Boundary‐Element Methods and Wave Loading on Ships

Abstract

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 T-splines-based parametric modeller for computer-aided ship design

“…T-splines constitute a generalisation of NURBS technology that removes several of NURBS deficiencies, e.g., enabling refinement without the need of adding redundant control points. Furthermore, they have been successfully used in conjunction with Isogeometric Analysis (IGA) in several areas of computational mechanics; see e.g., [1], [17], [18], [19], [20], [21], [22], [23]. IGA is a new methodology that eliminates the need of geometry discretisation (meshing), as it is the case for standard FEM (Finite Element Methods) and BEM (Boundary Element Method), enabling a seamless and strong coupling between the geometry representation and the solver 8 .…”