A BEM-isogeometric method for the ship wave-resistance problem

Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies

Numerical investigations on seakeeping and added resistance in head waves based on nonlinear potential flow methods

Dynamic analysis of two-dimensional elasticity problems using the Isogeometric analysis method and its comparison with the finite element method is the subject of this research. For this purpose, formulation of the governing differential equation is obtained by using the B-spline basis functions. Some numerical examples employing consistent and lumped mass matrices are presented in order to compare the results of Isogeometric analysis and finite elements. The effect of increasing the number of control points and the degree of B-spline basis functions on the accuracy of the solution are also investigated. Furthermore, since the Newmark method is employed for transient dynamic analysis, the effects of parameters α and β on the solution accuracy are investigated. The obtained results demonstrate higher accuracy of the isogeometric analysis method in comparison with the FEM, despite employing fewer numbers of degrees of freedom and consequently reduction in the dimensions of system of equations and computational effort.

A new Rankine panel method and an extended Reynolds-Averaged Navier–Stokes (RANS) solver were employed to predict added resistance in head waves at different Froude numbers of a Wigley hull, a large tanker, and a modern containership. The frequency domain panel method, using Rankine sources as basic flow potentials, accounts for the interaction of the linear periodic wave-induced flow with the nonlinear steady flow caused by the ship's forward speed in calm water, including nonlinear free surface conditions and dynamic squat. Added resistance in waves is obtained by the pressure integration method. The time domain RANS solver, based on a finite volume method, is extended to solve the nonlinear equations of the rigid body six-degrees-of-freedom ship motions. The favorable comparison of the panel and RANS predictions demonstrated that the Rankine method is suitable to efficiently obtain reliable predictions of added resistance of ships in waves. Comparable model test predictions correlated less favorably, although the overall agreement was felt to be acceptable, considering the difficulties associated with the procedures to obtain accurate measurements.

The hydrodynamic problem of a ship moving with constant forward speed while undergoing small‐amplitude oscillatory motions about its mean steady‐state position is modeled as a boundary‐integral equation (BIE) involving surface distributions of the fundamental solution of Laplace's equation and its derivatives and alternative Green functions. The chapter reviews the various low‐order and higher order boundary‐element methods (BEMs) developed for the numerical solution of these BIEs via collocation or Galerkin techniques involving finite‐dimensional bases for representing the involved geometric configuration and approximating the unknown physical quantities. Then, we focus on presenting and discussing recent experience gained from embedding BEMs into isogeometric analysis (IGA) for the linear wave‐resistance problem. Two IGA‐BEM solvers, based on nonuniform rational B‐spline (NURBS) and T‐spline representations of the ship hull, are presented and compared for the so‐called Neumann–Kelvin formulation of this problem. The local refinement capabilities of the adopted T‐spline representation of the ship geometry leads to a solver with higher accuracy and efficiency as compared to the corresponding NURBS‐based solver. Furthermore, the developed hydrodynamic solvers, along with the corresponding ship‐parametric models, are integrated within an optimization environment, which is tested in two optimization problems. The first problem, of local optimization character, focuses on the optimization of the bulbous shape of a container ship against the criterion of minimum wave resistance. The second case performs a global hull‐shape optimization of a container ship targeting the minimization of both the total resistance and the deviation from a target deadweight. The chapter ends with a brief discussion for further research toward broadening the coverage of IGA‐BEM methods in application areas related to ship wave loads.

A closed form for low-order panel methods

As the interest in arctic shipping and arctic exploration of oil and gas is increasing in recent years, the number of ice class vessels is increasing rapidly. Also the choices for propulsion devices are getting wider and these include podded propulsion systems. This study is a framework for the numerical prediction of the ice interaction loads acting on a podded propeller blade. The results of this study will help us to understand the propeller-ice interaction problem more comprehensively. Several studies for propeller-ice interaction have been carried out in the past few decades. Propeller-ice interaction, however, is a complicated process with a high level of uncertainties due to ice properties, ship operating conditions, and environmental conditions. Full-scale measurements involve high costs. In order to overcome these difficulties, model tests were carried out with model ice in an ice tank. The model tests provide well-controlled ice properties and interaction conditions to reduce the uncertainties. The tests were carried out in the ice tank with scaled down model ice at the National Research Council of Canada’s Institute for Ocean Technology. The ice loads acting on the propeller blade were measured with a six-component force and moment load cell fitted to the shaft and one of the propeller blades. Based on the experimental results, a numerical prediction model was developed to estimate the ice loads on the propeller blade. The numerical prediction is composed of three parts: the hydrodynamic calculations including separable and inseparable hydrodynamic loads, and the ice milling loads calculation. The separable and inseparable hydrodynamic loads can be obtained from clear water and blocked flow respectively. The hydrodynamic calculations were done by a low order panel method. The subroutines for calculating the ice milling loads are implemented into the panel method. The numerical prediction model for ice milling loads is described and the results are compared with those of experiments.

Application of isogeometric analysis in structural shape optimization

In the present work we propose to compare the conventional finite element analysis and isogeometric analysis methods. We explore these two modeling methods in the same application in order to identify their differences. From the analytical point of view there is a difference in the type of the shape functions, the Lagrange polynomials used in finite element analysis interpolate the nodal points, and are C0 continuity at the nodal points, in the isogeometric analysis, the NURBS basis functions (Non Uniform Rational B-Spline) have a high continuity and do not interpolate control points. For the comparative study of the two modeling methods, we chose the standard Modal Assurance Criterion (MAC) to compare the eigenmodes. Because of the equality of the first order Lagrange polynomials and the first order NURBS functions, we obtain a perfect eigenmodes correlation of the two methods, but the correlation for the second order shows a slight difference, which highlights a different classification of the two modeling methods.DOI: http://dx.doi.org/10.5755/j01.mech.23.1.13890

Isogeometric analysis of large thin shell structures based on weak coupling of substructures with unstructured T-splines patches

We present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second‐order, fourth‐order, and sixth‐order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean‐curvature‐variation flow, which are generally derived by minimizing the associate energy functionals with ‐gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box‐splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high‐order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi‐implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high‐order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.

A zonal method based on the iterative coupling between an in viscid panel method and a Navier-Stokes (NS) method has been developed to analyze the complex flowfield associated with the V/STOL flow environment in order to improve the prediction of aerodynamic characteristics. The low-order panel method, VSAERO, developed by Analytical Methods, Inc. is used to solve for the entire flow region, which includes the V/STOL configuration and jet boundary model. In two separate investigations presented here, ARC3D, a well-known compressible thin layer NS code developed at NASA Ames Research Center, and APPL, a parabolized NS code developed at Amtec Engineering, are used to solve for the details of the jet region subject to the boundary condition provided by VSAERO. Overlapping boundaries are used for the purpose of coupling. Comparisons with the available experimental data for a jet-in-crossflow and a V/STOL configuration with lift-jet in a subsonic freestream show qualitative agreement with experiment and improved correlations over those by inviscid computations alone.

Morphogenesis of free-form surfaces by an effective approach based on isogeometric analysis and particle swarm optimization

The isogeometric analysis (IGA) method was extended for the solution of the coupled thermoelastodynamic equations. The dimensionless formulation was accepted in discretization of the uncoupled and coupled thermoelasticity equations and the Generalized Newmark method was used in the time integration procedure. First, the performance of the proposed method was verified against a two-dimensional benchmark example subjected to constant thermal shock with available exact analytical solutions. Then a two-dimensional half-space benchmark example under thermal shock was solved. Finally, cyclic thermal shock (CTS) loading was applied on the half-space problem. The results dedicated that IGA can be used as a suitable approach in the analysis of the general thermomechanical problems.

SummaryThree low-order panel methods developed for the analysis of supersonic flows have been used to make calculations for a number of test configurations, with the aim of establishing the range of problems for which this class of computational method yields adequate solutions. The programs investigated were the Woodward USSAERO/C program, the related NLRAERO program, and the British Aerospace Warton supersonic panel program. Results obtained using these programs have been evaluated against theoretical and experimental data for a number of test cases covering wing-alone, body-alone and wing-body geometries. It is concluded that low-order panel methods can provide adequate solutions for supersonic flows about wings, bodies and wing-body combinations, provided the assumptions implicit in the linearised potential flow model are not violated. Examples show that the prediction of lift and pitching moment curve slopes for quite complex configurations may be acceptable, but that the detailed pressure distributions are not always predicted satisfactorily. In particular, serious problems are encountered in calculating the flow about wings with rounded supersonic leading edges due to the linearised flow model which is used.