 2 -continuous surfaces, which interpolate point-sets lying on parallel planes. The working function space consists of skinning surfaces, whose skeletal lines and blending functions are polynomial splines of nonuniform degree. The asymptotic behaviour of these surfaces and their sectional curvature, as the segment degrees tend to infinity globally or semilocally, is thoroughly studied. This study provides sufficient geometrical conditions on the given data ensuring that, it the segment degrees increase semilocally then the surface will eventually become scp in the corresponding parameter subdomain. Based on the obtained asymptotic results, an automatic algorithm for constructing scp interpolatory surfaces is developed and numerically tested.

A BEM-ISOGEOMETRIC METHOD WITH APPLICATION TO THE WAVEMAKING RESISTANCE PROBLEM OF SHIPS AT CONSTANT SPEED

In the present work IsoGeometric Analysis (IGA), initially proposed by Hughes et al (2005), is applied to the solution of the boundary integral equation associated with the Neumann-Kelvin (NK) problem and the calculation of the wave resistance of ships, following the formulation by Brard (1972) and Baar & Price (1988). As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the NURBS basis, which is used for representing exactly the body geometry and adopts the very same basis functions for approximating the singularity distribution (or in general the dependent physical quantities). In order to examine the accuracy of the present method, in a previous paper Belibassakis et al (2009), numerical results obtained in the case of submerged bodies are compared against analytical and benchmark solutions and low-order panel method predictions, illustrating the superior efficiency of the isogeometric approach. In the present paper we extent previous analysis to the case of wavemaking resistance problem of surface piercing bodies. The present approach, although focusing on the linear NK problem which is more appropriate for thin ship hulls, it carries the IGA novelty of integrating CAD systems for ship-hull design with computational hydrodynamics solvers.Copyright

Shape-optimization of 2D hydrofoils using an Isogeometric BEM solver

Abstract In this paper, an optimization procedure, based on an Isogeometric BEM solver for the potential flow, is developed and used for the shape optimization of hydrofoils. The formulation of the exterior potential-flow problem reduces to a Boundary-Integral Equation (BIE) for the associated velocity potential exploiting the null-pressure jump Kutta condition at the trailing edge. The numerical solution of the BIE is performed by an Isogeometric Boundary-Element Method (BEM) combining a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight parameters, the very same basis of the geometric representation for representing the velocity potential and collocation at the Greville abscissas of the knot vector of the hydrofoil’s B-splines representation. Furthermore, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the Isogeometric BEM solver and an optimizer employing a controlled elitist genetic algorithm. Multi-objective hydrofoil shape optimization examples are demonstrated with respect to the criteria (i) maximum lift coefficient and (ii) minimum deviation of the hydrofoil area from a reference area.

Planar C 2 cubic spline interpolation under geometric boundary conditions

This paper deals with the problem of C2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to necessary and sufficient conditions for all possible boundary-data configurations. A robust scheme for the numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples.

A scan-line algorithm for clustering line segments

Transformation of hardcopy ship drawings to electronic ones is usually accomplished through scanning and raster-to-vector conversions. Such conversions are, however, limited to produce low-degree vector entities, such as line segments, poly-lines and circular arcs. As a consequence, free-form curves, appearing in the original hardcopy, are usually disintegrated to a significant number of overlapping line and/or arc segments. The algorithm presented in this paper, consists of a scan-line processing of line segments that are grouped (clustered) with the aid of a moving scan-line and an appropriately defined distance to previously grouped entities. The performance of the algorithm is illustrated for the body-plan of a bulk carrier.

VELOS - A VR environment for ship applications: current status and planned extensions

Virtual Environment for Life On Ships (VELOS) is a multi-user Virtual Reality (VR) system that supports designers to assess (early in the design process) passenger and crew activities on a ship for both normal and hectic conditions of operations and to improve the ship design accordingly [10]. Realistic simulations of behavioral aspects of crowd in emergency conditions require modeling of panic aspects and social conventions of inter-relations. The present paper provides a description of the enhanced crowd modeling approach employed in VELOS for the performance of ship evacuation assessment and analysis based on the guidelines provided by IMO’s Circular MSC 1238/2007 [20].

Motions Effect for Crowd Modeling Aboard Ships

Pre-computed ship-motion history has been used in the multi-user Virtual Reality (VR) system VELOS in conjunction with a kinematically-oriented inclination steering behavior as simple means for considering the effects of ship motion on simulated passengers’ movement. This first approach does not account for the dynamic nature of the phenomenon, thus ignoring motion accelerations. Ship-motion accelerations, however, are critical to the assessment of a person’s balancing and/or sliding aboard ships and consequently to its capability of performing an assigned task. In this work, we are focusing on the exploitation of pre-computed ship motions and accelerations and we investigate the usage of the concepts of Motion-Induced Interruptions (MIIs) and tipping coefficients in modeling the effects of ship-motion accelerations on passengers.

Quantifying the effect of a control point on the sign of curvature

We present a method for computing the domain, where a control point is free to move so that the corresponding planar curve is regular and of constant sign of curvature along a subinterval of its parametric domain of definition. The approach encompasses all curve representations that adopt the control-point paradigm and is illustrated for a quintic Bézier curve and a B-spline curve of degree 10.

Construction of smooth branching surfaces using T-splines

The request for designing or reconstructing objects from planar cross sections arises in various applications, ranging from CAD to GIS and Medical Imaging. The present work focuses on the one-to-many branching problem, where one of the planes can be populated with many, possibly tortuous and densely packed, contours. The proposed method combines the proximity information offered by the Euclidean Voronoi diagram with the concept of surrounding curve, introduced inGabrielides etal. (2007), and T-splines technologySederberg etal. (2003) for securing a flexible and portable representation. Our algorithm delivers a single cubic T-spline that deviates from the given contours less than a user-specified tolerance, measured via the so-called discrete Frchet distanceEiter and Mannila (1994) and is C2 everywhere except from a finite set of point-neighborhoods. Subject to minor enrichment, the algorithm is also capable to handle the many-to-many configuration as well as the global reconstruction problem involving contours on several planes. Construction of smooth branching surfaces from parallel planar contours using T-splines.Branching surface is C2 everywhere except from a finite set of point-neighborhoods where smoothness degrades to G1.Approximation of planar contours using discrete Frchet distance.