Bodies Of Arbitrary Shape Research Articles

A Computing Method for the Analysis of Water Impact of Arbitrary Shaped Bodies (2nd Report)

Traditionally, circular cylinders have been adopted as structural members of offshore structures due to structural simplicity, strength, cost and facility of construction, etc. However, investigations on the slamming of the circular cylinders indicate that they suffer very high impact loads. Furthermore, despite the impact loads are strongly influenced by their geometry, almost no alternative cross sectional shape has been systematically studied.This paper describes an optimization of the cross sectional shape of the horizontal members of offshore structures in the view point of slamming. Investigations are performed by using a numerical method for the analysis of water impact of arbitrary shaped bodies that the authors have presented in the first report.First, we numerically study water impact on a circular cylinder to clarify the mechanism of slamming on the existing structural members. Next, alternative cross sectional shapes for the horizontal members are obtained by an analysis based on the momentum theory associated with the concept of added mass. The results are checked by the numerical simulations. The analyses show that cylinders with parabolic section minimize total impact force. Finally, the acceptable range of angle of the parabolic section to the water surface is determined. The cross sectional shapes we obtained can be reasonable alternatives for the horizontal members of offshore structures.

Fast multipole method solution using parametric geometry

AbstractThe fast multipole method is used to solve the electromagnetic scattering from three‐dimensional conducting bodies of arbitrary shape. The electric field integral equation is discretized by the method of moments. Instead of directly computing the matrix‐vector multiplication, which needs N2 multiplications, this approach reduces the complexity to O(N1.5). © 1994 John Wiley & Sons, Inc.

On the inversion of subsurface residual stresses from surface stress measurements

Matter removal is necessary in order to measure the stress tensor at an interior point of a solid by means of X-ray diffraction. This induces stress redistribution so that the measured stress is different from the original residual stress. This paper addresses the problem of reconstructing the original stress field from the measurements. A method of solution is described for the reconstruction problem, which leads to explicit inversion formulae for the case of some simple geometries. Closed-form expressions are obtained for the two- and three-dimensional half-space. For bodies of arbitrary shape, a numerical algorithm is proposed.

Lift analysis of a variable camber foil using the discrete vortex-blob method

ECENT research activities in the area of active or smart material systems have generated significant interest to develop adaptive lifting surfaces for advanced aircraft and submarine structures. By using integrated actuators and sensors, advanced problems are being addressed in aeroelastic tailoring, vibration and attitude control, and high lift devices.16 For example, on submarine aftbodies, compliant attitude control appendages that utilize large out-of-plane foil deformation can provide enhanced lift with reduced wake disturbance compared to conventional full-flying and trailing-edge flapped designs.7~9 To quantify the performance improvements of such control surfaces, an analysis technique is required which can model separated flow at high Reynolds numbers and provide pressure distributions for structure and control system design. The purpose of this Note is to present use of a discrete vortex-blob method to compare lift performance between fixed and variable camber NACA 0012 foils at a Reynolds number of 1 x 10 7 for incompressible flow in two dimensions. The vortex method provides a natural and numerically efficient description of eddies and the vorticity they carry. Since a large number of discrete vortex blobs are used to produce a vorticity field in a Lagrangian reference frame, the method becomes grid free and allows modeling of unsteady flows10 even around multielement bodies of arbitrary shape (conformal mappings are not involved) in nonuniform motion or rotation. Formulation of the Discrete Vortex-Blob Method The discrete vortex-blob method, furthered by Spalart and coworkers11'12 at NASA Ames Research Center, and incorporated in the computer code KPD12, is based on a vorticity formulation of the Navier-Stokes equations for incompressible flow in two dimensions:

Forward modeling: Gravity anomalies of two-dimensional bodies of arbitrary shape with hyperbolic and parabolic density functions

Computer programs in FORTRAN 77 to compute the gravity anomaly of a two-dimensional (2-D) body of irregular cross section with hyperbolic and parabolic variations in density contrast are developed and presented. The gravity anomaly of San Jacinto Graben, California, using a hyperbolic function and that of Los Angeles Basin, California, using a parabolic function, are computed and compared with respective observed anomalies.

Sound scattering by slender bodies of arbitrary shape

Scattering of a spherical wave from a perfectly rigid slender body of arbitrary shape is considered. The point source is assumed to be located in the far field of each body cross section but may be placed in the near field of the target. The problem is investigated theoretically with the matched asymptotic expansions method and an approximate solution is derived for the scattered pressure, which takes into account the curvature of the incident wave front. The presented formalism combines the so-called slender-body approximation and the two-dimensional Kirchhoff theory. It allows a great simplification in the geometrical description of the body surface and leads to a practical method even for bodies of complex shape. In the monostatic case, it is theoretically shown that the obtained solution is asymptotically equivalent to that provided by geometrical optics for a large class of finite scatterers. Lastly, monostatic and bistatic angular distributions are computed for a prolate spheroid in the near and far fields to support the present theory.

Influence of molecular shape on vapour-liquid equilibria

Plačkov, Đ., Mainwaring, D.E. and Sadus, R.J., 1994. Influence of molecular shape on vapour-liquid equilibria. Application of a modified Christoforakos-Franck equation of state. Fluid Phase Equilibria , 95: 371-381. The Christoforakos-Franck equation of state, originally derived for spherical molecules, is modified to account for deviations from spherical geometry. The contribution from repulsive interactions is obtained from the Boublik-Nezbeda model for the compressibility of hard bodies of arbitrary shape. The deviation from sphericity (α) is deduced from the hard convex body model of molecular geometry. Attractive intermolecular interactions are characterized by the depth (-ϵ) and relative width (λ) of a square-well potential. The influence of molecular shape on the vapour-liquid equilibrium properties of pure fluids is investigated by using the modified equation to predict the vapour pressure of non-spherical molecules. It is concluded that incorporating molecular shape in the conventional equation of state methodology does not significantly influence the quality of the predicted vapour-liquid equilibria.

Equi-Partition of Outflow of Joule's Heat Generated in a Homogeneous Body of Arbitrary Shape

Joule's heat generated in a homogeneous body of arbitrary shape flows out just equally through each of two electrodes, when the body is isolated from the environment both electrically and thermally except at the electrodes, which are attached onto the surface of the body. This “Theorem of equi-partition of Joule's heat” holds even when both electrical and thermal conductivity of the material vary with temperature in an arbitrary way.

A Half-Space Boundary Element Method for Acoustic Problems With a Reflecting Plane of Arbitrary Impedance

In this paper, the boundary element method (BEM) is used to model acoustic radiation and scattering from bodies of arbitrary shape in close proximity of an infinite plane that has a general impedance boundary condition. A new half-space Green's function for positive reactance boundary conditions is derived and incorporated in the boundary element formulation so that there is no need to model the infinite plane. Attempt is also made to derive the Green's function for negative reactance boundary conditions. However, the derived Green's function for negative reactance boundary conditions contains a term that is not known a priori. Only an approximate Green's function for negative reactance boundary conditions is used in the BEM. Several numerical examples are given to verify this new formulation.

Combining the moment method with geometrical modelling by NURBS surfaces and Bezier patches

Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS (non uniform rational B-splines) surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE). The NURBS surfaces are expanded in terms of Bezier patches by applying the Cox-de Boor transformation algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. New basis functions have been developed which extend over pairs of Bezier patches. These basis functions can be considered as a generalization of "rooftop" functions. The method is applied to obtain RCS values of several objects modelled with NURBS surfaces. Good agreement with results from other methods is observed. The method is efficient and versatile because it uses geometrical modelling tools that are quite powerful.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simulation of Nonlinear Ship Flows by Density-Function Method

A new computational method that can cope with three dimensional breaking waves in the framework of curvilinear body- fitted coordinate system has been developed. The free-surface treatment in this study is based on the marker-density technique developed in the TUMMAC-VIII method, and the algorithm of solving the discretized N-S equation is that of the WISDAM-V method. By simulations with three hull forms, it is demonstrated that this new method can simulate three dimensional breaking waves around a body of arbitrary shape with a certain degree of accuracy.

Nonsimilar free convection boundary layer in non-Newtonian fluid-saturated porous media

Finite difference method with and without the local similarity assumption are described for the nonsimilar free convection boundary-layer flow over a body of arbitrary shape, embedded in a non-Newtonian fluidsaturated porous medium, with an arbitrarily varying surface temperature. For illustration, numerical results are obtained with and without the local similarity assumption for the case of a vertical flat plate with exponential, power-law, and sinusoidal surface temperature distributions. A simple integral method is also proposed, and its results are compared against those from the exact as well as the finite difference solutions. Comparison of the results reveals that all proposed integral and numerical methods perform equally well for both dilatant and pseudoplastic fluids.

A Computing Method for the Analysis of Water Impact of Arbitrary Shaped Bodies

In this paper, a computing method for water impact of arbitrary shaped bodies will be proposed. We use body-fitted coordinate system to model the arbitrary profile of the rigid body surface and the transient deformation of the free surface is solved by the fractional volume of fluid method. With this combination of the numerical techniques the rigid surface and the free surface boundary conditions are naturally treated at the intersection of both surfaces that improves remarkably the stability and accuracy of the numerical simulation.For the purpose of verifying the present computing method, classical problems of water impact of wedges and circular cylinders are studied. Moreover, water impact of a ship bow section is simulated to illustrate the applicability of the present computing method to practical ship design problems. In these basic studies, we considered the cases in which the body enters an initially calm water surface with a constant velocity. The results of the simulations are examined against the existing analytical theories and published experimental data.

A generalization of the demagnetizing tensor for nonuniform magnetization

The demagnetizing tensor for ferromagnets is generalized to include interactions between uniformly magnetized bodies. This “mutual” demagnetizing tensor is symmetric, has a trace of zero, and has other simple geometric properties. The tensor is then used to develop an expression for the macroscopic magnetic field in non‐uniformly magnetized bodies of arbitrary shape. Finally, the theory is applied to a block model of magnetization and explicit formulae for the tensor components are given.

Modeling complexly magnetized two‐dimensional bodies of arbitrary shape

A method has been devised for the forward computation of magnetic anomalies due to two‐dimensional (2-D) polygonal bodies with heterogeneously directed magnetization. The calculations are based on the equivalent line source approach wherein the source is subdivided into discrete elements that vary spatially in their magnetic properties. This equivalent dipole line method provides a fast and convenient means of representing and computing magnetic anomalies for bodies possessing complexly varying magnitude and direction of magnetization. The algorithm has been tested and applied to several generalized cases to verify the accuracy of the computation. The technique has also been used to model observed aeromagnetic anomalies associated with the structurally deformed, remanently magnetized Keweenawan volcanic rocks in eastern Lake Superior. This method is also easily adapted to the calculation of anomalies due to two and one‐half‐dimensional (2.5-D) and three‐dimensional (3-D) heterogeneously magnetized sources.

Dissipative force on a sphere moving in vacuum.

We derive the spectrum of fluctuations of the vacuum radiation pressure on a spherical perfectly reflecting mirror. From the fluctuation-dissipation theorem, we obtain the dissipative force exerted upon the mirror when it moves in vacuum. As in the classical problem of scattering by a plane wave, the spectrum presents a resonant behavior at wavelengths of the order of the sphere's radius. The high-frequency limit agrees with Barton's general result for a large body of arbitrary shape.

Inverse Analysis of the Magnitude and Direction of Impact Force.

This paper treats an inverse problem for estimating the magnitude and direction of an impact force acting on a body of arbitrary shape. It is shown that three directional components of the impact force vector can be estimated from responses measured at more than three points of the body by means of deconvolution. It is pointed out that the impact force cannot always be estimated satisfactorily since the inverse problem is ill-posed and/or ill-conditioned in some situations. For improving the estimation accuracy, the singular value decomposition technique is adopted. The validity of the present method is demonstrated through an experiment in which an impact force acting on a simply supported beam is estimated from strain responses measured by strain gages.

Second-order theory and calculations of motions and loads of arbitrarily shaped 3D bodies in waves

This paper deals with the development of a complete second-order theory for the evaluation of motions and loads of arbitrarily shaped 3D bodies in waves at finite water depth. The developed second-order potential theory leads to the solution of integral equations for the evaluation of second-order potentials and corresponding second-order pressures, forces, motions, etc. The developed algorithm for the treatment of the second-order inhomogeneity of the free-surface boundary condition allows the application of the related computer program to bodies of arbitrary shape, in contrast to previous theories applicable only to axisymmetric bodies. The paper includes typical numerical results for the second-order motions and loads for various bodies of both axisymmetric and nonaxisymmetric shape.

Time‐Domain Second‐Order Wave Diffraction in Three Dimensions

A time-domain second-order method is developed to study nonlinear wave diffraction around a surface-piercing body of arbitrary shape in three dimensions. The free-surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time, and the field solution at each time step is obtained by an integral equation method based on Green’s theorem. The solution is separated into a known incident potential and a scattered potential to be determined. The radiation condition applied to the scattered potential is modified to incorporate a time-dependent celerity to account for the transient and second-order effects. With initial conditions corresponding to a Stokes second-order wave field in the domain, the scattered potential is allowed to develop im time and space through the imposition of the body-surface boundary condition. The computed wave force and free-surface elevation components at second order are compared with previous theoretical results for the case of a surface-piercing circular cylinder and a favorable agreement is indicated.

The forces on a body moving through a viscous fluid

The forces on a body moving through a viscous fluid are related to the asymptotic flow field at large distances from the body and can be deduced therefrom. Explicit formulae are derived for the force and couple in terms of the parameters defining the asymptotic flow field. The form of these results remains unchanged for a body of arbitrary shape moving in two or three dimensions, and for a body rotating as well as translating, provided the flow is steady relative to an appropriate set of axes. They are also applicable when the Navier–Stokes equations are replaced by approximate equations, as in the work of Stokes and Oseen.