Acta Mechanica最新文献

In this paper a new Lode dependence will be formulated starting from the well known hexagonal section of the Mohr-Coulomb criterion. On the basis of a previous formulation, the new deviatoric function will provide different shapes depending on the rounding portion of curves introduced to remove the singularity of first and second derivatives in the corners of Mohr-Coulomb criterion. The resulting (C^2) continuous function has very simple expressions of first and second derivatives and then is very easy to implement. What was a simple tool to round the corners of the Mohr-Coulomb deviatoric section is then transformed to a flexible Lode dependence. Comparison with experimental data highlights the effectiveness of the formulation.

A thirteen-moment model for dilute granular gases is developed within the framework of Rational Extended Thermodynamics. A quasilinear system of partial differential equations, consisting of 13 field equations for the 13 field variables, is derived. The constitutive relations are determined by applying fundamental physical principles, in particular the entropy principle. To ensure the consistency of this macroscopic model, both the hyperbolicity region of the differential system and the region of entropy production are analyzed. The model is also solved in the homogeneous and stationary one-dimensional cases, and the validity of these solutions is examined. It is shown that the entropy principle imposes constraints on the admissibility of certain types of solutions.

To realize easy production and optimize the overall performances, nanocomposite structures made of graphene platelets (GPLS)-reinforced materials are usually functionally graded (FG). The FG distribution patterns of the fillers are commonly categorized into FG-A, FG-X and FG-O types. To promote engineering applications, a series of investigations on structural responses of FG nanocomposite structures have been conducted. Nevertheless, of them, the studies within the generalized thermoelastic theories remain limited, especially for microstructures. To bridge this gap, the magneto-thermoelastic vibration of a FG multilayer microbeam composed of an aluminum matrix reinforced by GPLs is considered in this study. The problem is formulated by incorporating the Euler–Bernoulli beam model, the Moore–Gibson–Thompson (MGT) generalized thermoelastic theory, the surface elasticity theory, and the nonlocal strain gradient theory along with the Maxwell’s equations. To assess the effective elastic modulus as well as other material properties, the Halpin–Tsai micromechanics model, and the mixture law are employed. Then, the governing equations are solved by using Navier’s method and the frequency of the microbeam is obtained. In calculation, parametric studies are carried out to examine the influences the distribution patterns of GPLs, the material length-scale parameter, the surface effect, the nonlocal elasticity parameter, the GPLs mass fractions, and the magnetic field parameter on the vibrational response. The FG-X material distribution achieves the highest vibration frequency due to optimal reinforcement. The inclusion of material length-scale parameter and surface effect greatly improves microbeam stiffness and vibration performance. An external magnetic field further increases the frequency by enhancing structural rigidity.

Numerical simulation is a widely adopted tool for understanding saltwater intrusion in coastal aquifers, simulating density-driven solute transport processes in porous media. However, most of these simulations exclusively model only groundwater flows and are mesh-based solvers, which may pose challenges for complex geometries. Here in this paper, we present an incompressible smoothed particle hydrodynamics (ISPH)-based combined surface–groundwater flow model for predicting density-driven flows in aquifers. The model consists of a modified momentum equation solution for less restrictive Courant–Friedrichs–Lewy (CFL) conditions when dealing with low-permeability sediments and taking into account viscosity variation. The developed ISPH code is validated using two benchmark problems to ensure acceptable performance with regard to the model’s ability to simulate physics of flow through porous media and density-driven flows. Simulations are performed for an unconfined and confined aquifer spanning a time period of 7320 s and 5220 s, respectively, the obtained numerical results were compared with experimental solute transport observations, and they were found to be in close agreement with each other. The calibrated hydraulic conductivity and dispersivity values are significantly lower than values obtained from solvers that simulate only groundwater flows, and our numerically calibrated values are much closer to real-world values for porous media.

To mitigate the risks associated with laser radiation and heat loading, it is critical to understand the biothermal response of skin tissue. With this information, the medical community can develop safe, evidence-based treatments for a variety of skin conditions. In this study, the Moore–Gibson–Thompson concept with memory-dependent higher derivatives is used to develop a theoretical basis for biothermal analysis. Clarifying the biothermal responses of skin tissues to heat loading and laser radiation is the aim of this work. Estimating the efficiency of biothermal transfer in biological tissues and predicting the thermal reactions that take place in human skin are made simpler by the developed model. A one-dimensional skin layer is used to achieve the suggested model. Laplace transforms are used to provide the analytical outcomes for tissue temperature. The proposed model incorporates both the impact of the kernel function and the thermal damage. Additionally, to evaluate the accuracy of the suggested model, the resulting analytical outcomes are contrasted with recognized theories. The results demonstrate that the modified Moore–Gibson–Thomson biothermal transfer model forecasts reduced temperatures than the traditional Pennes model when the memory-dependent upper derivatives and the thermal relaxation time constant are added.

A parametric analysis of the nanocomposite-reinforced sandwich beam with initial curvature is presented. The kinematic, constitutive and governing relations are extended based on the higher-order stretching included, generalized Hooke’s law and virtual work principle, respectively. The sandwich nanocomposite is assumed composed of the graphene origami-reinforced nanocomposite core between two piezoelectric/piezomagnetic layers actuated by initial electric/magnetic potentials. The effective form of the material characteristics is developed using the Halpin–Tsai micromechanical model and rule of mixture for stiffness, and density/Poisson’s ratio/heat expansion coefficient, respectively. The multi-filed hybrid formulation is presented in terms of multi-field components. The parametric solution is presented in order to seek the impact of material constituent and multi-field loading characteristics. The results of the present work can be used for controllable and tuneable design of nanocomposite-reinforced structures. The novelties of this work is investigating the impact of graphene origami characteristics and initial electric/magnetic potentials on the vibrational responses of the sandwich curved beam. Because of the temperature/foldability/content-dependent material properties of the graphene origami included sandwich structure, the vibrational responses reflect the un-predictable responses.

This work presents novel mixed-type finite elements for geometrically nonlinear analysis of curved structures in high precision. In nonlinear problems, it is possible to approach exact results using a numerical method when an energy-based functional is used. However, the generation of such a functional structure has mathematical difficulties. In this study, these difficulties are overcome and a functional that is perfectly close to exact results is presented. The functional structure of the finite elements is derived based on the fact that the operator which corresponds to the equilibrium equations, constitutive equations and boundary conditions is potential. A necessary and sufficient condition that the operator is potential is used in two different aims. Instead of using the virtual work expression, both the equilibrium equations consistent with generalized strains subject to the first-order approximation of strain tensor and the proper relations for the generalized strains consistent with the equilibrium equations written directly on the deformed configuration are obtained. It is thought that the structure presented in this study provides highly accurate numerical results that can be obtained with the finite element method in the geometric nonlinear analysis of the beams.

This paper investigates free vibration characteristics of rotating functionally graded (FG) sandwich blade, which is modeled as cantilevered pre-twisted shallow cylindrical shell with thickness variation mounted on a rotating rigid hub. The tapered blade consists of one isotropic core layer and two symmetric porous FG face sheet layers, which contain internal pores following different porosity distributions. The material properties of the FG layers are temperature-dependent and graded in the thickness direction in accordance with a modified sigmoid law. An isoparametric finite element (FE) formulation is established in the framework of the higher-order shear deformation theory (HSDT) for the present investigation, considering various configurations of the FG sandwich blade. Lagrange’s equation of motion is employed to derive the dynamic equilibrium equation that accounts for the nonlinear strains due to rotational and thermal loads. Comparisons with the benchmark results are provided to verify the present FE formulation. Parametric studies are performed to analyze the effects of volume fraction index, porosity coefficient, thickness variation ratio, pre-twist angle, radius-to-span length ratio, rotational speed, and temperature of the environment on the natural frequency of the blade considering different porosity distributions and sandwich configuration schemes. Also, some representative mode shapes are depicted for different values of thickness variation ratios of the FG blades. The study reveals that ceramic enrichment and chordwise thickness variation enhance frequencies, while increased porosity, spanwise variation, pre-twist angle, radius-to-span length ratio, and thermal gradients reduce stiffness and frequencies; additionally, rotational speed induces centrifugal stiffening, thereby increasing the fundamental frequencies.

The subject of this study is the dynamics of variable-mass systems in which the mass varies as a function of time or position. The research is particularly focused on determining the system velocity, which is usually obtained by solving the equations of motion which are very complex for variable-mass systems. The aim of this paper is to develop a new method that is simpler and more suitable for determining velocity. By applying the analytical theory of impact and assuming that the change of mass is due to a perfectly plastic impact of particles, the Meshchersky–Lagrange equation is derived, which includes the impulse of the reactive force. The impulse of the reactive force, resulting from the mass variation, is equal to the product of the mass of the particle that is attached to or detached from the system and its absolute velocity. The equation represents the first integral of the Lagrange equation for variable-mass systems in which the kinetic energy has a quadratic form in the velocity, and the coefficient depends either on time or on position. Under these constraints, the newly obtained formula has been applied to calculate velocity in the Tsiolkovsky rocket problem, in surface coating systems, and in mass collection facilities.