Acta Mechanica最新文献

This work deals with damage mechanics of materials and is not concerned with fracture mechanics. The reduction in stiffness of the material and other material properties characterize this. This is also linked to the microstructure using fabric tensors. A new decomposition of fabric tensors is derived. The decomposition is implicit and is based on the decomposition of the damage tensor that was derived previously by the authors. The general fabric tensor G is decomposed into individual fabric tensors G^A and G^B for different individual damage processes. The superscripts A and B may, for example, represent cracks and voids, etc. or any other damage processes. Furthermore, another decomposition is formulated that is exponential in nature. In addition, the decomposition is generalized to three different damage processes, including a third unidentified defect. Finally, an unsymmetrical decomposition of fabric tensors is also derived.

This paper investigates the nonlinear free vibration of sandwich plates with carbon nanotube (CNT) reinforced composite core subjected to uniaxial compressive loads in thermal environments. Unlike previous studies, CNTs are reinforced in core layer to optimize the performance of sandwich plate. The CNTs are reinforced into matrix phase through functionally graded distributions. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are determined using an extended rule of mixture. Motion and compatibility equations are derived within the framework of first-order shear deformation theory taking into account von Kármán nonlinearity and geometric imperfection. All boundary edges are simply supported, and two uncompressed edges are elastically restrained against tangential displacement. Analytical solutions and Galerkin method are employed to solve governing equations and obtain a nonlinear ordinary differential equation. Fourth-order Runge–Kutta numerical integration scheme is applied to compute the nonlinear frequencies of sandwich plates. The results indicate that the uniaxial compressive loads decrease and strengthen the natural frequencies and frequency nonlinearity of sandwich plates, respectively. The study also reveals that the frequency nonlinearity is more significant when the unloaded edges are restrained more rigorously and temperature is more elevated. Furthermore, the analysis detects that the natural frequencies and frequency ratios respectively are the highest and lowest for a relatively small value of thickness of face sheets.

This study utilizes the modified extended direct algebra technique to examine the effect of internal heat source phenomena on thermoelastic media with temperature-dependent characteristics, under Green–Lindsay (G–L) theory. The study focuses on nonlinear thermoelasticity, which is of especially essential in a material’s response to fluctuating thermal loads, causing significant changes in both its structural form and inherent properties. This area of research plays a crucial role in accurately modeling real-world behaviors, such as the intricate interaction between thermal and mechanical effects, the performance of materials at different temperatures, and the variation of thermal stresses in large-scale structures. Utilizing the proposed technique, we have derived many exact solutions characterized by distinct free parameters, which include exponential, Jacobi’s elliptic functions, and rational and hyperbolic solutions. Furthermore, to facilitate a better interpretation and understanding of the findings, some of these solutions encompassing stress tensor, displacement, and temperature are displayed on both 2D and 3D plots.

This study addresses the anti-plane steady-state SH wave scattering problem in circular laminated structures with circular hole defects. An analytical method integrating multipolar coordinate transformation, Graf’s addition theorem, and wave function expansion is proposed, constructing for the first time an asymmetric Green’s function solution under the synergistic effect of bi-material media and defects. This approach overcomes the theoretical limitations of traditional one-phase media models in characterizing interfacial wave coupling effects. Based on the governing Helmholtz equations, a full-domain wavefield coupling model for bi-material media interfaces and defect boundaries is established using complex-plane coordinate transformation and multipolar coordinate expansion techniques. Integral transforms and Graf’s formula are introduced to rigorously satisfy the interfacial stress-displacement continuity conditions and the stress-free boundary conditions near the circular hole defects. The Green’s function solution set with explicit physical significance is ultimately obtained by solving the coefficient equations. A predictive model for the circumferential dynamic stress concentration factor (DSCF) is derived from the analytical solution, revealing the multiscale modulation mechanisms of shear modulus ratio, defect eccentricity, and incident wavenumber. Numerical validation shows that the absolute error between the maximum DSCF predicted by this method and the degenerated result is 0.74 across a wide frequency range. The research provides a high-precision analytical tool for SH wave scattering analysis in defective laminated structures, offering theoretical value and engineering potential for composite damage assessment and aerospace structural health monitoring.

This study aims to use the improved modified extended tanh-function technique (IMETFT) as an analytical approach to investigate the impact of laser pulses on thermoelastic materials with temperature-dependent properties, modeled within the framework of the Lord–Shulman (L-S) theory. Nonlinear thermoelasticity explores scenarios where thermal loading induces significant alterations in both the material characteristics and geometry of a system, which is critical for describing phenomena such as high-rate laser heating and thermal stress generation. Using IMETFT, various families of analytic solutions were derived, involving rational, hyperbolic, and exponential forms. To validate their physical relevance, numerical simulations were conducted for copper with thermoelastic constants ((lambda _{0}=7.76times 10^{10}) N/m(^{2}), (mu _{0}=3.86times 10^{10}) N/m(^{2}), (rho _{0}=8954) kg/m(^{3}), (k_{0}=386) W/mK) under laser pulse excitation ((I_{0}=10^{5}) J, (t_{0}=22) ps, (r=60~mu )m). The results reveal a symmetric contractive displacement trough centered at (breve{y}=0), a bell-shaped thermal peak with rapid attenuation, and compressive stresses exceeding (-0.58) in normalized units. These findings provide quantitative insight into the interplay between thermal waves and elastic deformation, offering a robust predictive framework for ultrafast laser–material interactions in micro- and nanoscale engineering applications.

This study develops an analytical framework to investigate shear–horizontal (SH) wave transmission in layered multiferroic cylinders composed of concentric piezoelectric (PE) and piezomagnetic (PM) materials under prestress and rotation. Both bi-layer and tri-layer configurations are examined, with the latter including a fiber-reinforced core, while the interfaces are modeled as mechanically, electrically, or magnetically imperfect using spring-type conditions. Closed-form dispersion relations are derived for electrically open/magnetically short and electrically short/magnetically open boundary cases. Numerical simulations are conducted to assess the influence of interfacial compliance, thickness ratio, rotation speed, and initial stress on phase and group velocities, as well as electromechanical coupling efficiency. The findings reveal that mechanical imperfection exerts a stronger influence on SH wave dispersion than electrical or magnetic defects, while PE/PM stiffening leads to monotonic phase velocity enhancement. Rotation and prestress are shown to significantly modify dispersion behavior, with PE layers more sensitive than PM layers. The novelty of this work lies in its unified treatment of multiferroic cylinders with simultaneous rotation, prestress, and multifield interface imperfections, bridging theoretical predictions with practical design considerations. Although the analysis assumes linear material behavior and neglects nonlinear dissipation or thermal coupling, it provides physically consistent predictions validated against limiting cases from prior literature. The results offer valuable guidelines for the design of piezoelectric–piezomagnetic devices such as SAW gyroscopes, rotation sensors, and magnetically controlled transducers, where interfacial integrity and prestress management are critical for performance optimization.

The residual contact responses (RCP) of a two-axle vehicle are exploited to extract the modal frequencies of damped thin-walled box bridges with road roughness in this study. This approach eliminates the need for multiple connected vehicles and their consistent operation conditions, and the masking effect of vehicle frequencies is effectively removed. To start with, an analytical solution for the RCP is derived to identify the dominant frequencies included in it. Subsequently, a finite element model of a three-dimensional vehicle-bridge interaction is established for numerical analyses. Finally, the effects of road roughness, vehicle speeds, vehicle eccentricities, bridge damping and environmental noise on bridge frequency identification are studied. Investigations reveal that the first few vertical and flexural–torsional frequencies of the bridge are successfully extracted from the RCP. Moreover, RCP-based bridge frequency identification demonstrates strong robustness against environmental noise. The excellent performance in the bridge frequency identification is achieved at a vehicle speed of 8 m/s and an eccentricity of 2 m.

The purpose of this manuscript is to investigate the impact of uncertain parameters on the electrical signal output performance and stability of functionally graded materials (FGMs) flexoelectric nanobeams using the quasi-Monte Carlo method. The model incorporates surface effects and the Winkler–Pasternak linear elastic foundation. Based on quasi-static theory, analytical expressions are derived for the output voltage (electrical open-circuit state), output charge (electrical short-circuit state), and effective piezoelectric coefficient (electrical short-circuit state). The analysis results indicate that the gradient index and flexoelectric coefficient substantially increase the output charge and effective piezoelectric coefficient under electrical short-circuit conditions while reducing the output voltage under electrical open-circuit conditions. Increasing the length and dielectric constant of the beam suppresses the output voltage in the electrical open-circuit state, while an increase in thickness reduces the system’s stability. Sensitivity analysis reveals that the dielectric constant has the most significant influence on the output voltage in the electrical open-circuit state, whereas the beam length exerts the most pronounced effect on the output charge and the effective piezoelectric coefficient under electrical short-circuit conditions. This study provides a theoretical foundation and practical guidance for optimizing the design of micro- and nanoenergy harvesters and sensors.

This study aims to develop a novel DQM matrix formulation for 2D non-tensor product basis Hermite polynomials without a mixed second derivative at the corners. This formulation can be used to solve fourth-order systems present in the nanomechanics field and thin plate problems. The proposed formulation is based on a new paradigm of building a 2D Hermite basis using only regular 1D Lagrange polynomials introduced in Part I of this study. This simplifies the implementation of the present formulation as it relies only on the well-documented Lagrange-based DQM. Another critical advantage of the proposed formulation is that, unlike classical implementations, the proposed formulation matches the required physical degrees of freedom while giving access to the analytical expression of the shape functions. To accomplish this, purpose-built transfer matrices between several 2D polynomial bases are developed. To assess the accuracy of the proposed formulation, these new DQM matrices are used to build a strong and a weak Quadrature Element Method formulation for 2D fourth-order systems based on a Gauss–Lobatto–Legendre grid. This ensures a faster convergence for SQEM and provides WQEM formulation with a diagonal mass matrix. A diagonal mass matrix is a significant numerical advantage for WQEM despite the reduced accuracy of Gauss–Lobatto–Legendre integration. An LaDQM formulation is also proposed using a grid without outer corner points. A convergence study is performed for all proposed methods. The accuracy of the proposed methods was evaluated and validated using results from the literature. It is noted here that despite requiring higher mesh density for the highly skew cases the proposed Gauss–Lobatto–Legendre-based WQEM requires less computational power to compute the natural frequency thanks to its diagonal mass matrix. Like most DQ-based methods, the application of the aforementioned formulations to nonlinear systems is of the essence, as DQ-based methods typically demonstrate high accuracy and efficient convergence.