scholarly journals A fully nonlinear, dynamically consistent numerical model for solid-body ship motion. I. Ship motion with fixed heading

2010 ◽  
Vol 467 (2128) ◽  
pp. 911-927 ◽  
Author(s):  
Ray-Qing Lin ◽  
Weijia Kuang
Keyword(s):  
Numerical Model ◽  
Solid Body ◽  
Initial Conditions ◽  
A Priori ◽  
Hydrodynamic Pressure ◽  
Ship Motion ◽  
Body Motion ◽  
Dynamical Equations ◽  
Fully Nonlinear ◽  
Nonlinear Dynamical

In this paper, we describe the details of our numerical model for simulating ship solid-body motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship–wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

scholarly journals Taming the Beast: Diffusion Method in Nonlocal Gravity

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 95 ◽  
Author(s):  
Gianluca Calcagni
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Form Factors ◽  
Specific Form ◽  
Diffusion Method ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Gravitational Theories

We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type. For these specific form factors, which appear in some renormalizable theories, the number of field degrees of freedom and of initial conditions is finite.

Numerical Sloshing Analysis of FLNG and LNGC Considering Two-Body Motion Effect

2011 ◽  
Author(s):  
Jong Jin Park ◽  
Hiroshi Kawabe ◽  
Mun Sung Kim ◽  
Byung Woo Kim ◽  
Jae Kwang Eom
Keyword(s):  
Numerical Model ◽  
Frequency Domain ◽  
Potential Theory ◽  
Three Dimensional ◽  
Coupled Model ◽  
Ship Motion ◽  
Body Motion ◽  
Liquid Motion ◽  
Motion Effect

Side by Side arrangement is considered for the LNG-FPSO offloading operations. In that case, two-body coupled effects are important for LNG-FPSO and LNGC motion and sloshing analysis. The present study is concerned with a ship motion and sloshing analysis considering two-body motion and sloshing-motion coupled effects. The methodology is based on three-dimensional potential theory on a coupled model of LNG-FPSO and LNGC in the frequency domain. To calculation sloshing impact pressures, the violent liquid motion inside tank is treated with three-dimensional numerical model adopting SOLA-VOF scheme.

The evolution of the gaseous envelope around a newborn protostar

2019 ◽  
Vol 28 (08) ◽  
pp. 1950103
Author(s):  
Mohammad Mahdi Memarian ◽  
Motahareh Mohammadpour
Keyword(s):  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Adomian Decomposition ◽  
Accretion Rates ◽  
Spherical Cloud ◽  
Isothermal Processes ◽  
Increasing Functions ◽  
The Magnetic Field

In this paper, we investigate the influence of nonisothermal processes on the evolution of the cloud's envelope around a newborn protostar. For this purpose, we study the evolution of a spherical cloud harboring a central hydrostatic newborn protostar. This model includes thermal effects due to heating of the cosmic rays and cooling of the gas and gas–dust energy transfer. We have ignored the effects of the magnetic field and rotation. The semianalytical Adomian decomposition method (ADM) is used to solve the system of nonlinear dynamical equations for different initial conditions. In this paper, the ADM allows us to follow the time evolution of the cloud's envelope and its mass accretion rate onto the newborn protostar. We find that the mass accretion rates of the envelope are increasing functions of time and highly depend on the choice of initial conditions. Moreover, we find that the nonisothermal processes affect the evolution of the mass accretion rates compared with the isothermal processes for different initial conditions.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates

2019 ◽  
Vol 21 (07) ◽  
pp. 1850053 ◽  
Author(s):  
J. V. da Silva ◽  
G. C. Ricarte
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
Integrability Condition ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Borderline Case ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Text Type ◽  
Nonlinear Elliptic

In this paper, we establish global Sobolev a priori estimates for [Formula: see text]-viscosity solutions of fully nonlinear elliptic equations as follows: [Formula: see text] by considering minimal integrability condition on the data, i.e. [Formula: see text] for [Formula: see text] and a regular domain [Formula: see text], and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting “fine” regularity estimates from a limiting operator, the Recession profile, associated to [Formula: see text] to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when [Formula: see text]. In such a scenery, we show that solutions admit [Formula: see text] type estimates for their second derivatives.

Dynamic Loading on Turbofan Blades Due to Bird-Strike

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Sunil K. Sinha ◽  
Kevin E. Turner ◽  
Nitesh Jain
Keyword(s):  
Dynamic Loading ◽  
Time History ◽  
Material Model ◽  
Bird Strike ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
History Of ◽  
Measured Strain ◽  
Dynamic Loading Condition ◽  
Fan Blade

In the present paper, a hydrodynamic bird material model made up of water and air mixture is developed, which produces good correlation with the measured strain-gauge test data in a panel test. This parametric bird projectile model is used to generate the time-history of the transient dynamic loads on the turbofan engine blades for different size birds impacting at varying span locations of the fan blade. The problem is formulated in 3D vector dynamics equations using a nonlinear trajectory analysis approach. The analytical derivation captures the physics of the slicing process by considering the incoming bird in the shape of a cylindrical impactor as it comes into contact with the rotating fan blades modeled as a pretwisted plate with a camber. The contact-impact dynamic loading on the airfoil produced during the bird-strike is determined by solving the coupled nonlinear dynamical equations governing the movement of the bird-slice in time-domain using a sixth-order Runge-Kutta technique. The analytically predicted family of load time-history curves enables the blade designer to readily identify the critical impact location for peak dynamic loading condition during the bird-ingestion tests mandated for certification by the regulatory agencies.

Numerical and Experimental Investigation of Interface Bonding Via Substrate Remelting of an Impinging Molten Metal Droplet

1996 ◽  
Vol 118 (1) ◽  
pp. 164-172 ◽  
Author(s):  
C. H. Amon ◽  
K. S. Schmaltz ◽  
R. Merz ◽  
F. B. Prinz
Keyword(s):  
Heat Transfer ◽  
Numerical Model ◽  
Molten Metal ◽  
Thermal Stresses ◽  
Initial Conditions ◽  
Metal Droplet ◽  
Solid Substrate ◽  
Numerical Results ◽  
Operating Conditions ◽  
Analytical Approaches

A molten metal droplet landing and bonding to a solid substrate is investigated with combined analytical, numerical, and experimental techniques. This research supports a novel, thermal spray shape deposition process, referred to as microcasting, capable of rapidly manufacturing near netshape, steel objects. Metallurgical bonding between the impacting droplet and the previous deposition layer improves the strength and material property continuity between the layers, producing high-quality metal objects. A thorough understanding of the interface heat transfer process is needed to optimize the microcast object properties by minimizing the impacting droplet temperature necessary for superficial substrate remelting, while controlling substrate and deposit material cooling rates, remelt depths, and residual thermal stresses. A mixed Lagrangian–Eulerian numerical model is developed to calculate substrate remelting and temperature histories for investigating the required deposition temperatures and the effect of operating conditions on remelting. Experimental and analytical approaches are used to determine initial conditions for the numerical simulations, to verify the numerical accuracy, and to identify the resultant microstructures. Numerical results indicate that droplet to substrate conduction is the dominant heat transfer mode during remelting and solidification. Furthermore, a highly time-dependent heat transfer coefficient at the droplet/substrate interface necessitates a combined numerical model of the droplet and substrate for accurate predictions of the substrate remelting. The remelting depth and cooling rate numerical results are also verified by optical metallography, and compare well with both the analytical solution for the initial deposition period and the temperature measurements during droplet solidification.

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

Experimental and Numerical Investigation Into the Effects of Initial Conditions on a Three Degree of Freedom Capsize Model

2006 ◽  
Vol 50 (01) ◽  
pp. 63-84
Author(s):  
Young-Woo Lee ◽  
Leigh McCue ◽  
Michael Obar ◽  
Armin Troesch
Keyword(s):  
Numerical Model ◽  
Numerical Investigation ◽  
Initial Conditions ◽  
Degree Of Freedom ◽  
Transient Effects ◽  
Ultimate State ◽  
Extreme Behavior ◽  
Three Degree Of Freedom ◽  
Physical Phenomena ◽  
Ship Capsizing

The dynamics and hydrodynamics of ship capsizing include strong nonlinearities, transient effects, and physical phenomena that have not been fully identified or studied. This paper presents a study of some of the various mechanisms associated with this extreme behavior. A quasi-nonlinear three degree of freedom numerical model is employed to examine the effects of initial conditions on the ultimate state of a box barge model. The numerical results are then used to provide structure and understanding to otherwise seemingly inconsistent and ambiguous experiments.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

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