Controlling a robot manipulator system with both uncertain kinematics and dynamics is a challenging problem since the traditional control schemes that relying on the robot system models are no longer applicable. Developing a neural network‐based adaptive tracking control for such uncertain robot manipulator systems with region constraints is especially changing. In this paper, region tracking controllers are designed for a robot manipulator systems with uncertain kinematics and dynamics. The developed region tracking controllers ensures that the uncertain robot manipulator can track a moving region other than the traditional fixed point, which has better redundancy characteristics. The results are obtained through the development of the sliding‐mode and a novel proportion‐integration‐differentiation (PID)‐like method to address the region tracking control problem. Numerical simulations are presented to verify the proposed controller's performance.
{"title":"Neural network‐based adaptive region tracking control for robot manipulator systems with uncertain kinematics and dynamics","authors":"Mengyang Wu, Jikang Yang, Xiaohong Zhang, Weihua Yang, Jinwei Yu","doi":"10.1002/zamm.202300383","DOIUrl":"https://doi.org/10.1002/zamm.202300383","url":null,"abstract":"Controlling a robot manipulator system with both uncertain kinematics and dynamics is a challenging problem since the traditional control schemes that relying on the robot system models are no longer applicable. Developing a neural network‐based adaptive tracking control for such uncertain robot manipulator systems with region constraints is especially changing. In this paper, region tracking controllers are designed for a robot manipulator systems with uncertain kinematics and dynamics. The developed region tracking controllers ensures that the uncertain robot manipulator can track a moving region other than the traditional fixed point, which has better redundancy characteristics. The results are obtained through the development of the sliding‐mode and a novel proportion‐integration‐differentiation (PID)‐like method to address the region tracking control problem. Numerical simulations are presented to verify the proposed controller's performance.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"6 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88932665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shafia Rana, Hadi Ali Madkhali, M. Nawaz, S. Alharbi
Hybrid nanofluids (HNFs) have potentials applications in automotive industry, heating and cooling systems, biomedical and other fields due to their ability to introduce higher thermal conductivity than standard nanofluids. The purpose of this study is to investigate and compare the thermal transport performance (in the presence of buoyancy force) of two sets of HNFs. The hybrid nanoparticles which is the combination of titanium carbide and aluminium oxide, and the combination of titanium carbide‐copper oxide are taken into account. Both types of hybrid nanoparticles are dispersed in C2H6O2$C_{2}H_{6}O_{2}$ as a subjective fluid over a vertical nonlinear stretching sheet embedded in a porous medium. This will be the first study on the MXene base material TiC$TiC$ , making it possible for MXene‐based materials to enter the fluid dynamics field. Further, MXene material as heat transporting material is studied less and much more is needed for explore its various aspect. The specific combination of Al2O3−TiC$Al_{2}O_{3}-TiC$ , and CuO−TiC$CuO-TiC$ is considered because of their promising thermophysical and thermal transport properties. Moreover, considered combination of nanoparticles and the base fluid form a mixture which has thermal relaxation characteristics due to which its deviates from classical Fourier law of heat conduction. Therefore, instead of conventional Fourier's law of heat conduction, the non‐Fourier law of heat conduction is used to formulate the energy equation. It is first time that fhe finite element of method (FEM) is used for such a coupled and nonlinear complex problems of computational fluid dynamics (CFD). The numerical and graphical impacts of magnetic fields, Grashof number, permeable parameter, and thermal relaxation time parameter on velocity, and heat transport are investigated by applying FEM on formulated boundary value problems. In each studied system, increasing the Hartmann number causes an increase the skin friction coefficient and a decrease in the Nusselt number. Moreover, by increasing the thermal relaxation parameter, the temperature of the fluid decreases significantly. The velocity of the modified nanofluids is directly proportional to the Grashof number. The thermal boundary layer thickness (TBLT) and momentum boundary layer thickness (MBLT) of Carreau‐Yasuda (CY)‐HNF (Set II) is greater than CY hybrid nanofluid (CY‐HNF) (Set I) and CY‐Nanofluid (NF), respectively. We believe that the current research work provides new insights to improve the heat transport of nanofluid using appropriate combination of hybrid nanoparticles for practical application.
{"title":"Numerical study of Cattaneo‐Christov heat transfer in MHD Carreau‐Yasuda hybrid nanofluid subjected to Buoyancy force","authors":"Shafia Rana, Hadi Ali Madkhali, M. Nawaz, S. Alharbi","doi":"10.1002/zamm.202300037","DOIUrl":"https://doi.org/10.1002/zamm.202300037","url":null,"abstract":"Hybrid nanofluids (HNFs) have potentials applications in automotive industry, heating and cooling systems, biomedical and other fields due to their ability to introduce higher thermal conductivity than standard nanofluids. The purpose of this study is to investigate and compare the thermal transport performance (in the presence of buoyancy force) of two sets of HNFs. The hybrid nanoparticles which is the combination of titanium carbide and aluminium oxide, and the combination of titanium carbide‐copper oxide are taken into account. Both types of hybrid nanoparticles are dispersed in C2H6O2$C_{2}H_{6}O_{2}$ as a subjective fluid over a vertical nonlinear stretching sheet embedded in a porous medium. This will be the first study on the MXene base material TiC$TiC$ , making it possible for MXene‐based materials to enter the fluid dynamics field. Further, MXene material as heat transporting material is studied less and much more is needed for explore its various aspect. The specific combination of Al2O3−TiC$Al_{2}O_{3}-TiC$ , and CuO−TiC$CuO-TiC$ is considered because of their promising thermophysical and thermal transport properties. Moreover, considered combination of nanoparticles and the base fluid form a mixture which has thermal relaxation characteristics due to which its deviates from classical Fourier law of heat conduction. Therefore, instead of conventional Fourier's law of heat conduction, the non‐Fourier law of heat conduction is used to formulate the energy equation. It is first time that fhe finite element of method (FEM) is used for such a coupled and nonlinear complex problems of computational fluid dynamics (CFD). The numerical and graphical impacts of magnetic fields, Grashof number, permeable parameter, and thermal relaxation time parameter on velocity, and heat transport are investigated by applying FEM on formulated boundary value problems. In each studied system, increasing the Hartmann number causes an increase the skin friction coefficient and a decrease in the Nusselt number. Moreover, by increasing the thermal relaxation parameter, the temperature of the fluid decreases significantly. The velocity of the modified nanofluids is directly proportional to the Grashof number. The thermal boundary layer thickness (TBLT) and momentum boundary layer thickness (MBLT) of Carreau‐Yasuda (CY)‐HNF (Set II) is greater than CY hybrid nanofluid (CY‐HNF) (Set I) and CY‐Nanofluid (NF), respectively. We believe that the current research work provides new insights to improve the heat transport of nanofluid using appropriate combination of hybrid nanoparticles for practical application.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"17 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88637406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of the present work is to examine the entropy production characteristics, thermal profile, and flow behaviour of two non‐miscible natures of Newtonian and micropolar fluids, which take place through a rectangular porous enclosure channel. The flow region is divided into two distinct porous zones of the channel and is subjected to a constant oriented magnetic field. The Eringen's micropolar fluid is taking place in the upper porous zone, whereas in the lower porous zone, the Newtonian fluid is flowing. The wall surface of a rectangular porous channel is isothermal, and the flow of immiscible fluid through a porous channel takes place because of a constant pressure gradient. No slip condition is imposed on the static walls and continuity of vorticity, velocity, shear stress component, thermal distribution, and thermal flux are prescribed at the interface. Here, the production of entropy due to fluid friction and thermal exchange for non‐miscible Newtonian and micropolar fluids is evaluated. The characteristics of various estimated parameters on thermal and flow properties, such as Bejan number distribution, flow velocity, entropy production, and thermal profile, are discussed. The obtained results show that entropy production is directly proportional to viscous dissipation and Reynolds number, whereas it has a reverse nature with micropolarity parameter, inclination angle parameter, and Hartman number. Our results corroborate with previous published results.
{"title":"Heat and mass transfer analysis for MHD non‐miscible micropolar and Newtonian fluid flow in a rectangular porous channel","authors":"Ankit Kumar, P. Yadav","doi":"10.1002/zamm.202200589","DOIUrl":"https://doi.org/10.1002/zamm.202200589","url":null,"abstract":"The aim of the present work is to examine the entropy production characteristics, thermal profile, and flow behaviour of two non‐miscible natures of Newtonian and micropolar fluids, which take place through a rectangular porous enclosure channel. The flow region is divided into two distinct porous zones of the channel and is subjected to a constant oriented magnetic field. The Eringen's micropolar fluid is taking place in the upper porous zone, whereas in the lower porous zone, the Newtonian fluid is flowing. The wall surface of a rectangular porous channel is isothermal, and the flow of immiscible fluid through a porous channel takes place because of a constant pressure gradient. No slip condition is imposed on the static walls and continuity of vorticity, velocity, shear stress component, thermal distribution, and thermal flux are prescribed at the interface. Here, the production of entropy due to fluid friction and thermal exchange for non‐miscible Newtonian and micropolar fluids is evaluated. The characteristics of various estimated parameters on thermal and flow properties, such as Bejan number distribution, flow velocity, entropy production, and thermal profile, are discussed. The obtained results show that entropy production is directly proportional to viscous dissipation and Reynolds number, whereas it has a reverse nature with micropolarity parameter, inclination angle parameter, and Hartman number. Our results corroborate with previous published results.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"1 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76617272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we show that within the class of isotropic Mindlin‐Toupin gradient theories there exist a particular variant of the theory, which allows a completely simplified form of traction boundary value problems. This theory can be obtained assuming that the high‐grade part of the strain energy density depends only on the vector‐type quantities, that are the gradient of dilatation and the curl of small rotation. Such incomplete gradient theory becomes positive semi‐definite and at the same time it obeys the strong ellipticity conditions of the general Mindlin‐Toupin first strain gradient elasticity. Based on the variational approach it is shown that the equilibrium equations of the developed theory and its definition for the surface traction can be given only in terms of the total stresses (like in classical elasticity). Such formulation can be useful for derivation of the closed form solutions for the problems with traction‐type boundary conditions. Examples of the solutions for the problem of cylindrical bending and for the inplane crack tip fields are presented. It is shown that considered theory allows to obtain a regularized solution for the crack problems and at the same time it does not predict a non‐physical infinite increase of the material's rigidity under bending.
{"title":"Variant of strain gradient elasticity with simplified formulation of traction boundary value problems","authors":"S. Lurie, Y. Solyaev","doi":"10.1002/zamm.202300329","DOIUrl":"https://doi.org/10.1002/zamm.202300329","url":null,"abstract":"In this paper, we show that within the class of isotropic Mindlin‐Toupin gradient theories there exist a particular variant of the theory, which allows a completely simplified form of traction boundary value problems. This theory can be obtained assuming that the high‐grade part of the strain energy density depends only on the vector‐type quantities, that are the gradient of dilatation and the curl of small rotation. Such incomplete gradient theory becomes positive semi‐definite and at the same time it obeys the strong ellipticity conditions of the general Mindlin‐Toupin first strain gradient elasticity. Based on the variational approach it is shown that the equilibrium equations of the developed theory and its definition for the surface traction can be given only in terms of the total stresses (like in classical elasticity). Such formulation can be useful for derivation of the closed form solutions for the problems with traction‐type boundary conditions. Examples of the solutions for the problem of cylindrical bending and for the inplane crack tip fields are presented. It is shown that considered theory allows to obtain a regularized solution for the crack problems and at the same time it does not predict a non‐physical infinite increase of the material's rigidity under bending.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"51 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89397685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials.
{"title":"Interaction among interfacial offset cracks in composite materials under the anti‐plane shear loading","authors":"A. Tanwar, Subir Das, E. Crăciun, H. Altenbach","doi":"10.1002/zamm.202300081","DOIUrl":"https://doi.org/10.1002/zamm.202300081","url":null,"abstract":"The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"37 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72814118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Nishad, S. Neelamani, Jeng-Tzong Chen, K. Vijay
{"title":"Gravity wave interaction with cage enveloped breakwaters using DBEM","authors":"C. Nishad, S. Neelamani, Jeng-Tzong Chen, K. Vijay","doi":"10.1002/zamm.202200064","DOIUrl":"https://doi.org/10.1002/zamm.202200064","url":null,"abstract":"","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"12 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73845659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flow over a linearly stretching sheet having constant temperature is examined in this article. The effects of frictional heating (viscous dissipation) and Ohmic heating (Joule dissipation) are also studied. As evidenced by the literature, energy equations are not always self‐similar when viscous dissipation is considered. It strongly depends on the form of stretching velocity and the surface temperature of the sheet. To facilitate the similarity transformations in these cases, one must find a constraint between the sheet velocity and the surface temperature. It is also observed that for the linearly stretching sheet with constant wall temperature, it is not possible to achieve self‐similar equations because in this case, a local variable appears in the viscous dissipation parameter. Hence, this problem corresponds to the non‐similar flow. In this analysis, pseudo‐similarity transformation is employed, and the viscous dissipation parameter is selected as a non‐similarity variable. Governing equations are transferred into non‐similar forms then a method known as Sparrow‐Quack‐Boerner (SQB) local non‐similarity (LNS) is used to derive the equations up to the second level of truncations which are then solved numerically. The slope linear regression (SLR) technique is used to compare the solutions obtained from the equations of the first and second levels of truncation.
{"title":"Heat transfer and flow analysis over a linearly stretching sheet with constant wall temperature: Novel local non‐similar solutions in the presence of viscous heating","authors":"M. I. Afridi, Zhi‐Min Chen, N. Riaz, M. Qasim","doi":"10.1002/zamm.202300003","DOIUrl":"https://doi.org/10.1002/zamm.202300003","url":null,"abstract":"Flow over a linearly stretching sheet having constant temperature is examined in this article. The effects of frictional heating (viscous dissipation) and Ohmic heating (Joule dissipation) are also studied. As evidenced by the literature, energy equations are not always self‐similar when viscous dissipation is considered. It strongly depends on the form of stretching velocity and the surface temperature of the sheet. To facilitate the similarity transformations in these cases, one must find a constraint between the sheet velocity and the surface temperature. It is also observed that for the linearly stretching sheet with constant wall temperature, it is not possible to achieve self‐similar equations because in this case, a local variable appears in the viscous dissipation parameter. Hence, this problem corresponds to the non‐similar flow. In this analysis, pseudo‐similarity transformation is employed, and the viscous dissipation parameter is selected as a non‐similarity variable. Governing equations are transferred into non‐similar forms then a method known as Sparrow‐Quack‐Boerner (SQB) local non‐similarity (LNS) is used to derive the equations up to the second level of truncations which are then solved numerically. The slope linear regression (SLR) technique is used to compare the solutions obtained from the equations of the first and second levels of truncation.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"11 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81895944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with a study the linear finite element approximation of a piezoelectric Signorini's contact problem with and without friction. We derive error estimates that depend on the penalty parameter ε and the mesh size h. Moreover, under some regularities of the solution to the contact problems and some requirements on parameters ε and h, we provide results on the convergence rate of the finite element approximation of the penalized solution.
{"title":"Error estimates of piezoelectric Signorini's contact problems","authors":"Hamid El Khalfi, O. Baiz, H. Benaissa","doi":"10.1002/zamm.202300112","DOIUrl":"https://doi.org/10.1002/zamm.202300112","url":null,"abstract":"This paper deals with a study the linear finite element approximation of a piezoelectric Signorini's contact problem with and without friction. We derive error estimates that depend on the penalty parameter ε and the mesh size h. Moreover, under some regularities of the solution to the contact problems and some requirements on parameters ε and h, we provide results on the convergence rate of the finite element approximation of the penalized solution.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"77 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76084708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy.
{"title":"Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method","authors":"M. Narayana, P. Siddheshwar","doi":"10.1002/zamm.202200472","DOIUrl":"https://doi.org/10.1002/zamm.202200472","url":null,"abstract":"The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"31 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75490865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study analytically examines internally pressurized power‐law functionally graded variable thickness disk. The power‐law consideration is applied to the Young's modulus and the Poisson's ratio of the graded material as well as the radial thickness profile variation of the disk. Under this scheme, the solution yields to different Bessel functions including the first, second, and modified types. Stress and displacement fields are investigated at the elastic limits by operating with these functions. The limits are calculated with the well‐known von Mises criteria. Following the analytical modeling, numerical examples are built. Therein the examples, some noteworthy nuances have been achieved. It has been observed that unlike the usual prediction in the literature, constant Poisson's ratio, the effect of variable Poisson's ratio on stresses and displacements is still evident, although not as much as variable Young's modulus and disk geometry. We suggest assigning it as a variable in similar applications to be more precise. Additionally, according to the von Mises criterion, yielding may begin at the inner radius, the outer radius, or both at the same time. Parameters in the simultaneous flow initiation state are critical. These parameters allow the disk to reach the highest elastic limit pressure.
{"title":"Comprehensive elastic analysis of functionally graded variable thickness pressurized disk","authors":"Ömer Can Farukoğlu, I. Korkut, A. Motameni","doi":"10.1002/zamm.202200506","DOIUrl":"https://doi.org/10.1002/zamm.202200506","url":null,"abstract":"This study analytically examines internally pressurized power‐law functionally graded variable thickness disk. The power‐law consideration is applied to the Young's modulus and the Poisson's ratio of the graded material as well as the radial thickness profile variation of the disk. Under this scheme, the solution yields to different Bessel functions including the first, second, and modified types. Stress and displacement fields are investigated at the elastic limits by operating with these functions. The limits are calculated with the well‐known von Mises criteria. Following the analytical modeling, numerical examples are built. Therein the examples, some noteworthy nuances have been achieved. It has been observed that unlike the usual prediction in the literature, constant Poisson's ratio, the effect of variable Poisson's ratio on stresses and displacements is still evident, although not as much as variable Young's modulus and disk geometry. We suggest assigning it as a variable in similar applications to be more precise. Additionally, according to the von Mises criterion, yielding may begin at the inner radius, the outer radius, or both at the same time. Parameters in the simultaneous flow initiation state are critical. These parameters allow the disk to reach the highest elastic limit pressure.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"49 5 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77472177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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