Physics-informed neural networks(PINNs)have emerged as a promising class of scientific machine learning techniques that integrate governing physical laws into neural network training.Their ability to enforce different...Physics-informed neural networks(PINNs)have emerged as a promising class of scientific machine learning techniques that integrate governing physical laws into neural network training.Their ability to enforce differential equations,constitutive relations,and boundary conditions within the loss function provides a physically grounded alternative to traditional data-driven models,particularly for solid and structural mechanics,where data are often limited or noisy.This review offers a comprehensive assessment of recent developments in PINNs,combining bibliometric analysis,theoretical foundations,application-oriented insights,and methodological innovations.A biblio-metric survey indicates a rapid increase in publications on PINNs since 2018,with prominent research clusters focused on numerical methods,structural analysis,and forecasting.Building upon this trend,the review consolidates advance-ments across five principal application domains,including forward structural analysis,inverse modeling and parameter identification,structural and topology optimization,assessment of structural integrity,and manufacturing processes.These applications are propelled by substantial methodological advancements,encompassing rigorous enforcement of boundary conditions,modified loss functions,adaptive training,domain decomposition strategies,multi-fidelity and transfer learning approaches,as well as hybrid finite element–PINN integration.These advances address recurring challenges in solid mechanics,such as high-order governing equations,material heterogeneity,complex geometries,localized phenomena,and limited experimental data.Despite remaining challenges in computational cost,scalability,and experimental validation,PINNs are increasingly evolving into specialized,physics-aware tools for practical solid and structural mechanics applications.展开更多
Cells interact with the extracellular matrix and generate traction forces,which play fundamental roles in many cytological activities,such as migration and differentiation.The quanti fication of these traction forces ...Cells interact with the extracellular matrix and generate traction forces,which play fundamental roles in many cytological activities,such as migration and differentiation.The quanti fication of these traction forces is a prerequisite for understanding the interaction and regulation between force and functions,which can be accomplished by traction force microscopy(TFM).In TFM,the forces are determined by tracking the displacement of fiducial markers through optical microscopy.The type of fiducial marker,microscopy modality,and image processing algorithms are key factors determining the final resolution of TFM.This review summarizes efforts in three aspects to enhance the performance of TFM and discusses the challenges of further development,particularly from an optical view.展开更多
UHMWPE fibers exhibit impressive modulus and strength,but they have not reached their theoretical limits.Researchers focus on molecular weight,orientation,and crystallinity of UHMWPE,yet their contributions to mechani...UHMWPE fibers exhibit impressive modulus and strength,but they have not reached their theoretical limits.Researchers focus on molecular weight,orientation,and crystallinity of UHMWPE,yet their contributions to mechanical properties are unclear.Molecular dynamics simulations are valuable but often limited by computational constraints.Our aim is to simulate higher molecular weights to better represent real UHMWPE fibers.We used Packmol and Polyply methodologies to construct PE systems,with Polyply reproducing more reasonable properties of UHMWPE fibers.Additionally,tensile simulations showed that orientation and crystallinity greatly impact Young's modulus more than molecular weight.Energy decomposition indicated that higher molecular weights lead to covalent bonds that can withstand more energy during stretching,thus increasing breaking strength.Combining simulations with machine learning,we found that orientation has the most significant impact on Young's modulus,contributing 60%,and molecular weight plays the most crucial role in determining the breaking strength,accounting for 65%.This study provides a theoretical basis and guidelines for enhancing UHMWPE's modulus and strength.展开更多
The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undis...The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invaxiant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invaxiant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invaxiant. An example is also given to illustrate the application of the results.展开更多
The airflow mechanics in adult nasal airways,whether healthy or abnormal,are extensively studied and investigated,but the flow mechanics in child nasal airways remain underexplored.This study investigates the airflow ...The airflow mechanics in adult nasal airways,whether healthy or abnormal,are extensively studied and investigated,but the flow mechanics in child nasal airways remain underexplored.This study investigates the airflow mechanics in the child’s nasal upper airway with adenoid hypertrophy,with an adenoid nasopharyngeal ratio(AN of 0.9),under cyclic inhalation and exhalation.An inlet respiratory cycle with three different flow rates(3.2 L/min calm breathing,8.6 L/min normal breathing,and 19.3 L/min intensive breathing)was simulated by using the computational fluid dynamics approach.To better capture the interaction between airflow and the flexible airway tissue,fluid-structure interaction analysis was performed at the normal breathing rate.Comparing the airflow dynamics during inhalation and exhalation,the pressure drops,nasal resistance,and wall shear stress show significant differences in the nasopharyngeal region for all different flow rates.This observation suggests that the inertial effect associated with the transient flow is important during exhalation and inhalation.Furthermore,the considerable temporal variation in flow rate distribution across a specific cross-section of the nasal airway highlights the critical role of transient data in virtual surgery planning and data for clinical decisions.展开更多
Incorporating ceramic particles into metal matrices is a proven strategy for boosting mechanical properties and wear resistance.The reinforcement potential of tungsten carbide(WC)particles in 316L stainless steel is r...Incorporating ceramic particles into metal matrices is a proven strategy for boosting mechanical properties and wear resistance.The reinforcement potential of tungsten carbide(WC)particles in 316L stainless steel is revealed,utilizing selective laser melting(SLM)to fabricate composites with 5 and 10 vol.%WC.The WC incorporation markedly alters the composite’s microstructure and mechanical attributes.Notably,5 vol.%WC-316L composite exhibits a refined submicron cellular structure,averaging 0.67μm in grain size.Elemental diffusion at WC-316L interface formed a 0.8μm gradient transition layer enriched with M_(2)C carbides(Fe,Cr,W),ensuring robust metallurgical bonding.Compared with unreinforced 316L,5%WC composite exhibits a 70%increase in tensile strength,reaching 1012.6 MPa,and a 25.3%rise in hardness,while maintaining acceptable ductility.10%WC composite achieves a 70.8%hardness enhancement,albeit with reduced elongation.Friction coefficient is reduced by up to 17.3%,and the wear mechanism shifts from adhesive to abrasive,significantly improving wear resistance.展开更多
This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and th...This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.展开更多
Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is disc...In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.展开更多
The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical...The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical foundations of Relativity Theory and its essential role in the clarification of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Particle Physics.展开更多
We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result ...We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 -?E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.展开更多
We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the m...We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.展开更多
Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear te...Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.展开更多
This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the...This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations.展开更多
In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal ...In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.展开更多
Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. ...Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.展开更多
This paper explains the basic steps form the classical turbulence mechanics (CTM) to the postclassical turbulence mechanics (PCTM). When the CTM stems from the characterization of the motion states in the infinitesima...This paper explains the basic steps form the classical turbulence mechanics (CTM) to the postclassical turbulence mechanics (PCTM). When the CTM stems from the characterization of the motion states in the infinitesimal surroundings of the flowfield points by the flow velocity at these points then the PCTM complements this characterization by the curvature of the velocity fluctuation streamlines passing these points. The complementation is formalized by the inclusion of the curvature of the velocity fluctuation streamlines to the arguments of the probability distribution of the motion states in the infinitesimal surroundings of the flow field points. The most radical physical outcome of the realized formalism is the characterization of the turbulence viscosity properties by two types of turbulence viscosity against only one shear viscosity within the CTM.展开更多
This paper surveys the formalism and applications of the postclassical turbulence mechanics (PCTM) grounded on the characterization of turbulent flow field in infinitesimal surroundings of the flow field points beside...This paper surveys the formalism and applications of the postclassical turbulence mechanics (PCTM) grounded on the characterization of turbulent flow field in infinitesimal surroundings of the flow field points besides the flow velocity at these points also by the curvature of the velocity fluctuation streamlines passing these points. The PCTM applies this step to found the turbulence split into the orientated and the non-orientated constituents. The split specifies the competence of the classical turbulence mechanics (CTM) to the description of the non-orientated turbulence constituent and delegates the description of the orientated turbulence constituent (in the spirit of the theory of micropolar fluids) to the equation of moment-of-momentum. The concurrent presence of the orientated (relatively large scale) and the non-orientated (relatively small scale) turbulence constituents enables to compile the CTM and the conception of L. F. Richardson and A. N. Kolmogorov about the cascading turbulence (RK conception) within a conjoint formalism. The compilation solves the classical conflict between the CTM and the RK conception, though evinces a conflict of another type characterized as paradigmatic.展开更多
基金funded by National Research Council of Thailand(contract No.N42A671047).
文摘Physics-informed neural networks(PINNs)have emerged as a promising class of scientific machine learning techniques that integrate governing physical laws into neural network training.Their ability to enforce differential equations,constitutive relations,and boundary conditions within the loss function provides a physically grounded alternative to traditional data-driven models,particularly for solid and structural mechanics,where data are often limited or noisy.This review offers a comprehensive assessment of recent developments in PINNs,combining bibliometric analysis,theoretical foundations,application-oriented insights,and methodological innovations.A biblio-metric survey indicates a rapid increase in publications on PINNs since 2018,with prominent research clusters focused on numerical methods,structural analysis,and forecasting.Building upon this trend,the review consolidates advance-ments across five principal application domains,including forward structural analysis,inverse modeling and parameter identification,structural and topology optimization,assessment of structural integrity,and manufacturing processes.These applications are propelled by substantial methodological advancements,encompassing rigorous enforcement of boundary conditions,modified loss functions,adaptive training,domain decomposition strategies,multi-fidelity and transfer learning approaches,as well as hybrid finite element–PINN integration.These advances address recurring challenges in solid mechanics,such as high-order governing equations,material heterogeneity,complex geometries,localized phenomena,and limited experimental data.Despite remaining challenges in computational cost,scalability,and experimental validation,PINNs are increasingly evolving into specialized,physics-aware tools for practical solid and structural mechanics applications.
基金supported by the Major Research Instrument Development Project of the National Natural Science Foundation of China(32527801)the National Natural Science Foundation of China(32301168)+1 种基金the Ningbo Natural Science Foundation of China(2023J351)the Yongjiang Innovative Talents Project of Ningbo City(2024A-172-G).
文摘Cells interact with the extracellular matrix and generate traction forces,which play fundamental roles in many cytological activities,such as migration and differentiation.The quanti fication of these traction forces is a prerequisite for understanding the interaction and regulation between force and functions,which can be accomplished by traction force microscopy(TFM).In TFM,the forces are determined by tracking the displacement of fiducial markers through optical microscopy.The type of fiducial marker,microscopy modality,and image processing algorithms are key factors determining the final resolution of TFM.This review summarizes efforts in three aspects to enhance the performance of TFM and discusses the challenges of further development,particularly from an optical view.
基金financially supported by the National Natural Science Foundation of China(Nos.52303298 and 52233002)。
文摘UHMWPE fibers exhibit impressive modulus and strength,but they have not reached their theoretical limits.Researchers focus on molecular weight,orientation,and crystallinity of UHMWPE,yet their contributions to mechanical properties are unclear.Molecular dynamics simulations are valuable but often limited by computational constraints.Our aim is to simulate higher molecular weights to better represent real UHMWPE fibers.We used Packmol and Polyply methodologies to construct PE systems,with Polyply reproducing more reasonable properties of UHMWPE fibers.Additionally,tensile simulations showed that orientation and crystallinity greatly impact Young's modulus more than molecular weight.Energy decomposition indicated that higher molecular weights lead to covalent bonds that can withstand more energy during stretching,thus increasing breaking strength.Combining simulations with machine learning,we found that orientation has the most significant impact on Young's modulus,contributing 60%,and molecular weight plays the most crucial role in determining the breaking strength,accounting for 65%.This study provides a theoretical basis and guidelines for enhancing UHMWPE's modulus and strength.
基金Project supported by the Natural Science Foundation of High Education of Jiangsu Province, China （Grant No 04KJA130135）.
文摘The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics axe studied. The exact inwriant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invaxiant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invaxiant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invaxiant. An example is also given to illustrate the application of the results.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFF0707601).
文摘The airflow mechanics in adult nasal airways,whether healthy or abnormal,are extensively studied and investigated,but the flow mechanics in child nasal airways remain underexplored.This study investigates the airflow mechanics in the child’s nasal upper airway with adenoid hypertrophy,with an adenoid nasopharyngeal ratio(AN of 0.9),under cyclic inhalation and exhalation.An inlet respiratory cycle with three different flow rates(3.2 L/min calm breathing,8.6 L/min normal breathing,and 19.3 L/min intensive breathing)was simulated by using the computational fluid dynamics approach.To better capture the interaction between airflow and the flexible airway tissue,fluid-structure interaction analysis was performed at the normal breathing rate.Comparing the airflow dynamics during inhalation and exhalation,the pressure drops,nasal resistance,and wall shear stress show significant differences in the nasopharyngeal region for all different flow rates.This observation suggests that the inertial effect associated with the transient flow is important during exhalation and inhalation.Furthermore,the considerable temporal variation in flow rate distribution across a specific cross-section of the nasal airway highlights the critical role of transient data in virtual surgery planning and data for clinical decisions.
基金supported by Opening funding of National Key Laboratory of Aerospace Liquid Propulsion(HTKJ2024KL011004)Aeronautical Science Fund of China(ASFC-20240042070001)+2 种基金Opening funding of State Key Laboratory of Metal Forming Technology and Heavy Equipment(B2408100.W05)National Key R&D Program of China(2022YFB4601804)National Natural Science Foundation of China(52250287,52275375).
文摘Incorporating ceramic particles into metal matrices is a proven strategy for boosting mechanical properties and wear resistance.The reinforcement potential of tungsten carbide(WC)particles in 316L stainless steel is revealed,utilizing selective laser melting(SLM)to fabricate composites with 5 and 10 vol.%WC.The WC incorporation markedly alters the composite’s microstructure and mechanical attributes.Notably,5 vol.%WC-316L composite exhibits a refined submicron cellular structure,averaging 0.67μm in grain size.Elemental diffusion at WC-316L interface formed a 0.8μm gradient transition layer enriched with M_(2)C carbides(Fe,Cr,W),ensuring robust metallurgical bonding.Compared with unreinforced 316L,5%WC composite exhibits a 70%increase in tensile strength,reaching 1012.6 MPa,and a 25.3%rise in hardness,while maintaining acceptable ductility.10%WC composite achieves a 70.8%hardness enhancement,albeit with reduced elongation.Friction coefficient is reduced by up to 17.3%,and the wear mechanism shifts from adhesive to abrasive,significantly improving wear resistance.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
文摘In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.
文摘The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical foundations of Relativity Theory and its essential role in the clarification of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Particle Physics.
文摘We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 -?E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.
文摘We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.
文摘Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.
文摘This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations.
文摘In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.
文摘Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.
文摘This paper explains the basic steps form the classical turbulence mechanics (CTM) to the postclassical turbulence mechanics (PCTM). When the CTM stems from the characterization of the motion states in the infinitesimal surroundings of the flowfield points by the flow velocity at these points then the PCTM complements this characterization by the curvature of the velocity fluctuation streamlines passing these points. The complementation is formalized by the inclusion of the curvature of the velocity fluctuation streamlines to the arguments of the probability distribution of the motion states in the infinitesimal surroundings of the flow field points. The most radical physical outcome of the realized formalism is the characterization of the turbulence viscosity properties by two types of turbulence viscosity against only one shear viscosity within the CTM.
文摘This paper surveys the formalism and applications of the postclassical turbulence mechanics (PCTM) grounded on the characterization of turbulent flow field in infinitesimal surroundings of the flow field points besides the flow velocity at these points also by the curvature of the velocity fluctuation streamlines passing these points. The PCTM applies this step to found the turbulence split into the orientated and the non-orientated constituents. The split specifies the competence of the classical turbulence mechanics (CTM) to the description of the non-orientated turbulence constituent and delegates the description of the orientated turbulence constituent (in the spirit of the theory of micropolar fluids) to the equation of moment-of-momentum. The concurrent presence of the orientated (relatively large scale) and the non-orientated (relatively small scale) turbulence constituents enables to compile the CTM and the conception of L. F. Richardson and A. N. Kolmogorov about the cascading turbulence (RK conception) within a conjoint formalism. The compilation solves the classical conflict between the CTM and the RK conception, though evinces a conflict of another type characterized as paradigmatic.
