Archive of Applied Mechanics最新文献

This study involves the nonlinear buckling of deep-buried functionally graded porous (FGP) pipelines with irregular (egg-shaped) cross-sections mixed with graphene platelets (GPLs). After heating, the pipeline deflects radially inward since it is constrained tightly and rigidly by the medium (soils/rocks). A refined sine formula is utilized to express this deformation. The response equations are derived by combining the thin-walled shell scheme and energy theory. The response equations are solved to acquire the minimum and critical temperature variations, respectively. Moreover, strict validation is completed to prove the analytical scheme. One may observe that the curves between the analytical scheme and other studies are closely fitted. Finally, this study evaluates the effects of several key indices on the stability of the FGP-GPLs egg-shaped submarine pipeline, involving the porosity coefficient, geometric profile, weight fraction, etc.

This study develops a first-order averaged model for a weakly perturbed Mathieu–Liénard oscillator with viscous damping, quadratic amplitude-dependent dissipation, periodic stiffness modulation, and a prescribed higher harmonic close to the linear natural frequency. A rotating-frame reduction yields an explicit amplitude–phase slow-flow for the near-resonant response. For positive effective linear damping and non-negative cubic damping, the leading slow-flow has one positive-amplitude synchronous equilibrium for each fixed bounded detuning, and this equilibrium is asymptotically stable. The mean stiffness correction shifts the predicted resonance center downward. For harmonic orders of two or higher, the oscillatory Mathieu term is non-resonant at first averaging order; finite-perturbation parametric effects are therefore assessed separately with Floquet multipliers. The reduced model is tested against periodic solutions of the full oscillator obtained by Newton shooting. Fourier projection of 143 sampled periodic responses gives a mean amplitude error of 1.30% and a mean phase error of 0.144 degrees at a nominal perturbation parameter of 0.05; all sampled full-orbit Floquet spectral radii are below one. In a separate perturbation-level study, both errors decrease approximately linearly over the tested perturbation range. The model therefore provides a low-cost predictor of the synchronous nth-harmonic response within the stated weak-perturbation and quadratic-damping assumptions.

Piezoelectric semiconductors represent a class of materials that simultaneously exhibit piezoelectric effects and semiconductor properties. These materials are capable of interconverting mechanical energy and electrical energy while enabling signal processing, thereby demonstrating extensive application potential in energy harvesting and sensor technologies. This study investigates the super-harmonic and subharmonic resonances of a rectangular piezoelectric semiconductor thin plate. A dynamical model of the thin plate was established based on Kirchhoff–Love plate theory, the von Kármán equations, and the second category of piezoelectric constitutive equations. The kinetic energy, strain energy, and the virtual work contributions from electric, thermal, and axial forces acting on the axially moving plate were derived using the kinetic energy theorem and the principle of virtual work. Hamilton’s principle was then applied to derive the governing equations of vibration, the electric potential compatibility equation, and a supplementary equation for carrier concentration for the axially moving rectangular piezoelectric semiconductor thin plate. Considering simply supported boundary conditions on all four edges, the governing partial differential equations were discretized into a nonlinear ordinary differential equation for forced vibration using the Galerkin method. The method of multiple scales was employed to obtain analytical solutions, yielding the amplitude–frequency response equations for both super-harmonic and subharmonic resonance. The validity of the analytical solutions was verified through favorable agreement with numerical results. Parametric analyses were conducted to elucidate the influence of variations in excitation force, axial speed, and applied voltage on the system’s natural frequency and resonant amplitude.

In regions with significant diurnal temperature variations, continuous welded turnouts (CWTs) are susceptible to excessive longitudinal rail displacement under cyclic thermal loading and progressive resistance degradation, ultimately leading to abnormal turnout conversion and service failure. To analyze the longitudinal mechanical behavior and assess the safety of CWTs in service, this paper develops a data-driven finite element analysis model for ballastless turnouts and presents a novel algorithm for service-state reconstruction and resistance constitutive curve updating. The model fully accounts for the hysteretic behavior and loading history of the fastening resistance, with cyclic thermal loading and various resistance degradation processes selected as typical working conditions to be simulated. The analysis is conducted from multiple perspectives, including the hysteretic loop morphologies of fasteners under different constraints, the longitudinal distribution of resistance curve offsets along the CWTs, rail residual displacement/stress, and longitudinal forces in load-transferring components. Results showed that the data-driven finite element model achieved a displacement error of less than 0.0002 mm in reconstructing the in-service status. The greater the asymmetry of the cyclic temperature loading, the more pronounced the effects of hysteresis loop offset and residual displacement accumulation become. After 25 extreme temperature cycles (− 45~10 °C), the maximum longitudinal residual rail deformation reached 4.32 mm, already 43.2% of the stress-release maintenance limit (10 mm). Neglecting continuous resistance degradation led to an underestimation of longitudinal cumulative plastic displacement, necessitating the inclusion of its long-term evolution in-service status predictions. This study provides a theoretical basis for longitudinal displacement control and long‑term condition assessment of CWTs.

The surface residual stress induces a very significant size-dependency in yield strengths of nanostructured materials. In this work, combined effects of nanovoid shape and size on the yield surface of metal nanoporous materials are examined. Both oblate and prolate shapes are considered for the spheroidal nanovoid. The effect of the surface residual stress is taken into account through separating its induced strains from strains due to external loading. Using field fluctuation method and von Mises criterion, a size dependent yield function is obtained for a nanoporous metal with aligned spheroidal nanovoids. Numerical studies are conducted for different external loading conditions, for which a finite element model is used to calculate the deformations caused by the surface stress. The results show that the yield surfaces of the material are significantly dependent on the shape and size of the nanovoids. Generally, this dependency is larger in the case of oblate nanovoids.

Functionally graded materials replace the abrupt interfaces of conventional laminates with a smooth through-thickness variation of the elastic moduli. For plate analysis, this regularity introduces a bending–membrane coupling: the asymmetric stiffness distribution shifts the neutral surface off the midplane, so an in-plane mode accompanies every curvature. This paper extends the hybrid-Trefftz stress element for plate bending to functionally graded Mindlin–Reissner plates. The neutral-surface offset drives an in-plane source that the homogeneous Trefftz space cannot absorb; the gap is closed with a closed-form basis built from a double Helmholtz decomposition, comprising harmonic, biharmonic, Helmholtz and pure-membrane families. A reduction theorem shows that the whole grading dependence enters through two rigidity scalars, and that the element collapses to its classical homogeneous counterpart when the coupling vanishes. An overflow-safe reformulation of the Helmholtz family restores stability of the assembled compliance matrix in the thin-plate limit, extending the usable slenderness range by two orders of magnitude. The transverse shear stiffness is evaluated for the actual through-thickness profile, not inherited from the homogeneous theory. A layered validation protocol reproduces published benchmark values for an alumina–aluminium plate to a worst-case relative difference of seven parts in ten thousand, across nine grading exponents and both homogeneous limits, and confirms convergence on a non-rectangular domain against an analytical reference.

This study develops a new higher-order continuum framework that couples the stress-driven nonlocal elasticity theory with the modified couple-stress theory (MCST) to analyze the stability of graded nanobeams resting on an elastic substrate. Integration of the stress-driven nonlocality with MCST captures the simultaneous effects of nonlocal stress convolution and microstructural rotation gradients. A graded Euler–Bernoulli beam is considered, and a unified constitutive relation is formulated by linking nonlocal stresses and symmetric couple stresses to local strain and curvature measures. The governing equilibrium equations are derived using Hamilton’s principle, and the resulting integrodifferential field equations are transformed into a solvable form through Laplace-domain techniques. Winkler and Pasternak foundation parameters are incorporated to represent elastic substrate interactions. Analytical expressions for critical buckling loads are obtained for simply supported and clamped beams across multiple buckling modes. Parametric investigations reveal that the stress-driven nonlocal parameter produces a monotonic stiffening effect, increasing the critical buckling load in all modes, while the couple-stress length scale further enhances stiffness with mode-dependent sensitivity. The graded microstructure significantly modulates these trends, demonstrating strong coupling between material gradation, nonlocality, and curvature effects. The framework thus establishes a new constitutive foundation for multiscale stability analysis.

A fully edge-based smoothed finite element method for static and dynamic elastoplastic analyses of axisymmetric structures is formulated in this paper, which incorporates a quasi-weak form of the smoothed integral into the edge-based smoothed finite element method framework. Based on the initial triangular meshes, an edge-based smoothing domain is constructed for each edge by connecting its two vertices to the centroids of adjacent triangular elements. To effectively tackle domain integrals related to the shape function in the strain and mass matrices, a quasi-weak form of the smoothed integral is introduced. This special integration necessitates the evaluation of indefinite integrals for shape functions without reducing the continuity requirements. Consequently, all the complex domain integrals can be transformed into the boundary integrals over the smoothing domains, thus completely eliminating the need for Jacobian calculations and isoparametric mapping throughout the solution process. Plastic strain evolution is governed by the associated flow rule, with isotropic hardening accounting for the increase in yield strength during plastic deformation. The resulting nonlinear governing equations are solved utilizing an unconditionally stable Newmark time integration scheme combined with the Newton–Raphson iterative algorithm. Numerical examples confirm that the proposed method yields optimal performance for both static and dynamic elastoplastic analyses of axisymmetric structures, especially relative to computational accuracy and robustness against mesh distortion.

This paper conducts numerical and experimental investigations on the band gap characteristics of a type of unique planar repetitive truss structure with local resonators. This unique structure is constructed by attaching spring–mass systems to the joints of the repetitive truss structure. The structural unit cell can be equivalent to a 6-DOF equivalent beam element using the principle of energy equivalence. Based on this 6-DOF equivalent beam element, this study proposes an equivalent wave finite element method and an equivalent vibration transmission analysis to calculate the band gap frequency range. The proposed equivalent wave finite element method and equivalent vibration transmission analysis are verified via numerical simulations and experimental tests. Results show that the repetitive truss structure can form a local resonant band gap with a width of about 100 Hz. The influences of designing parameters on the band gap properties of the planar repetitive truss structure are also investigated in detail. Finally, to achieve enhanced band gap performance, this study systematically conducts grading analysis and optimization analysis of the mass distributions in the resonators. The contents of this paper are expected to provide new insights for the research of vibration and noise reduction of repetitive truss structures.