Applicability of the method of fundamental solutions to interaction of fully nonlinear water waves with a semi-infinite floating ice plate

Mollazadeh, Mahdi; Khanjani, M. J.; Tavakoli, Ali

doi:10.1016/j.coldregions.2011.07.004

Cited by 7 publications

(13 citation statements)

References 23 publications

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“…The same numerical algorithm was applied for steady-state nonlinear heat conduction in composite materials [Karageorghis and Lesnic 2008b]. A similar approach with the MFS was used for the water wave problem [Kołodziej and Mierzwiczak 2008;Mollazadeh et al 2011;Wu and Tsay 2009;Wu et al 2006;2008].…”

Section: Methods Of Fundamental Solutions and Its Applications To Solving Nonlinear Problemsmentioning

confidence: 99%

Laminar flow of a power-law fluid between corrugated plates

Grabski

Kołodziej

2016

J. Mech. Mater. Struct.

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This paper deals with the problem of a steady, fully developed, laminar flow of a power-law fluid between corrugated plates. A nonlinear governing equation is transformed into a sequence of linear inhomogeneous equations by the Picard iteration method. At each iteration step, the inhomogeneous equation is solved using the method of particular solutions in which the solution consists of two parts: the general solution and the particular solution. The right-hand side of the inhomogeneous equation is interpolated using the radial basis functions and monomials, and simultaneously unknown coefficients of the particular solution are obtained. The method of fundamental solutions is applied in order to obtain the general solution. Unknown coefficients of the general solution are calculated by fulfilling the boundary conditions. In this paper, dimensionless velocity of the fluid and the product of the friction factor and Reynolds number f Re are presented for different values of corrugation amplitude and different parameters of the power-law fluid model.

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Section: Methods Of Fundamental Solutions and Its Applications To Solving Nonlinear Problemsmentioning

confidence: 99%

Laminar flow of a power-law fluid between corrugated plates

Grabski

Kołodziej

2016

J. Mech. Mater. Struct.

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“…Figure 4. The block diagram [Mendelson 1968] that shows how to compute successive approximations of the plastic strain increments.…”

Section: The Successive-approximation Iteration Process and The Meshless Methodsmentioning

confidence: 99%

“…Subsequently, we take into consideration the boundary-value problem as proposed in [Mendelson 1968]. For its formulation the components of the total strain (5) with the relations (6)-( 7) are substituted into the compatibility and equilibrium equations for the plane problems (see, e.g., [Mendelson 1968…”

Section: Problem Formulationmentioning

confidence: 99%

“…An application of the method considered for nonlinear problems is quite popular in the area of fluid mechanics and there are many papers that take into account this issue. Namely, for a governing equation given in a form of Burgers' equation we have [Young et al 2008], similarly as for the Navier-Stokes equation [Young et al 2009] and for nonlinear water waves [Feng et al 2013;Mollazadeh et al 2011]. A solution of a boundary value problem governed by a nonlinear Poisson equation is presented in, e.g., [Balakrishnan and Ramachandran 1999;2001;Balakrishnan et al 2002;Burgess and Mahajerin 1987;Fallahi and Hosami 2011;Shanazari and Fallahi 2010;Tri et al 2011;Tsai 2012;Wang and Qin.…”

Section: Introductionmentioning

confidence: 99%

“…Then, for the nonlinear stress-strain relationship, we apply a model presented by Chakrabarty in [Chakrabarty 1987]. In Section 3 a new approach to the successive-approximation iteration process [Mendelson 1968] is proposed. It employs a combination of the meshless methods (the MFS-MPS) and the finite difference schemes (required for the approximation of values of partial derivatives present in the right-hand side function of the problem).…”

Section: Introductionmentioning

confidence: 99%

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A study of elastic-plastic deformation in the plate with the incremental theory and the meshless methods

Jankowska

Kołodziej

2016

J. Mech. Mater. Struct.

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The paper concerns an application of the successive-approximation iteration process together with the meshless methods, i.e., the method of fundamental solutions (MFS) and the method of particular solutions (MPS), for the analysis of strains and stresses in the plate with some kind of narrowing subjected to uniaxial tension. The elastoplastic boundary-value problem is based on the incremental theory of plasticity with the stress-strain relation given in the form proposed by Chakrabarty. In the iteration procedure a sequence of the successive distributions of the plastic strain increments corresponding to the appropriate increments of load is produced. A final set of the plastic strain increments is further used to obtain the total plastic strains. Furthermore, the solution of the elastoplastic boundary-value problem can be simultaneously taken into account when the stress state of the plate is required. Such approach is designated here to identify the regions of elastic and plastic behavior of the material.

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