Acta Mechanica最新文献

This work develops a rigorous analytical framework to examine the scattering behavior and dynamic stress response of semi-elliptical notches in piezoelectric half-planes subjected to anti-plane shear (SH) waves. The framework unifies the treatment of cracks, circular holes, and notches within a consistent wave–defect interaction model, while explicitly incorporating piezoelectric coupling and nanoscale surface/interface effects. The analysis employs the complex function method in combination with the Helmholtz equation and wavefield superposition theory, resulting in an infinite system of equations that rigorously enforces continuity and boundary conditions. A systematic truncation scheme is then applied to ensure stable and convergent solutions. The results reveal that surface/interface effects play a crucial role in suppressing the dynamic stress concentration factor (DSCF), particularly under vertical SH-wave excitation, while sharper resonance peaks emerge at low modulus ratios and higher piezoelectric constants, such as PZT-5H and BaTiO₃. In the absence of piezoelectric coupling, the formulation seamlessly reduces to classical elasticity, ensuring strong theoretical consistency. Validation is achieved through recovery of benchmark solutions (semicircular notch and edge crack), graphical comparisons with prior results, and the rapid convergence of the truncated system, confirming the model’s accuracy and robustness. The findings hold significant implications for structural health monitoring, non-destructive evaluation, and the design of advanced piezoelectric composites, where accurate prediction of stress amplification and defect evolution is essential. Although the present study focuses on semi-elliptical notches in half-plane geometries under SH-wave loading, the approach can be readily extended to more general defect shapes and mixed-mode disturbances. The novelty of this work lies in capturing piezoelectric surface/interface effects within an exact analytical framework, thereby enhancing predictive capability for defect-induced stress concentrations and providing a reliable basis for the design and durability assessment of high-performance piezoelectric materials.

In this study, the thermal post-buckling behavior of a truncated composite conical shell with a lattice core and two composite layers is investigated. The shell is subjected to a uniform and linear temperature rise in thickness direction with simply supported boundary conditions at both ends. The shell is assumed to have an initial geometric imperfection and a lattice core composed of three stiffeners types: longitudinal (stringer), radial (ring), and helical with constant helical angles. The governing equations are derived based on the classical shell theory, incorporating nonlinear stress–strain relations under thermal loading. The compatibility equations are solved using the Galerkin method and the method of undetermined coefficients to predict the thermal buckling loads and post-buckling response. Numerical results validate the proposed model by comparison with previous studies and show that the reinforcement pattern significantly affects the thermal buckling performance. Among the configurations, the helical stiffeners yield the highest thermal resistance.

The reflection behavior of a multiple physical fields coupled waves for four kinds of possible surface conditions of piezoelectric solid with void is studied in this paper. First, the dispersion equation for multiple physical fields coupled waves propagation in the piezoelectric porous media is derived through inserting the multiple physical fields coupled constitutive equations into the general governing equation. Different from the classic piezoelectric medium, there are four coupled elastic waves in the piezoelectric material with void. Due to the consideration of porous effects of the piezoelectric material, the surface conditions can be proposed in different forms. These surface conditions, which include the free surface and elastic surface, electrical short circuit and electrical open circuit, as well as zero volume fraction disturbance surface and zero equivalent force surface, are then used to determine the reflection coefficients of reflection waves. The numerical results are provided for incident QP wave and incident QSV wave, respectively, and are validated by the energy conservation law. Based on these numerical results, the influences of the four kinds of surface conditions on the reflection behavior of multiple physical fields coupled waves are discussed.

The buckling behavior of sandwich annular plates comprising a honeycomb core and graphene platelet-reinforced top and bottom layers is studied in this paper using the high-order deformation theory. The structure is in hygrothermal environment with assuming the foundation with spring and shear layer assuming frictional effects. This modeling framework also captures a wider range of deformation behavior that is often missed by lower-order models. Considering this complicated problem, the numerical highly accurate technique of diffrential quadrature method (DQM) is used which efficiently manages the complicated boundary conditions. Finally, extensive numerical simulations are performed in order to analyze the buckling response in depth, focusing on major design parameters like the annular plates inner radius, temperature, moisture, foundation, boundary conditions, friction coefficient and GPL’s volume fraction in the nanocomposite layers. The results highlight the sensitivity of buckling behavior to these changes in design and provide greater insight into the mechanics that controls composite sandwich structures under compressive loads. A larger volume fraction of GPL will increase the buckling load. Increasing temperature from 30 to 45 °C decreases the buckling load by about 14%. and moisture content up to 40% lowers the buckling load by approximately 23%. In addition, changing boundary conditions from C–F to C–C raises the buckling load by up to 70%.

Piezoelectric beams are widely used as energy harvesting from mechanical vibration. For nanoscale beams, the flexoelectric effect is remarkable. This paper investigates the vibration of a clamped–clamped nanobeam with flexoelectric and piezoelectric effects carrying a concentrated nanoparticle. A governing equation and associated boundary conditions are derived from Hamilton’s principle. An exact frequency equation is obtained. Further, through the integral equation method, an explicit expression for the fundamental resonance frequency can be given with satisfactory accuracy. A comparison between the exact and approximate resonance frequency is made. Numerical results show the influence of flexoelectricity, piezoelectricity, and attached mass on the resonance frequencies of a vibrating beam-mass system, in particular for nanoscale beams.

A thermo-magneto-vibrational model is developed for sandwich nanoplates composed of composite metallic–ceramic face sheets and a hexachiral auxetic core. The formulation integrates higher-order shear deformation theory with nonlocal strain gradient theory to incorporate shear–flexural coupling and nanoscale size effects. Present research simultaneously addresses the influence of hexachiral geometry, elastic foundation parameters, magnetic field, and face-sheet composition within a unified framework. The governing equations are derived using Hamilton’s principle and solved through the Navier approach under simply supported boundary conditions. A systematic parametric study is carried out to assess the role of geometric ratios, material gradation, and scale-dependent parameters on vibration and thermal stability. Combining composite layers and core hexachiral auxetic lattice structure with multiphysics fields and nanoscale elasticity, offering a generalized formulation that captures interactions not previously considered together. The outcomes provide a basis for the design of thermally and magnetically durable sandwich nanoplates in aerospace, automotive, acoustic, and protective structural applications.

Unconventional elastoplasticity models, whether in small strain or finite strain regimes, have been developed to accurately depict material responses under diverse loading conditions. Due to the unrealistic and unphysical predictions of certain existing models in such scenarios, the proposing and refining of time integration schemes becomes imperative. This paper introduces a novel numerical implementation for the subloading surface model, an unconventional approach, within the framework of finite strain elastoplasticity. The proposed method is based on intermediate configurations in hyperelastoplasticity, utilizing dual multiplicative decompositions. Additionally, detailed calculations of partial derivatives, which are essential for the time integration scheme, are provided. Compared to recently published papers, the proposed time integration scheme is simpler in terms of the number of equations, unknown variables, and partial derivatives. The implementation is demonstrated through the solution of simple shear and tension/compression deformations, incorporating kinematic and combined hardenings for various materials including metals and polymers. Results are compared with available data from literature and experimental findings. The presented examples demonstrate a good agreement between the results under different conditions.

This paper presents a novel model for analyzing the behavior of a generalized photo-microelongated thermoelastic semiconductor system that incorporates hydrodynamic and poroelastic effects. Motivated by the need to understand semiconductor dynamics under coupled mechanical, thermal, and photonic stimuli for advanced technological applications, the study develops a one-dimensional (1D) framework using Laplace transformation to derive analytical solutions. Numerical computations and graphical representations illustrate the evolution of critical physical quantities such as carrier density, temperature distribution, displacement, pore water pressure, and stress functions, emphasizing the influence of time progression, relaxation parameters, and microelongation effects. The results highlight the unique contributions of hydrodynamic and poroelastic interactions, providing insights into semiconductor behavior at microscales. This comprehensive analysis advances the understanding of semiconductor materials, offering potential applications in photonic devices, energy systems, and thermal management technologies while providing a theoretical framework to predict material behavior under diverse external stimuli, minimizing the need for costly experiments.

Piezoelectric materials have been extensively used as energy collector due to their excellent character of environmental vibration energy conversion. However, the existing piezoelectric energy collector model is not suitable for complex multi-layered beam structures. The objective of this paper is to explore the dynamic response and piezoelectric patch energy harvesting of four-layered beams with single unimorph piezoelectric patch subjected to multiple moving loads, and the governing equations are derived by using Hamilton’s principle. The effects of structural lamina parameters and piezoelectric patch parameters of four-layered beams with single piezoelectric patch on dynamic response and optimal energy harvesting are investigated. A detailed parametric analysis of the structural lamina and piezoelectric patch of the four-layered beam model is conducted, and the optimality of energy harvesting parameters of the layered beam is discussed. It is found that the dynamic central deflection of layered beam and output voltage are quite related to the geometrical and physical parameters of each functional layer including the fiber orientation angles. The dynamic central deflection of layered beam is not sensitive to the piezoelectric patch, and so it is suitable of introducing the piezoelectric patch to produce the electric power. The optimum energy harvesting efficiency of the layered beam is also discussed in detail.

This paper intends to explore the effects of cracks characteristics on free vibration behavior of functionally graded plates and shells by means of Lagrangian formulation in conjunction with the variational principle on the basis of three-dimensional theory of elasticity. The discretization of the equation of motion is achieved by using a four-noded 3D tetrahedral finite element taking into account the normal component of the displacement field in the thickness direction. The material properties of the plates and shells are assumed to vary continuously and smoothly in the thickness direction according to a general four-parameter power-law distributions in terms of volume fractions of the constituents. The consistency and reliability of the present formulation is demonstrated through several numerical tests, by comparing the obtained natural frequencies with the existing results from the literature. Three numerical examples, including the vibrational response of functionally graded rectangular and annular plates, as well as, cylindrical shells under different crack positions, orientations and lengths are studied and presented. Parametric studies on crack characteristics, geometric and material parameters are explored in deep. It was demonstrated that the crack orientation, length and positions, additionally to material characteristics of FGM structures have a significant impact on vibrational behavior of cracked FGM plates and shells, which must be considered in the structural design and performance of functionally graded plates and shells.