Acta Mechanica最新文献

Contact problems involving deformable bodies are widespread in both industrial and everyday situations. They have a crucial impact on structural and mechanical systems, which has led to significant efforts in modeling and numerical simulations. These efforts aim to improve understanding and optimization in various engineering applications. This study examines the contact problem involving a functionally graded (FG) orthotropic layer resting on a rigid foundation, without considering frictional influences. A point load is applied to the layer through a rigid punch on its top surface. Additionally, the gravitational effects of the FG orthotropic layer are considered in the analyses. Material parameters and density of the FG orthotropic layer are presumed to exhibit exponential variations along the vertical axis. The resolution of the problem involves deriving stress and displacement expressions through the application of elasticity theory and integral transformation techniques. By imposing the pertinent boundary conditions onto these expressions, a singular integral equation is formulated, wherein the contact stress under the punch remains unknown. Employing the Gauss–Chebyshev integration method, this integral equation is subsequently numerically solved, particularly for a flat punch profile. The outcomes of this investigation encompass the determination of contact stresses under the punch, the critical separation load, and the critical separation point—marking the initial separation between the FG orthotropic layer and the rigid foundation. Additionally, the analysis yields dimensionless representations of normal stresses along the symmetry axis within the FG orthotropic layer, as well as shear stresses along a designated section proximate to the symmetry axis. Furthermore, it provides insights into the normal stresses along the x axis at the bottom surface of the FG orthotropic layer, contingent upon various parameters and distinct orthotropic material compositions.

We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneuvers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulum model to represent the sloshing dynamics and suggest a novel parameter identification scheme suitable for arbitrary container shapes and any number of sloshing modes. By computing natural modes and fluid reaction forces and torques for imposed harmonic container motions via a finite element model, we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We also provide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameter estimates. The proposed feedforward control method uses a virtual tray pendulum on which we place the container (in the form of its equivalent pendulum model). Designing the virtual tray such that the fluid’s dominant sloshing mode cannot be excited by horizontally moving the tray pendulum pivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property of the resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in higher modes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed method is demonstrated through extensive simulations and experimental results using a Martini cocktail glass, whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept.

In this paper, a variable-order fractional model is proposed to characterize the complex nonlinear temperature-dependent mechanical behaviors of amorphous glassy polymers, which play a crucial role in the wide applications. At a specific temperature, the variable order is defined to follow the microbial growth curve, which is consisted of a logarithmic growth stage and decay stage. The two stages are naturally connected on the conception that the growth rate is approaching to 0. The variable order is further physically interpreted based on microscopic mechanism. Furthermore, the relationships between elastic modulus, relaxation time and temperature are incorporated into the established model to demonstrate the temperature dependence. Various experimental results are observed to be well characterized by the proposed model, which validates the rationality and reliability. The predictive ability of the proposed model is also explored to verify its effectiveness.

This paper presents a multi-dimensional variable-kinematics finite element model for nonlinear static analyses of structures with complex geometries. The approach incorporates higher-order beam models and classical solid finite elements in a unified framework, enabling refined modeling of complex geometries. The finite element procedure proposed follows the Carrera Unified Formulation (CUF) and uses a pure displacement-based methodology. The governing equations are derived within the classical continuum mechanics framework, and weak-form equilibrium equations are established using the Principle of Virtual Displacements (PVD). Within the CUF framework, higher-order beam and hexahedral solid models are defined in a unified manner, and the governing equations are written in terms of invariants of mathematical models used and the theory of structures approximation. A coupling technique is used between the beam and solid elements at the nodal level using superposition. The capabilities of fully nonlinear variable-kinematics models are investigated for the static analysis of various rectangular and curved structures. The numerical results are compared with solutions obtained using commercial software. Finally, the proposed methodology is applied to analyze more complex geometries in engineering applications. The results show the capabilities of variable-kinematics models in terms of both accuracy and computational efficiency for the computation of highly nonlinear deformed states and localized phenomena, such as stress concentrations and buckling.

The current manuscript focuses on the photo-thermoelastic interactions in a rotating plate with a porous structure and temperature-dependent properties. The analysis is performed using the dual phase lag theory and by considering a two-dimensional isotropic homogeneous plate. The upper surface of the plate experiences the application of a mechanical source, while the lower surface of the plate is insulated thermally. The application of the normal mode technique enables the derivation of analytical expressions for various field variables such as displacement, stress, change in volume fraction field, carrier density and temperature within the physical domain. Numerical computations are performed for a plate composed of silicon material and the results are represented graphically with the support of MATLAB software to demonstrate the consistency of the obtained results. To outline the influences of rotation, photothermal transport process, temperature-dependent properties and void parameters on the physical fields, certain collations are presented. Some specific cases of interest have also been deducted.

Previous studies on the dynamic problems of magneto-electro-elastic (MEE) beams mainly focused on the buckling and free vibration, no literature paid attention to the low-velocity impact response problem. More importantly, no one conducted the investigation on the nonlinear low-velocity impact of MEE beams with considering the effect of initial geometric imperfection. To fill this gap, this article aims to study the low-velocity impact problem of MEE beams with initial geometric imperfection. Firstly, the nonlinear Hertz contact law is used to describe the displacement and contact force of the MEE beam, and the initial conditions for the beam and impactor are given. Subsequently, considering the multiple coupling effect, the dynamic model is established through Hamilton’s principle. Taking the simply-supported boundary condition into account, the Galerkin principle is utilized to reduce the dimensionality, resulting in a nonlinear equation regarding contact time, lateral central displacement and contact force. Meanwhile, two comparative analyses are conducted to confirm the rationality of the present work. Finally, the Runge–Kutta method is employed to solve the low-velocity impact response, in which the effects of electric potential, magnetic potential, initial geometric imperfection, temperature rise, prestress, damping coefficient, the radius and velocity of the impactor as well as the geometric dimension of the beam are discussed.

This paper studies multi-physical fields in a piezoelectric semiconductor (PS) fiber with consideration of heat conduction, pyroelectric, and thermoelectric effects. Based on the three-dimensional (3D) framework of piezoelectricity, drift–diffusion theory, Seebeck effect, and Peltier effect, we develop a highly nonlinear one-dimensional (1D) model that incorporates axial deformation, axial variations of the electric field, the redistribution of carriers, and temperature deviation. Combining the 1D nonlinear governing equations and the corresponding boundary conditions, the influence of the thermoelectric coefficients and axial forces on electrostatic potential, carrier redistribution, and temperature variation are solved numerically. Due to the nonlinearity of the model, these solutions are observed without symmetry or asymmetry. Our research shows that the temperature will increase near the action point of the axial force. Therefore, the temperature deviation in the fiber can be controlled by applying axial force at different points. Finally, we examine how the axial forces applied in the fiber affect the current–voltage relation. The presented study provides a potential application for mechanical switches, sensors, or thermal control for PSs.

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

This paper deals with the local bifurcation analysis of a nanotube with a nanostring passing through it. Eringen’s two-phase local/nonlocal model and Eringen’s differential model are employed as constitutive equations. The governing equations are derived as two nonlinear first-order systems of ordinary differential equations. Nonlinear analysis is performed by using the Lyapunov–Schmidt method. The influence of the small length scale parameter and the phase parameter on critical buckling load, type of bifurcation and post-buckling shape of the nanotube is examined for both types of constitutive equations. Depending on the values of the small length scale parameter and the phase parameter, the critical buckling load corresponding to Eringen’s two-phase local/nonlocal model can be greater or less than that corresponding to Eringen’s differential model. It is shown that for both models supercritical pitchfork bifurcation occurs. The post-buckling shapes of nanotube, obtained by numerical integration, exhibit a qualitative difference between the two models.