Acta Mechanica最新文献

We apply complex variable methods to develop analytical solutions of the inhomogeneity problem in which an inhomogeneity is embedded in an infinite matrix subjected to remote uniform thermal loads. We assume a nonlinear thermoelastic constitutive relationship and study the corresponding thermoelastic field as well as the effective thermal expansion under the assumption of non-uniform thermal expansion. Numerical results reveal the significant effect of temperature-dependent properties on the distribution of thermoelastic fields. In addition, the magnitude of the effective thermal expansion is shown to have a linear relationship with a newly introduced parameter K, which indicates that the temperature dependency of the matrix should not be neglected under non-uniform thermal expansion.

As an important class of functional materials, the multiferroic piezoelectric/piezomagnetic nanocomposites are widely used in sensors and actuators of advanced functional devices. The interface effects have become a key issue in designing and regulating the physical properties of such nanocomposites. This paper investigates the magneto-electro-elastic (MEE) responses for multiferroic fibrous nanocomposites with imperfectly bonded interface under far-field anti-plane shear and in-plane electric and magnetic loadings. On this basis, the analytical solutions of the effective MEE moduli of the multiferroic nanocomposites are obtained by using a generalized self-consistent method combined with the complex variable method. The present analytical solutions considering the nanointerface stresses and imperfect interface effect are verified by comparing with existing analytical solutions for simplified problem. Numerical analysis is conducted for different types of composite materials, and the effect of nanointerface stresses, imperfect interface parameters and volume fraction on the six components of MEE effective modulus is discussed in detail. The proposed theoretical estimation of effective moduli has certain theoretical value for the design and optimization of multiferroic nanocomposites.

This paper presents bending deformation, free vibration and buckling behaviors of three-dimensional (3D) layered piezoelectric semiconductor (PS) nanoplates with modified couple-stress effect. Analytical solutions of the extended displacements and stresses of layered PS nanoplates of bending deformation, natural frequency of free vibration and the critical buckling load under compression are derived by using the propagator matrix method. Numerical examples are provided to show the effects of the initial carrier concentration, material length scale parameter, stacking sequence of nanoplates, thickness of nanoplates, width-to-length ratio of nanoplates and loading type on the bending deformation, vibrational response, and stability of layered PS nanoplates. The results indicate that the initial carrier concentration has a significant impact on electron concentration perturbation. An increase in material length scale parameter results in enhancement of natural frequency and critical buckling load. The present results provide a new thought for the adjustment and controlling of 3D static and dynamic behaviors in the layered PS structures.

Recently, bio-inspired composite structures with helicoidal schemes and designs are used in many applications instead of the classical composite structures due to their high damage tolerance and high impact energy absorption properties. However, their static and dynamic stability under variable axial loads is not addressed. Thus, this study intends to analyze the uniaxial, biaxial buckling and vibration behaviors of bio-inspired helicoidal composite plate under variable in-plane edge load, for the first time. Based on the first order shear deformation theory (FOSDT), mathematical model of helicoidal orientation schemes of bio-inspired composite plate structure under variable in plane edge loads are presented. Six different profiles of the axial loads are included in the analysis. The governing equilibrium equations and the associated boundary conditions are deduced in detail. After that, the two-dimensional differential quadrature method (2D-DQM) is exploited to discretize the buckling problem in the space domain and convert the linear partial differential equations with variable coefficients to linear eigenvalue problem in terms of displacement field. Combining the separation of variables method and 2D-DQM to solve the linear vibration problem with variable in-plane axial load. Numerical analysis is presented to discuss effects of the fiber orientation schemes, type of axial load, boundary conditions, on the buckling loads, natural frequencies, and mode shapes of bio-inspired composite plates. The proposed methodology as well as obtained results are supportive in design and manufacturing of advanced bio-inspired composite structures which can be widely in medical, environmental as well as energy-saving technologies.

This study modeled and analyzed the thermomechanical buckling behavior of smart magneto-electro-elastic (MEE) sandwich nanoplates using nonlocal elasticity, strain gradient elasticity, and higher-order plate theory. The sandwich nanoplate consists of ceramic and metal functional graded foam structure in the core layer and is composed of magneto-strictive and electro-elastic materials in the surface layers. Due to the functionally graded feature in the core layer, pure metal/metal foam, pure ceramic/ceramic foam, and metal + ceramic foam structures are modeled. The foam structure can be distributed uniformly and symmetrically throughout the thickness of the core layer. The effects of nonlocal elasticity, strain gradient elasticity, foam distribution, and foam void ratio of the core layer on the thermomechanical buckling behavior of the smart sandwich nanoplate have been examined in a broad framework. Additionally, the effects of electro-elastic and magneto-strictive material characteristics of smart surface plates on thermomechanical buckling response were examined according to the applied external electric and magnetic potential intensities. It is observed that the foam structure and foam void fraction ratio in the core layer are effective on the thermomechanical buckling behavior of the smart sandwich nanoplate. Moreover, it is concluded that the applied external electric and magnetic potential can change the thermomechanical buckling behavior of the sandwich nanoplate.

This paper presents an analytical approach for the nonlinear buckling and postbuckling responses of functionally graded graphene platelets-reinforced composite (FG-GPLRC) complexly curved caps with porous core under uniformly distributed thermal and external pressure resting on the nonlinear elastic foundation using the first-order shear deformation theory (FSDT) with the geometrical nonlinear sense of von Kármán. Four cap types are considered including spherical caps, ellipsoid caps, sinusoid caps, and paraboloid caps in this paper, and the results of circular plates can be obtained by the radius of the shell’s curvature approaches infinity. The graphene platelet (GPL) nanofillers are distributed into the polymer matrix of two coatings according to the uniformly and functionally graded laws in the thickness direction. The Galerkin method is applied and the expressions of thermal critical buckling loads and thermal and mechanical postbuckling curves of the caps are determined. The effects of cap types, geometrical properties, imperfect deflection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of the caps and plates are discussed in numerical results.

In this paper, we consider the linear theory for a model of a thermopiezoelectric nonsimple body as presented in Passarella (Entropy 24:1229, 2022) in which the second displacement gradient and the second gradient of electric potential are included in the set of independent constitutive variables and in which an entropy production inequality model proposed by Green and Laws is considered. After recalling the constitutive equations of the theory, the focus is on isotropic materials, for which the constitutive coefficients were first derived and used to determine the constitutive and field equations. An exponential stability result will be established and a qualitative analysis of plane harmonic wave propagation in the isothermal case will be discussed. Exponential stability will be proved, through the Hurwitz criterion, for a one-dimensional system of a thermopiezoelectric material whose equations involve as unknown fields the displacement, the relative temperature and the electric potential. The qualitative properties of wave propagation for some specific piezoelectric materials (quartz, tourmaline, PZT and LGS), of which values of constitutive constants are known, will be shown.

Significant restrictions have been found in the selection of piezoelectric materials and the direction of wave propagation in earlier studies on surface acoustic wave sensors. The primary goal of the current work is to investigate how wave propagation direction influences the performance of SAW macro- and nano-sensors in an effort to remove such barriers in the technological revolution of SAW sensors. A proposed model is established to study Shear Horizontal (SH) and anti-plane SH wave propagation in piezoelectric materials with surface effects. The theoretical forms are constructed and used to present the wavenumber of surface waves in any direction of the piezoelectric medium, based on the Extended Stroh formalism. In addition, we take into account surface elasticity theory in order to obtain the phase velocity equation based on the wavenumber expression. The model incorporates surface elasticity, piezoelectricity, and permittivity to account for nanoscale surface phenomena. Two configurations are examined: an orthotropic piezoelectric material layer over an elastic framework and a piezoelectric material half-space with a nano substrate. Analytical expressions for frequency equations are derived for both symmetric and anti-symmetric waves. Numerical results highlight the critical thickness of the piezoelectric layer, where surface energy significantly influences dispersion properties. The effects of surface elasticity and density on wave velocity are analyzed, revealing a spring force-like influence on boundaries. The research investigates SH wave transmission in anisotropic, transversely isotropic piezoelectric nanostructures. The findings could aid in designing SAW devices and piezoelectric sensors, as well as producing more effective surface acoustic wave sensors, based on recent theoretical work summaries.

This investigation employs a three-dimensional coupled thermomechanical finite element analysis to ascertain the characteristics of the initiation of cracks in railway curves. The proposed numerical simulation of wheel–rail contact aims to examine the influence of different curvature radii and slip ratios on the temperature rise, fatigue parameters, and fatigue life of crack initiation. The load history is obtained via Universal Mechanism software and utilized in the FE model. This is the inaugural investigation wherein the cyclic plastic material response, as delineated by the hardening model proposed by Chaboche and Lemaitre, and the thermomechanical coupling have been considered in the context of a curved track. Abaqus software uses numerical modeling to determine the stress fields, temperature distributions, and contact pressure during the wheel–rail interaction. To ascertain the fatigue parameter (FP) and the direction of fatigue crack initiation in the rail, the Jiang and Sehitoglu damage model is employed. The critical plane concept is used to establish the initiated crack’s direction. As the FP grows in critical conditions, the crack creation orientation moves toward the depth of the rail rather than the surface. This phenomenon may cause dangerous rail failure and should be prevented by accurately controlling the wheel–rail contact conditions. Incorporating nonlinear thermal effects into the mechanical model resulted in a maximum increase in fatigue parameters and life of 32% and 80%, respectively.

In this paper, the development and application of a perturbation technique is carried out to analyze the behavior of unshearable and inextensible planar beams, with specific attention to the buckling phenomenon and to the application of prescribed shortening, under different boundary conditions. The mechanical model is driven from the literature and revisited in order to specifically address the case of large longitudinal force, which naturally arises in the considered applications. The problem is tackled by deriving an analytical solution, accounting for a proper scaling and expansion of the variables, depending on the considered case (namely, free or prescribed shortening). The mechanical response is then systematically compared to a numerical solution derived via a finite difference approach, showing an excellent agreement within the considered ranges.