It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.
{"title":"Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations","authors":"L. Kiss, A. Messaoudi, G. Szeidl","doi":"10.3390/applmech4010015","DOIUrl":"https://doi.org/10.3390/applmech4010015","url":null,"abstract":"It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"36 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75631066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The inverted pendulum is stabilized if the frequency and amplitude of the vibrating foundation exceed certain critical values. The system is analogous to static bending a wavy (patterned) beam subjected to a tensile load with appropriate boundary conditions. We analyze the buckling stability of such a wavy beam, which is governed by the Mathieu equation. Micro/nanopatterned structures and surfaces have various applications including the control of adhesion, friction, wettability, and surface-pattern-induced phase control.
{"title":"Kirchhoff’s Analogy between the Kapitza Pendulum Stability and Buckling of a Wavy Beam under Tensile Loading","authors":"Rahul Ramachandran, Michael Nosonovsky","doi":"10.3390/applmech4010014","DOIUrl":"https://doi.org/10.3390/applmech4010014","url":null,"abstract":"The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The inverted pendulum is stabilized if the frequency and amplitude of the vibrating foundation exceed certain critical values. The system is analogous to static bending a wavy (patterned) beam subjected to a tensile load with appropriate boundary conditions. We analyze the buckling stability of such a wavy beam, which is governed by the Mathieu equation. Micro/nanopatterned structures and surfaces have various applications including the control of adhesion, friction, wettability, and surface-pattern-induced phase control.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"27 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81643605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Y. Izumi, K. Saitoh, Tomohiro Sato, M. Takuma, Y. Takahashi
This study aims to understand the mechanical properties of cellulose nanofibers (CNFs), a nano-sized material element of woods or plants. We develop all-atom (AA) molecular dynamics models of cellulose microfibrils (CMFs), which are the smallest constituent of CNFs. The models were designed for the process of structural failure or the degradation of a hierarchical material of multiple CMF fibers, due to shear deformation. It was assumed that two CMFs were arranged in parallel and in close contact, either in a vacuum or in water. The CMF models in water were built by surrounding AA-modeled water molecules with a few nanometers. Shear deformation was applied in the axial direction of the CMF or in the direction parallel to molecular sheets. Shear moduli were measured, and they agree with previous experimental and computational values. The presence of water molecules reduced the elastic modulus, because of the behavior of water molecules at the interface between CMFs as a function of temperature. In the inelastic region, the CMF often broke down inside CMFs in a vacuum condition. However, in water environments, two CMFs tend to slip away from each other at the interface. Water molecules act like a lubricant between multiple CMFs and promote smooth sliding.
{"title":"Shear Deterioration of the Hierarchical Structure of Cellulose Microfibrils under Water Condition: All-Atom Molecular Dynamics Analysis","authors":"Y. Izumi, K. Saitoh, Tomohiro Sato, M. Takuma, Y. Takahashi","doi":"10.3390/applmech4010013","DOIUrl":"https://doi.org/10.3390/applmech4010013","url":null,"abstract":"This study aims to understand the mechanical properties of cellulose nanofibers (CNFs), a nano-sized material element of woods or plants. We develop all-atom (AA) molecular dynamics models of cellulose microfibrils (CMFs), which are the smallest constituent of CNFs. The models were designed for the process of structural failure or the degradation of a hierarchical material of multiple CMF fibers, due to shear deformation. It was assumed that two CMFs were arranged in parallel and in close contact, either in a vacuum or in water. The CMF models in water were built by surrounding AA-modeled water molecules with a few nanometers. Shear deformation was applied in the axial direction of the CMF or in the direction parallel to molecular sheets. Shear moduli were measured, and they agree with previous experimental and computational values. The presence of water molecules reduced the elastic modulus, because of the behavior of water molecules at the interface between CMFs as a function of temperature. In the inelastic region, the CMF often broke down inside CMFs in a vacuum condition. However, in water environments, two CMFs tend to slip away from each other at the interface. Water molecules act like a lubricant between multiple CMFs and promote smooth sliding.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"17 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82506992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents the static performance of composite steering knuckle due to drive on an equivalent road, including different types of roughness and maneuvers. To achieve this purpose, the driving of a full-vehicle model was simulated using the multi-body dynamics (MBD) method, and the imposed loads on connection points of the steering knuckle to different components of the suspension system were extracted considering various maneuvers. Next, CATIA software was used to prepare a smooth model of the steering knuckle by employing coordinate measuring machine (CMM) data. Stress analysis was performed under the maximum value of the loading history in finite element (FE) software. Eventually, the safety factor was calculated based on some well-known criteria for static failure of the composite materials. Moreover, the optimum value of tungsten carbide as a reinforcing substance in aluminum composite was estimated to increase failure strength. The results show that an increase in tungsten carbide leads to an increase in the strength of the steering knuckle under purely axial loads (normal stress criterion) and also that an increase in this substance leads to a decrease in the strength of the part under shear loads (shear stress criterion). Therefore, based on the nature of the loads (i.e., multi-axial non-proportional random amplitude loading conditions) applied to the automotive steering knuckle due to actual conditions, this metal matrix composite (aluminum matrix and tungsten carbide as reinforcement) is not practical.
{"title":"Failure Strength of Automotive Steering Knuckle Made of Metal Matrix Composite","authors":"K. Reza Kashyzadeh","doi":"10.3390/applmech4010012","DOIUrl":"https://doi.org/10.3390/applmech4010012","url":null,"abstract":"This article presents the static performance of composite steering knuckle due to drive on an equivalent road, including different types of roughness and maneuvers. To achieve this purpose, the driving of a full-vehicle model was simulated using the multi-body dynamics (MBD) method, and the imposed loads on connection points of the steering knuckle to different components of the suspension system were extracted considering various maneuvers. Next, CATIA software was used to prepare a smooth model of the steering knuckle by employing coordinate measuring machine (CMM) data. Stress analysis was performed under the maximum value of the loading history in finite element (FE) software. Eventually, the safety factor was calculated based on some well-known criteria for static failure of the composite materials. Moreover, the optimum value of tungsten carbide as a reinforcing substance in aluminum composite was estimated to increase failure strength. The results show that an increase in tungsten carbide leads to an increase in the strength of the steering knuckle under purely axial loads (normal stress criterion) and also that an increase in this substance leads to a decrease in the strength of the part under shear loads (shear stress criterion). Therefore, based on the nature of the loads (i.e., multi-axial non-proportional random amplitude loading conditions) applied to the automotive steering knuckle due to actual conditions, this metal matrix composite (aluminum matrix and tungsten carbide as reinforcement) is not practical.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"1 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90099089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Tănasă, A. Bosioc, A. Stuparu, S. Muntean, R. Susan-Resiga
This paper represents a welcome synthesis of the results obtained by the authors over more than a decade. The reason why such an approach is perfectly justified is found in the novelty of the control techniques of decelerated swirling flows from the conical diffuser of hydraulic turbines. The results presented in this paper refer strictly to the new passive control techniques of the swirling flows instabilities. Although the results of these new techniques have been disseminated in various papers, it is difficult to outline an overview from a collection of articles. Therefore, the present paper achieves a welcome unitary synthesis, useful to specialists in the field of turbomachines hydrodynamics. The reluctance of the turbine manufacturers on active control techniques that use external/additional energy source, led us to the choice of passive control techniques review, especially the ones developed in the last years. The first part of the paper analyzes the specialized literature that includes a variety of passive solutions for mitigating self-induced instabilities of decelerated swirling flow downstream of hydraulic turbines. Such inherent instabilities manifest intensely at far from optimal operating regimes, and represent one of the challenges of modern hydraulic turbines. The mitigation of these instabilities is an open problem, so far there are no unanimously accepted technical solutions implemented on prototype turbines. The second part of the paper includes detailed investigations on axial water injection with flow-feedback, but also more recent approaches using adjustable diaphragm in the conical diffuser.
{"title":"A Perspective Review of Passive Techniques Applied to Control the Swirling Flow Instabilities From The Conical Diffuser of Hydraulic Turbines","authors":"C. Tănasă, A. Bosioc, A. Stuparu, S. Muntean, R. Susan-Resiga","doi":"10.1115/1.4056895","DOIUrl":"https://doi.org/10.1115/1.4056895","url":null,"abstract":"\u0000 This paper represents a welcome synthesis of the results obtained by the authors over more than a decade. The reason why such an approach is perfectly justified is found in the novelty of the control techniques of decelerated swirling flows from the conical diffuser of hydraulic turbines. The results presented in this paper refer strictly to the new passive control techniques of the swirling flows instabilities. Although the results of these new techniques have been disseminated in various papers, it is difficult to outline an overview from a collection of articles. Therefore, the present paper achieves a welcome unitary synthesis, useful to specialists in the field of turbomachines hydrodynamics. The reluctance of the turbine manufacturers on active control techniques that use external/additional energy source, led us to the choice of passive control techniques review, especially the ones developed in the last years. The first part of the paper analyzes the specialized literature that includes a variety of passive solutions for mitigating self-induced instabilities of decelerated swirling flow downstream of hydraulic turbines. Such inherent instabilities manifest intensely at far from optimal operating regimes, and represent one of the challenges of modern hydraulic turbines. The mitigation of these instabilities is an open problem, so far there are no unanimously accepted technical solutions implemented on prototype turbines. The second part of the paper includes detailed investigations on axial water injection with flow-feedback, but also more recent approaches using adjustable diaphragm in the conical diffuser.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"41 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81314672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A numerical approach was implemented, to study a boiling flow in a horizontal serpentine tube. A NEPTUNE_CFD two-fluid model was used, to study the behavior of the refrigerant R141b in diabatic cases. The model was based on the Euler–Euler formalism of the Navier–Stokes equations, in which governing equations are solved for both phases of the fluid at each time step. The conjugate heat transfer—between the tube wall and the fluid—was considered via a coupling with the SYRTHES 4.3 software, which solves solid conduction in three dimensions. A mesh convergence study was carried out, which found that a resolution of 40 meshes per diameter was necessary for our case. The approach was validated by comparison with an experimental study of the literature, based on the faithful reproduction of the positions of two-phase flow regime transitions in the domain. Original post-processing was used, to unravel the flow characteristics. The mean and RMS fields of void fraction, temperatures and stream wise velocities in several sections were analyzed, when statistical convergence was reached. A thermal equilibrium was reached in the saturated liquid, but not in the vapor phase, due to the flow dynamic and possibly the presence of droplets. Finally, a thermal analysis of the configuration was proposed. It demonstrated the strong coupling between the temperature distribution in the solid, and the two-phase flow regimes at stake in the fluid domain.
{"title":"Euler–Euler Multi-Scale Simulations of Internal Boiling Flow with Conjugated Heat Transfer","authors":"E. Butaye, A. Toutant, S. Mer","doi":"10.3390/applmech4010011","DOIUrl":"https://doi.org/10.3390/applmech4010011","url":null,"abstract":"A numerical approach was implemented, to study a boiling flow in a horizontal serpentine tube. A NEPTUNE_CFD two-fluid model was used, to study the behavior of the refrigerant R141b in diabatic cases. The model was based on the Euler–Euler formalism of the Navier–Stokes equations, in which governing equations are solved for both phases of the fluid at each time step. The conjugate heat transfer—between the tube wall and the fluid—was considered via a coupling with the SYRTHES 4.3 software, which solves solid conduction in three dimensions. A mesh convergence study was carried out, which found that a resolution of 40 meshes per diameter was necessary for our case. The approach was validated by comparison with an experimental study of the literature, based on the faithful reproduction of the positions of two-phase flow regime transitions in the domain. Original post-processing was used, to unravel the flow characteristics. The mean and RMS fields of void fraction, temperatures and stream wise velocities in several sections were analyzed, when statistical convergence was reached. A thermal equilibrium was reached in the saturated liquid, but not in the vapor phase, due to the flow dynamic and possibly the presence of droplets. Finally, a thermal analysis of the configuration was proposed. It demonstrated the strong coupling between the temperature distribution in the solid, and the two-phase flow regimes at stake in the fluid domain.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"28 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76564845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In accidents involving cars with pedestrians, the impact of the head on structural parts of the vehicle presents a significant risk of injury. If the head hits the windshield, the injury is highly influenced by glass fracture. In pedestrian protection tests, a head form impactor is shot on the windshield while the resultant acceleration at the centre of gravity of the head is measured. To assess the risk of fatal or serious injury, a head injury criterion (HIC) as an explicit function of the measured acceleration can be determined. The braking strength of glass, which has a major impact on the head acceleration, however, is not deterministic but depends on production-related microcracks on the glass surface as well as on the loading rate. The aim of the present paper is to show a pragmatic method for how to include the stochastic failure of glass in crash and impact simulations. The methodology includes a fracture mechanical model for the strain rate-dependent failure of glass, an experimental determination of the glass strength for the different areas of a windshield (surface, edge, and screen-printing area), a statistical evaluation of the experimental data, and a computation of an HIC probability distribution by stochastic simulation.
{"title":"A Methodology for Stochastic Simulation of Head Impact on Windshields","authors":"C. Brokmann, C. Alter, S. Kolling","doi":"10.3390/applmech4010010","DOIUrl":"https://doi.org/10.3390/applmech4010010","url":null,"abstract":"In accidents involving cars with pedestrians, the impact of the head on structural parts of the vehicle presents a significant risk of injury. If the head hits the windshield, the injury is highly influenced by glass fracture. In pedestrian protection tests, a head form impactor is shot on the windshield while the resultant acceleration at the centre of gravity of the head is measured. To assess the risk of fatal or serious injury, a head injury criterion (HIC) as an explicit function of the measured acceleration can be determined. The braking strength of glass, which has a major impact on the head acceleration, however, is not deterministic but depends on production-related microcracks on the glass surface as well as on the loading rate. The aim of the present paper is to show a pragmatic method for how to include the stochastic failure of glass in crash and impact simulations. The methodology includes a fracture mechanical model for the strain rate-dependent failure of glass, an experimental determination of the glass strength for the different areas of a windshield (surface, edge, and screen-printing area), a statistical evaluation of the experimental data, and a computation of an HIC probability distribution by stochastic simulation.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"51 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84688697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.
{"title":"On the Countering of Free Vibrations by Forcing: Part II—Damped Oscillations and Decaying Forcing","authors":"L. Campos, Manuel J. S. Silva","doi":"10.3390/applmech4010009","DOIUrl":"https://doi.org/10.3390/applmech4010009","url":null,"abstract":"The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"196 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86932766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The ability to predict and characterize bifurcations from the onset of unsteadiness to the transition to turbulence is of critical importance in both academic and industrial applications. Numerous tools from dynamical system theory can be employed for that purpose. In this review, we focus on the practical computation and stability analyses of steady and time-periodic solutions with a particular emphasis on very high-dimensional systems such as those resulting from the discrete Navier-Stokes equations. In addition to a didactically concise theoretical framework, we introduce nekStab, an open source and user-friendly toolbox dedicated to such analyses using the spectral element solver Nek5000. Relying on Krylov methods and a time-stepper formulation, nekStab inherits the flexibility and high performance capabilities of Nek5000 and can be used to study the stability properties of flows in complex three-dimensional geometries. The performances and accuracy of nekStab are presented on the basis of standard benchmarks from the literature. For the sake of pedagogy and clarity, most of the algorithms implemented in nekStab are presented herein using Python pseudocode. Because of its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid dynamics.
{"title":"Krylov Methods for Large-Scale Dynamical Systems: Application in Fluid Dynamics","authors":"R. Frantz, Jean-Christophe Loiseau, J. Robinet","doi":"10.1115/1.4056808","DOIUrl":"https://doi.org/10.1115/1.4056808","url":null,"abstract":"\u0000 The ability to predict and characterize bifurcations from the onset of unsteadiness to the transition to turbulence is of critical importance in both academic and industrial applications. Numerous tools from dynamical system theory can be employed for that purpose. In this review, we focus on the practical computation and stability analyses of steady and time-periodic solutions with a particular emphasis on very high-dimensional systems such as those resulting from the discrete Navier-Stokes equations. In addition to a didactically concise theoretical framework, we introduce nekStab, an open source and user-friendly toolbox dedicated to such analyses using the spectral element solver Nek5000. Relying on Krylov methods and a time-stepper formulation, nekStab inherits the flexibility and high performance capabilities of Nek5000 and can be used to study the stability properties of flows in complex three-dimensional geometries. The performances and accuracy of nekStab are presented on the basis of standard benchmarks from the literature. For the sake of pedagogy and clarity, most of the algorithms implemented in nekStab are presented herein using Python pseudocode. Because of its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid dynamics.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"1 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77279367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.
{"title":"An Intuitive Derivation of Beam Models of Arbitrary Order","authors":"Hart Honickman","doi":"10.3390/applmech4010008","DOIUrl":"https://doi.org/10.3390/applmech4010008","url":null,"abstract":"This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.","PeriodicalId":8048,"journal":{"name":"Applied Mechanics Reviews","volume":"19 1","pages":""},"PeriodicalIF":14.3,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85364238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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