Search Results (22)

A simple analytic procedure for the linear static analysis of short thin-walled beams with monosymmetric open cross-sections subjected to eccentric axial loading is presented. Under eccentric compressive loading, the beam is subjected to compression/extension, to torsion with influence of shear with respect to the principal pole and to bending with influence of shear in two principal planes. The approximate closed-form solutions for displacements consist of the general Vlasov’s solutions and additional displacements due to shear according to the theory of torsion with the influence of shear, as well as the theory of bending with the influence of shear. The internal forces and displacements for beams clamped at one end and simply supported on the other end, where eccentric loading is acting, are calculated using the method of initial parameters. The shear coefficients for the monosymmetric cross-sections introduced in these equations are provided. Solutions for normal stress and total displacements according to Vlasov’s general thin-walled beam theory, and those obtained with the proposed method taking shear influence into account, are compared with shell finite element solutions analyzing isotropic and orthotropic I-section beams. According to the results for normal stress relative differences, and Euclidean norm for displacements, it has been demonstrated that shear effects must be accounted for in the analysis of such structural problems. Full article

The interaction between thermal fields and mechanical loads in thin-walled cylindrical shells introduces complex dynamic behaviors relevant to aerospace and mechanical engineering applications. This study investigates the axial stress wave propagation in a circular cylindrical shell subjected to combined thermal gradients and time-dependent harmonic compression. A semi-analytical model based on Donnell–Mushtari–Vlasov (DMV) shells theory is developed to derive the governing equations, incorporating elastic, inertial, and thermal expansion effects. Modal solutions are obtained to evaluate displacement and stress distributions across varying thermal and mechanical excitation conditions. Empirical Mode Decomposition (EMD) and Instantaneous Frequency (IF) analysis are employed to extract time–frequency characteristics of the dynamic response. Complementary Finite Element Analysis (FEA) is conducted to assess modal deformations, stress wave amplification, and the influence of thermal softening on resonance frequencies. Results reveal that increasing thermal gradients leads to significant reductions in natural frequencies and amplifies stress responses at critical excitation frequencies. The combination of analytical and numerical approaches captures the coupled thermomechanical effects on shell dynamics, providing an understanding of resonance amplification, modal energy distribution, and thermal-induced stiffness variation under axial harmonic excitation across thin-walled cylindrical structures. Full article

In this paper, we focus on mean-field stochastic differential equations driven by G-Brownian motion (G-MFSDEs for short) with a drift coefficient satisfying the local one-sided Lipschitz condition with respect to the state variable and the global Lipschitz condition with respect to the law. We are concerned with the well-posedness and the numerical approximation of the G-MFSDE. Probability uncertainty leads the resulting expectation usually to be the G-expectation, which means that we cannot apply the numerical approximation for McKean–Vlasov equations to G-MFSDEs directly. To numerically approximate the G-MFSDE, with the help of G-expectation theory, we use the sample average value to represent the law and establish the interacting particle system whose mean square limit is the G-MFSDE. After this, we introduce the modified stochastic theta method to approximate the interacting particle system and study its strong convergence and asymptotic mean square stability. Finally, we present an example to verify our theoretical results. Full article

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like structures in probability spaces, resolves degeneracies inherent in kinetic operators. Centered around the Boltzmann and Fokker–Planck equations, we derive sharp exponential convergence estimates under minimal regularity assumptions, improving on prior methods by incorporating Wasserstein gradient flow techniques. Our framework is further applied to the study of hydrodynamic limits, collisional relaxation in magnetized plasmas, the Vlasov–Poisson system, and modern data-driven algorithms, highlighting the central role of entropy as both a physical and variational tool across disciplines. By bridging entropy dissipation, optimal transport, and geometric analysis, our work offers a new perspective on stability, convergence, and structure in high-dimensional kinetic models and applications. Full article

This study explores the applications of extended Gauss–Hertz variational principles to determine the evolution of complex systems under the influence of impulse actions, coherent accelerations, and their application to electrophysical systems with fractal elements. Impulsive effects on systems initiate coherent accelerations (including higher-order accelerations, such as modes with intensification), leading to variations in connections, structure, symmetry, and inertia; the emergence of coherence; and the evolution of fractal elements in electrophysical circuits. The combination of results from the non-local Vlasov theory and modifications to the Gauss–Hertz principle allows for the formulation of a variational principle for the evolution of fractal systems. A key feature of this variational principle is the ability to simultaneously derive equations for both the system’s dynamics and the self-harmonizing evolution of its internal symmetry and structure (e.g., fractal parameters). Full article

This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton’s principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads. Full article

In this article, we address the reliance on probability density functions to obtain macroscopic properties in systems with multiple degrees of freedom as plasmas, and the limitations of expensive techniques for solving Equations such as Vlasov’s. We introduce the Ehrenfest procedure as an alternative tool that promises to address these challenges more efficiently. Based on the conjugate variable theorem and the well-known fluctuation-dissipation theorem, this procedure offers a less expensive way of deriving time evolution Equations for macroscopic properties in systems far from equilibrium. We investigate the application of the Ehrenfest procedure for the study of adiabatic invariants in magnetized plasmas. We consider charged particles trapped in a dipole magnetic field and apply the procedure to the study of adiabatic invariants in magnetized plasmas and derive Equations for the magnetic moment, longitudinal invariant, and magnetic flux. We validate our theoretical predictions using a test particle simulation, showing good agreement between theory and numerical results for these observables. Although we observed small differences due to time scales and simulation limitations, our research supports the utility of the Ehrenfest procedure for understanding and modeling the behavior of particles in magnetized plasmas. We conclude that this procedure provides a powerful tool for the study of dynamical systems and statistical mechanics out of equilibrium, and opens perspectives for applications in other systems with probabilistic continuity. Full article

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios. Full article

We investigate the kinetic model of the relativistic Vlasov–Maxwell–Chern–Simons system, which originates from gauge theory. This system can be seen as an electromagnetic fields (i.e., Maxwell–Chern–Simons fields) perturbation for the classical Vlasov equation. By virtue of a nondecreasing function and an iteration method, the uniqueness and existence of the global solutions for the 1.5D case are obtained. Full article

During the operational phase of a bridge, the crossbeam, acting as a supporting member, plays an important role in keeping the cross-sectional shape constant in addition to resisting against various lateral and longitudinal loads and distributing the dead and the live loads to the adjacent main girders. The complex functional requirements lead to a complex internal force composition of the crossbeam. When subjected to torque, the two main beams of the twin I-girder bridge will have deformation in opposite longitudinal directions (known as warping deformation) to counteract the torque. The existing research has not considered the impact of main beam warping deformation on the internal force of the crossbeam. Based on the existing research, this article further considers the impact of main beam warping deformation on the internal force of the crossbeam, making the calculation of the internal force of the crossbeam more accurate. The results show that the torsional characteristics of the continuous twin I-girder bridge can be calculated using Vlasov’s theory of thin-walled structures combined with the displacement method. As for the effect of the crossbeam on the torsional stiffness of the structure, it can be managed by making the crossbeam stiffness continuous; however, in general, the equivalent stiffness is small compared to the stiffness of the main beam and it can be ignored. The crossbeam can be simplified to a bar with two solid ends for the internal force calculation whose formula is proposed in this paper, based on the existing frame model, and it can further consider the influence of warping deformation of the main beam on the internal force of the beam, and the calculation accuracy is high. Full article

This paper presents a beam model for a geometrically nonlinear stability analysis of the composite beam-type structures. Each wall of the cross-section can be modeled with a different material. The nonlinear incremental procedure is based on an updated Lagrangian formulation where in each increment, the equilibrium equations are derived from the virtual work principle. The beam model accounts for the restrained warping and large rotation effects by including the nonlinear displacement field of the composite cross-section. First-order shear deformation theories for torsion and bending are included in the model through Timoshenko’s bending theory and a modified Vlasov’s torsion theory. The shear deformation coupling effects are included in the model using the six shear correction factors. The accuracy and reliability of the proposed numerical model are verified through a comparison of the shear-rigid and shear-deformable beam models in buckling problems. The obtained results indicated the importance of including the shear deformation effects at shorter beams and columns in which the difference that occurs is more than 10 percent. Full article

The present paper deals with the exact calculation of the Principal Elastic Reference System of R/C Cores, which have thin-walled open section. A new modified technique based on Vlasov torsion theory is developed that examines the warping phenomenon of cores. The exact position of the elastic center (or shear center) of a core and the orientation of the principal axes of elasticity, as well as the exact calculation of warping constant, are special parameters since, on the one hand it strongly affects the in plan stiffness distribution of the building members, and on the other hand it affects the values of the building eigen-frequencies and mode-shapes. These parameters are particularly critical in seismic design of asymmetric multistorey buildings. Based on Vlasov torsion theory of cores with thin-walled open sections, a repetitive mathematical procedure about the calculation of the location of the elastic center of core and the principal start point of the section is proposed. This new modified technique can be applied to cores of any shape. Afterwards, the exact diagram of sectorial coordinates of the section, as well as the warping constant, are calculated. All the above-mentioned parameters are very useful in the simulation of the cores in numerical models that are going to use in linear and nonlinear seismic analysis of the structures. Knowing all mentioned parameters, the numerical accuracy of the finite element method on cores can be checked. Finally, a numerical example, where the proposed new modified technique is applied on a fully asymmetric core, is presented. Full article

A beam model for thermal buckling analysis of a bimetallic box beam is presented. The Euler–Bernoulli–Vlasov beam theory is employed considering large rotations but small strains. The nonlinear stability analysis is performed using an updated Lagrangian formulation. In order to account for the thermal effects of temperature-dependent (TD) and temperature-independent (TID) materials, a uniform temperature rise through beam wall thickness is considered. The numerical results for thin-walled box beams are presented to investigate the effects of different boundary conditions, beam lengths and material thickness ratios on the critical buckling temperature and post-buckling responses. The effectiveness and accuracy of the proposed model are verified by means of comparison with a shell model. It is revealed that all of the abovementioned effects are invaluable for buckling analysis of thin-walled beams under thermal load. Moreover, it is shown that the TD solutions give lower values than the TID one, emphasizing the importance of TD materials in beams. Full article

An analytical methodology is developed for thin-walled composite beams with arbitrary geometries and material distributions. The approach uses a mixed variational theorem which sets the shell displacements, and the shear stress resultants and hoop moments as the unknowns to obtain the stiffness constants at the level of Timoshenko–Vlasov beam. All the field equations and the continuity conditions that should be satisfied over the shell wall are derived in closed form as the part of the analysis. Numerical simulations are conducted to show the validity of the proposed analysis. The comparison of the predicted stresses and the stiffness constants indicates close correlation with those of the detailed finite element (FE)-based analysis and up-to-date beam approaches. Symbolically generated stiffness constants and the sectional warping deformation modes of coupled composite beams are presented explicitly to illustrate the strength of the proposed theory. Full article

This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems. Full article