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1

Application of Smoothed Particle Hydrodynamics Method in Metal Processing: An Overview

Nguyen Trang Thi Thu, Hojny Marcin

Archives of Foundry Engineering

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2022

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Vol. 22, iss. 3

67--80

EN

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian formula-based non-grid computational method for simulating fluid flows, solid deformation, and fluid structured systems. SPH is a method widely applied in many fields of science and engineering, especially in the field of materials science. It solves complex physical deformation and flow problems. This paper provides a basic overview of the application of the SPH method in metal processing. This is a very useful simulation method for reconstructing flow patterns, solidification, and predicting defects, limitations, or material destruction that occur during deformation. The main purpose of this review article is to give readers better understanding of the SPH method and show its strengths and weaknesses. Studying and promoting the advantages and overcoming the shortcomings of the SPH method will help making great strides in simulation modeling techniques. It can be effectively applied in training as well as for industrial purposes.

2

Numerical study of coupled oscillator system usingthe classical Euler-Lagrange equations

Shanak H., Khalilia H., Jarrar R., Asad J.

Mechanics and Mechanical Engineering

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2021

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Vol. 25, nr 1

1--5

EN

Problems involving vibrations (mechanical orelectrical) can be reduced to problems of coupled oscil-lators. For this, we consider the motion of coupled oscilla-tors system using Lagrangian method. The Lagrangian ofthe system was initially constructed, and then the Euler-Lagrange equations (i.e., equations of motion of the system)have been obtained. The obtained equations of motion are ahomogenous second-order equation. These equations weresolved numerically using the ode45 code, which is basedon Runge-Kutta method.

3

Symplectic structure on colorings, Lagrangian tangles and Tits buildings

Dymara Jan, Januszkiewicz Tadeusz, Przytycki Józef H.

Bulletin of the Polish Academy of Sciences. Mathematics

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2020

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Vol. 68, no. 2

169--194

EN

We define a symplectic form ϕ on a free R-module R2n-2 associated to 2n points on a circle. Using this form, we establish a relation between submodules of R2n-2 induced by Fox R-colorings of an n-tangle and Lagrangians or virtual Lagrangians in the symplectic structure (R2n-2; ϕ) depending on whether R is a field or a PID. We prove that when R = Zp, p > 2, all Lagrangians are induced by Fox R-colorings of some n-tangles and note that for p = 2 and n > 3 this is no longer true. For any ring, every 2π/n-rotation of an n-tangle yields an isometry of the symplectic space R2n-2. We analyze invariant Lagrangian subspaces of this rotation and we partially answer the question whether an operation of rotation (generalized mutation) defined in [A-P-R] preserves the first homology group of the double branched cover of S3 along a given link.

4

Variational equations on the Möbius strip

Urban Z., Volná J.

Systemy Wspomagania w Inżynierii Produkcji

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2017

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Vol. 6, iss. 4

325--333

EN

In this paper, systems of second-order ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by the canonical embedding of the two-dimensional Möbius strip into the Euclidean space, are considered in the class of variational equations. For a given non-variational system, the conditions assuring variationality (Helmholtz conditions) for the induced system on the Möbius strip are formulated. The theory contributes to variational foundations of geometric mechanics.

CS

V tomto clánku je studována variacnost systému obycejných diferenciálních rovnic (dynamických forem v geometrické mechanice) druhého rádu, kterou indukuje kanonické vložení dvojrozmerné Möbiovy pásky do Euklidova prostoru. Pro daný nevariacní systém rovnic jsou formulovány nutné a postacující podmínky variacnosti (Helmholtzovy podmínky). Práce je príspevkem k variacním základum geometrické mechaniky na Möbiove pásce.

5

On homogeneous functions in second-order field theory

Brajercík J., Urban Z.

Systemy Wspomagania w Inżynierii Produkcji

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2017

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Vol. 6, iss. 4

230--236

EN

The classical concept of a homogeneous function is introduced and extended within the theory of differential groups, known in the theory of differential invariants. Invariance under reparametrizations of solutions of partial differential equations is studied. On this basis the wellknown generalizations of the Euler theorem are obtained (the Zermelo conditions). The positive homogeneity concept is then applied to second-order variational equations in field theory.

SK

Standardní koncept homogenní funkce je zaveden a zobecnen pomocí užití diferenciálních grup, známých v teorii diferenciálních invariantu. Studujeme invarianci vzhledem k reparametrizacím integrálních krivek parciálních diferenciálních rovnic. Na základe tohoto prístupu obdržíme známé zobecnení Eulerova teorému, tzv. Zermelovy podmínky. Koncept pozitivní homogenity aplikujeme na variacní rovnice druhého rádu v teorii pole.

6

Lagrangian simulation and analysis of the power-law fluid mixing in the two-blade circular mixers using a modified WCSPH method

Shamsoddini R., Sefid M.

Polish Journal of Chemical Technology

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2015

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Vol. 17, nr 2

1--10

EN

In the present study, we introduce a robust modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method in order to examine miscible mixing within a two-blade paddle mixer. Since it has a Lagrangian nature and it is based on particles, Smoothed Particle Hydrodynamics (SPH) is an appropriate and convenient method for simulating the moving boundary problems and tracking the particles in the mixing process. The present study thus introduces a convenient SPH method for modelling the mixing process for the power-law fluids. Two geometries for the mixer are examined and the effects of the power-law index on the fluid mixing are investigated. The results show that the geometric change from circular chamber to twin chamber considerably increases the mixing rate (by at least 49%). The results also indicate that the twin chamber mixer is more efficient for the fluids with higher power-law index.

7

On consequences of the principle of stationary action for dissipative bodies

Kosiński W., Perzyna P.

Archives of Mechanics

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2012

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Vol. 64, nr 1

95-106

EN

The aim of this note is to show possible consequences of the principle of stationary action formulated for dissipative bodies. The material structure with internal state variables is considered for those bodies. The appropriate action functional is proposed for a typical dissipative body. Possible variations of fields of dependent state variables are introduced together with a non-commutative rule between operations of taking variations of the field and their partial time derivatives. Assuming vanishing of the first variation of the functional, the balance of linear momentum in differential form is received together with evolution equations for internal state variables and stress boundary condition.