of an arbitrary order, which does not contain x explicitly, one can propose to specify differential equations which belong to such type and that can be satisfied by meromorphic double-periodic functions. Here, I indicate a property of such equations which simplifies the given problem, without study in depth and which translates into a very simple and practical rule. Suppose the equation is written as
{"title":"On a property of differential equations integrable using meromorphic double-periodic functions","authors":"M. Petrovitch","doi":"10.2298/TAM1801121P","DOIUrl":"https://doi.org/10.2298/TAM1801121P","url":null,"abstract":"of an arbitrary order, which does not contain x explicitly, one can propose to specify differential equations which belong to such type and that can be satisfied by meromorphic double-periodic functions. Here, I indicate a property of such equations which simplifies the given problem, without study in depth and which translates into a very simple and practical rule. Suppose the equation is written as","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"5 1","pages":"121-127"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79421373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Although much employed, wind energy systems still present an open, contemporary topic of many research studies. Special attention is given to precise aerodynamic modeling performed in the beginning since overall wind turbine performances directly depend on blade aerodynamic performances. Several models different in complexity and computational requirements are still widely used. Most common numerical approaches include: i) momentum balance models, ii) potential flow methods and iii) full computational fluid dynamics solutions. Short explanations, reviews and comparison of the existing computational concepts are presented in the paper. Simpler models are described and im- plemented while numerous numerical investigations of isolated horizontal-axis wind turbine rotor consisting of three blades have also been performed in ANSYS FLUENT 16.2. Flow field is modeled by Reynolds Averaged Navier– Stokes (RANS) equations closed by two different turbulence models. Results including global parameters such as thrust and power coefficients as well as local distributions along the blade obtained by different models are compared to available experimental data. Presented results include fluid flow visualizations in the form of velocity contours, sectional pressure distributions and values of power and thrust force coefficients for a range of operational regimes. Although obtained numerical results vary in accuracy, all presented numerical settings seem to slightly under- or over-estimate the global wind turbine parameters (power and thrust force coefficients). Turbulence can greatly affect the wind turbine aerodynamics and should be modeled with care.
{"title":"Estimation of wind turbine blade aerodynamic performances computed using different numerical approaches","authors":"J. Svorcan, Ognjen Peković, Toni Ivanov","doi":"10.2298/tam171130004s","DOIUrl":"https://doi.org/10.2298/tam171130004s","url":null,"abstract":". Although much employed, wind energy systems still present an open, contemporary topic of many research studies. Special attention is given to precise aerodynamic modeling performed in the beginning since overall wind turbine performances directly depend on blade aerodynamic performances. Several models different in complexity and computational requirements are still widely used. Most common numerical approaches include: i) momentum balance models, ii) potential flow methods and iii) full computational fluid dynamics solutions. Short explanations, reviews and comparison of the existing computational concepts are presented in the paper. Simpler models are described and im- plemented while numerous numerical investigations of isolated horizontal-axis wind turbine rotor consisting of three blades have also been performed in ANSYS FLUENT 16.2. Flow field is modeled by Reynolds Averaged Navier– Stokes (RANS) equations closed by two different turbulence models. Results including global parameters such as thrust and power coefficients as well as local distributions along the blade obtained by different models are compared to available experimental data. Presented results include fluid flow visualizations in the form of velocity contours, sectional pressure distributions and values of power and thrust force coefficients for a range of operational regimes. Although obtained numerical results vary in accuracy, all presented numerical settings seem to slightly under- or over-estimate the global wind turbine parameters (power and thrust force coefficients). Turbulence can greatly affect the wind turbine aerodynamics and should be modeled with care.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"149 1","pages":"53-65"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86658724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter λ over the range [0,1]. To probe the role of parameter λ and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simul- taneous effects of varying yield stress and parameter λ on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel–Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of λ .
{"title":"Analysis of dynamics variation against thixotropic parameter’s preferential range","authors":"N. Shahid","doi":"10.2298/TAM180819013S","DOIUrl":"https://doi.org/10.2298/TAM180819013S","url":null,"abstract":". Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter λ over the range [0,1]. To probe the role of parameter λ and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simul- taneous effects of varying yield stress and parameter λ on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel–Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of λ .","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"7 1","pages":"231-251"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72863932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska–Brezzi) condition and Lax–Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on L2 and Sobolev norms. We discuss the so-called phenomena of “necrosis” inside a solid tumor using the energy of the system.
{"title":"Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor","authors":"Meraj Alam, Bibaswan Dey, G. Raja","doi":"10.2298/TAM180810014A","DOIUrl":"https://doi.org/10.2298/TAM180810014A","url":null,"abstract":"In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska–Brezzi) condition and Lax–Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on L2 and Sobolev norms. We discuss the so-called phenomena of “necrosis” inside a solid tumor using the energy of the system.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"46 1","pages":"253-278"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86048800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The objective of the present review is twofold. First, it aims at highlighting some sigmoid and reverse-sigmoid response patterns observed re- cently in the course of simulations of the high-strain-rate loading of (mostly, quasibrittle) solids. Second, it aims at reviewing various properties of two models used frequently as curve fitting tools for nonlinear and saturable phenomena. These two models-inspired by the Hill and the Weibull cumula- tive distribution functions-are bounded by two horizontal asymptotes with a smooth transition between the baseline and the final saturation state, char- acterized by a non-negative (a non-positive) derivative at each point for the sigmoid (the reverse-sigmoid) shape. Although they were used primarily for data fitting because of their flexibility and effectiveness, these nonlinear models possess other properties useful for the analysis of the irreversible, nonlinear and far-from-equilibrium phenomena. The main features of these two models are systematically examined in this review. In spite of the fact that satis- factory curve-fitting of data could not be considered a proof of causality it could underline a pattern of behavior and, perhaps, provide an investigation guidance.
{"title":"Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids","authors":"S. Mastilovic","doi":"10.2298/TAM171203007M","DOIUrl":"https://doi.org/10.2298/TAM171203007M","url":null,"abstract":". The objective of the present review is twofold. First, it aims at highlighting some sigmoid and reverse-sigmoid response patterns observed re- cently in the course of simulations of the high-strain-rate loading of (mostly, quasibrittle) solids. Second, it aims at reviewing various properties of two models used frequently as curve fitting tools for nonlinear and saturable phenomena. These two models-inspired by the Hill and the Weibull cumula- tive distribution functions-are bounded by two horizontal asymptotes with a smooth transition between the baseline and the final saturation state, char- acterized by a non-negative (a non-positive) derivative at each point for the sigmoid (the reverse-sigmoid) shape. Although they were used primarily for data fitting because of their flexibility and effectiveness, these nonlinear models possess other properties useful for the analysis of the irreversible, nonlinear and far-from-equilibrium phenomena. The main features of these two models are systematically examined in this review. In spite of the fact that satis- factory curve-fitting of data could not be considered a proof of causality it could underline a pattern of behavior and, perhaps, provide an investigation guidance.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"26 1","pages":"95-119"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78267797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
U. Mahabaleshwar, Igor Pažanin, M. Radulović, F. S. Grau
In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude ǫ is applied on cross-section of the duct. Using the asymptotic analysis with respect to ǫ, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.
{"title":"Effects of small boundary perturbation on the MHD duct flow","authors":"U. Mahabaleshwar, Igor Pažanin, M. Radulović, F. S. Grau","doi":"10.2298/TAM170511004M","DOIUrl":"https://doi.org/10.2298/TAM170511004M","url":null,"abstract":"In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude ǫ is applied on cross-section of the duct. Using the asymptotic analysis with respect to ǫ, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"68 1","pages":"83-101"},"PeriodicalIF":0.7,"publicationDate":"2017-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86897696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a theory of strain gradient plasticity for isotropic bodies undergoing small deformation in the absence of plastic spin. The proposed theory is based on a system of microstresses which include a microstress vector consistent with microforce balance; the mechanical form of the second law of thermodynamics which includes work performed by the microstresses during plastic flow; and a constitutive theory that allows the free energy to depend on the elastic strain Ee, divergence of plastic strain divEp and the Burgers tensor G. Substitution of the constitutive relations into the microforce balance leads to a nonlinear partial differential equation in the plastic strain known as flow rule which captures the presence of an additional energetic length scale arising from the accounting of microstress vector. In addition to the flow rule, nonstandard boundary conditions are obtained, and as an aid to finite element solution a variational formulation of the flow rule is deduced. Finite element solution is obtained of one-dimensional problem of viscoplastic simple shearing under gravity force, where it is shown that for a fixed dissipative length scale, increase in the energetic length scales will result in decrease in the plastic strain.
{"title":"A theory of strain-gradient plasticity with effect of internal microforce","authors":"A. Borokinni, A. Akinola, O. Layeni","doi":"10.2298/TAM160312010B","DOIUrl":"https://doi.org/10.2298/TAM160312010B","url":null,"abstract":"This paper develops a theory of strain gradient plasticity for isotropic bodies undergoing small deformation in the absence of plastic spin. The proposed theory is based on a system of microstresses which include a microstress vector consistent with microforce balance; the mechanical form of the second law of thermodynamics which includes work performed by the microstresses during plastic flow; and a constitutive theory that allows the free energy to depend on the elastic strain Ee, divergence of plastic strain divEp and the Burgers tensor G. Substitution of the constitutive relations into the microforce balance leads to a nonlinear partial differential equation in the plastic strain known as flow rule which captures the presence of an additional energetic length scale arising from the accounting of microstress vector. In addition to the flow rule, nonstandard boundary conditions are obtained, and as an aid to finite element solution a variational formulation of the flow rule is deduced. Finite element solution is obtained of one-dimensional problem of viscoplastic simple shearing under gravity force, where it is shown that for a fixed dissipative length scale, increase in the energetic length scales will result in decrease in the plastic strain.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"44 1","pages":"1-13"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90218923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Mušicki, 2004), which began with the modification of the mechanics of such systems (V. Vujičić, 1987), is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.
{"title":"Extended Lagrangian formalism for rheonomic systems with variable mass","authors":"D. Mušicki","doi":"10.2298/TAM170601006M","DOIUrl":"https://doi.org/10.2298/TAM170601006M","url":null,"abstract":"In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Mušicki, 2004), which began with the modification of the mechanics of such systems (V. Vujičić, 1987), is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"36 1","pages":"115-132"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77738670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On damage tensor in linear anisotropic elasticity","authors":"J. Jarić, D. Kuzmanović","doi":"10.2298/TAM170306018J","DOIUrl":"https://doi.org/10.2298/TAM170306018J","url":null,"abstract":"","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"151 1","pages":"141-154"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75668467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski’s original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.
{"title":"Discriminantly separable polynomials and the generalized Kowalevski top","authors":"V. Dragović, K. Kukić","doi":"10.2298/TAM170926016D","DOIUrl":"https://doi.org/10.2298/TAM170926016D","url":null,"abstract":"The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski’s original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"9 1","pages":"229-236"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80166269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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