scholarly journals Hydroelastic behaviour and analysis of marine structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Fuat Kara
Keyword(s):  
Three Dimensional ◽  
Bending Moment ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Forward Speed ◽  
Floating Bodies ◽  
Numerical Predictions ◽  
Wigley Hull ◽  
Elastic Modes ◽  
Surface Green Function

The numerical predictions of the hydroelasticity of floating bodies with and without forward speed are presented using a direct time domain approximation. Boundary-Integral Equation Method (BIEM) with three-dimensional transient free surface Green function and Neumman-Kelvin approximation is used for the solution of the hydrodynamic part and solved as impulsive velocity potential whilst Euler-Bernoulli beam approach is used for the structural analysis with analytically defined modeshapes. The hydrodynamic and structural parts are then fully coupled through modal analysis for the solution of the hydroelastic problem. A stiff structure is then studied assuming that contributions of rigid body modes are much bigger than elastic modes. A rectangular barge with zero speed and Wigley hull form with forward speed are used for the numerical analyses and the comparisons of the present ITU-WAVE numerical results for response amplitude operator, bending moment, shear force etc. show satisfactory agreement with existing experimental results.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

Comparative Frequency Domain Seakeeping Analysis of a Fast Monohull in Regular Head Waves

2002 ◽  
Author(s):  
Thomas E. Schellin ◽  
Christian Beiersdorf ◽  
Xiao-Bo Chen ◽  
Adolfo Maron
Keyword(s):  
Green Function ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Forward Speed ◽  
Software Module ◽  
Mathematical Basis ◽  
Numerical Predictions ◽  
Head Waves ◽  
Seakeeping Analysis ◽  
Function Code

Two sets of seakeeping computations and comparative model teats were performed for a fast monohull in regular waves. The first set of computations used an existing three-dimensional frequency domain panel code that formulates the potential flow problem by means of the zero-speed Green function. The second set used a modified version of this code that implemented an advanced software module, newly developed within the European research project WAVELOADS, where the free-surface forward-speed Green function method based on the Fourier-Kochin formulation accounts for forward speed effects. Although this formulation provided a solid mathematical basis for obtaining robust and accurate numerical predictions, numerical inaccuracies prevented obtaining satisfactory results. For nearly all cases investigated, predictions from the original (zero-speed Green function) code correlated more favorably with test data than those from the modified (forward-speed Green function) code. For the fast monohull investigated here, practically relevant global load predictions based on the zero-speed Green function correlated favorably with measurements.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength panels on the exact submerged body surface, the boundary integral equations are solved numerically at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceed until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared with the experiments for both linear computations and body-exact computations.

Fully coupled seakeeping, slamming, and whipping calculations

2009 ◽  
Vol 223 (3) ◽  
pp. 439-456 ◽  
Author(s):  
J T Tuitman ◽  
Š Malenica
Keyword(s):  
Linear Time ◽  
Three Dimensional ◽  
Bending Moment ◽  
Fatigue Loading ◽  
Element Model ◽  
Beam Model ◽  
Full Wave ◽  
Elastic Modes ◽  
Large Container ◽  
Fully Coupled

This paper presents a methodology to solve the seakeeping, slamming, and whipping problems coupled within a single calculation. The coupled problem is solved within a partly non-linear time domain seakeeping program. The elastic modes used in this hydroelastic problem can be calculated using a beam model or full three-dimensional (3D) finite element model of the ship structure. The slamming loading is calculated by a two-dimensional (2D) method. The main focus of this paper is the creation of an accurate and consistent coupling between the 3D seakeeping program and the 2D slamming calculation. Differences in timescale and integration methods make this coupling complex. A large container ship is used to illustrate the application of the presented methodology. The contribution of the non-linearities and the whipping response to the expected maximum bending moment and fatigue damage of this ship for a full-wave scatter diagram is calculated. The results show that the slamming-induced whipping response has a significant contribution to both the ultimate bending moment and the fatigue loading of the ship.

scholarly journals NUMERICAL ANALYSIS OF THE DYNAMICS OF THREE-DIMENSIONAL ANISOTROPIC BODIES BASED ON NON-CLASSICAL BOUNDARY INTEGRAL EQUATIONS

2021 ◽  
Vol 83 (1) ◽  
pp. 76-86
Author(s):  
A.A. Belov ◽  
A.N. Petrov
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Classical Approach ◽  
Classical Boundary ◽  
Nonclassical Formulation

The application of non-classical approach of the boundary integral equation method in combination with the integral Laplace transform in time to anisotropic elastic wave modeling is considered. In contrast to the classical approach of the boundary integral equation method which is successfully implemented for solving three-dimensional isotropic problems of the dynamic theory of elasticity, viscoelasticity and poroelasticity, the alternative nonclassical formulation of the boundary integral equations method is presented that employs regular Fredholm integral equations of the first kind (integral equations on a plane wave). The construction of such boundary integral equations is based on the structure of the dynamic fundamental solution. The approach employs the explicit boundary integral equations. The inverse Laplace transform is constructed numerically by the Durbin method. A numerical solution of the dynamic problem of anisotropic elasticity theory based on the boundary integral equations method in a nonclassical formulation is presented. The boundary element scheme of the boundary integral equations method is built on the basis of a regular integral equation of the first kind. The problem is solved in anisotropic formulation for the load acting along the normal in the form of the Heaviside function on the cube face weakened by a cubic cavity. The obtained boundary element solutions are compared with finite element solutions. Numerical results prove the efficiency of using boundary integral equations on a single plane wave in solving three-dimensional anisotropic dynamic problems of elasticity theory. The convergence of boundary element solutions is studied on three schemes of surface discretization. The achieved calculation accuracy is not inferior to the accuracy of boundary element schemes for classical boundary integral equations. Boundary element analysis of solutions for a cube with and without a cavity is carried out.

Numerical Simulation of Motions of Two-Dimensional Floating Bodies

1993 ◽  
Vol 37 (04) ◽  
pp. 307-330
Author(s):  
D. Sen
Keyword(s):  
Wave Train ◽  
Boundary Integral ◽  
Nonlinear Phenomena ◽  
Computational Domain ◽  
Two Dimensional ◽  
Floating Bodies ◽  
Basic Algorithm ◽  
Numerical Predictions ◽  
Nonlinear Free Surface ◽  
Surface Constraints

A potential-flow numerical model is described for time-simulation of motions of two-dimensional floating bodies subjected to an oncoming wave train. The model is fully nonlinear in that no assumptions of smallness either in wave steepness or in body motions are made. The basic algorithm is based on a boundary integral formulation and time-stepping of the nonlinear free-surface constraints in an Eulerian frame of reference. Simple techniques are devised to overcome numerical instability problems that are encountered in the proposed method. The simulation time can be extended over several periods of steady-state oscillations depending on the size of the computational domain. Several illustrative results simulating large heave and roll motions as well as drifting of a rectangular body are presented and discussed. The numerical predictions are also evaluated against model tests which include several nonnegligible nonlinear phenomena, and the agreement is encouraging.

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