Archive of Applied Mechanics最新文献

This paper reports on a comprehensive nonlinear transient dynamic analysis of nanocomposite beams reinforced with graphene oxide powders (GOPs) dispersed in a functionally graded (FG) manner within the polymer matrix (PM). The Bernoulli–Euler beam structural model, incorporating von Kármán-type geometric nonlinearities, is adopted for modeling composite beams. The nanocomposite beams’ effective mechanical properties are determined using the modified Halpin–Tsai micromechanical model and the rule of mixture. The nonlinear governing equations of motion are derived using Hamilton’s principle and solved within a numerical framework that combines the finite element method for spatial discretization, the Newton–Raphson method for nonlinear resolution, and the Newmark time integration scheme for temporal discretization. After validating the results by ABAQUS software, parametric investigations are conducted to examine the influence of the GOPs diameter-to-thickness ratio, GOPs weight fraction, and various functionally graded distribution patterns on the nonlinear transient dynamic response of composite beams. The results reveal that an increase in the nanofillers’ geometric dimensions and content significantly enhances stiffness, leading to reduced deflection amplitudes and shorter oscillation periods of the beams. Additionally, among the distribution patterns, the FG-X configuration demonstrates the most favorable dynamic performance, followed by UD, FG-V, and FG-O. These findings offer valuable insights into the nonlinear dynamic characteristics of advanced nanocomposite beams and highlight the potential of FG-GOPs-reinforced PM nanocomposite structures for vibration-critical applications, such as aerospace and mechatronics. This work makes a substantial contribution to the ongoing development of smart materials and nonlinear structural dynamics in engineered systems.

This study presents a method for determining globally optimal solutions to optimization problems in analytical form. The method is based on the Cylindrical Algebraic Decomposition (CAD) algorithm, in tandem with powerful symbolic computations. Exact solutions are derived for several widely used benchmark engineering optimization problems. These analytical solutions are final in the sense that they are feasible and cannot be improved. Building upon earlier work by Charalampakis and Chatzigiannelis on truss sizing optimization using CAD, the present study extends the methodology to a broader class of benchmark problems. To the best of our knowledge, no previous work has attempted such a general application of CAD-based symbolic optimization. Future advancements in CAD algorithm implementation and computing power may lead to the solution of even more complex problems.

In this work, we investigate the optimal control problem associated with a truncated version of the Timoshenko–Ehrenfest beam model, which captures essential features of transverse vibrations in elastic structures. We begin by establishing the well-posedness of the system through the Faedo–Galerkin approximation method, ensuring existence and uniqueness of solutions. The associated optimal control problem is then formulated, and the Pontryagin maximum principle is employed to characterize the optimality conditions. To obtain the analytical solution aiming numerical issues, we apply a Fourier series expansion, which allows for the explicit representation of both the state and the adjoint variables. Finally, we present numerical simulations that demonstrate the efficiency of the proposed control strategy in suppressing unwanted vibrations, confirming the theoretical results and highlighting the practical relevance of the method.

Traditional modeling approaches for mooring lines exhibit limitations in capturing nonlinear behaviors under large displacement and deformation conditions. In this study, a buoy-enhanced mooring line model incorporating seabed contact is developed based on the Absolute Nodal Coordinate Formulation (ANCF). The influence of the buoy on tension characteristics is analyzed to provide insights for the optimization of mooring system design. First, the mass matrix, stiffness matrix, and generalized elastic force vector of the mooring line element are derived based on ANCF. The model incorporates external forces such as Morison’s hydrodynamic load, seabed contact forces, and the buoyancy provided by the added buoy. The dynamic equations of the mooring line are then formulated using the Lagrange multiplier method. Second, the accuracy and efficiency of the proposed model are validated through dynamic simulation case studies involving a flexible coiled beam model, an underwater buoy-mooring line model, a mooring system subjected to irregular wave excitation, and a system under harmonic motion excitation. Finally, the effects of buoy configuration and installation position on both static and dynamic tensions in the mooring line are analyzed. The influence of the buoy on the impact amplification factor and system stability under various harmonic excitations and ocean current conditions is also discussed. Results indicate that appropriate buoy configuration can significantly reduce the tension in the mooring line, mitigate the alternating slackening and tightening phenomena, and thereby enhance overall system stability.

This study presents a semi-analytical approach for analyzing the bending and free vibration behavior of three-phase bi-directional functionally graded porous sandwich plates (2D-FGPSW). The sandwich plates considered feature face sheets with biaxial material gradation composed of three distinct constituents and a thickness-varying functionally graded porous core. Such structural configurations are relevant to advanced engineering applications requiring high strength-to-weight ratios and tailored mechanical performance. The analysis is based on Reddy’s third-order shear deformation theory and employs the pb2-Ritz method to obtain accurate solutions under various boundary conditions, with convergence checked through appropriate term selection. The model is validated through comparison with available benchmark solutions. A comprehensive parametric study is conducted to evaluate the effects of material gradation, geometric parameters, sandwich configurations, and boundary conditions on the structural response. The results contribute to a deeper understanding of the mechanical behavior of complex sandwich structures and support the design of efficient and lightweight composite systems.

The study of nonstationary vibrations and wave propagation in deformable waveguides is of considerable interest in many fields of science and engineering. This work addresses wave processes in extended multilayer cylindrical bodies. The aim of the study is to investigate the problems of wave propagation in an elastic hollow three-layered cylinder and to develop efficient analytical methods for solving the problem of nonstationary wave propagation in layered cylindrical structures. The problem is formulated and solved in a cylindrical coordinate system. Normal (radial) loads are applied at the free boundaries (either inner or outer) of the cylinder. The solution is constructed using the Laplace integral transform with respect to time, followed by its inversion. The solution in the original (time) domain is presented in a form that is convenient for numerical implementation. This formulation makes it possible to analyze wave propagation in a multilayer cylinder with an arbitrary number of coaxial layers. A spectral boundary value problem is derived for a system consisting of ordinary differential equations and partial differential equations, which is reduced to a system of ordinary differential equations with complex coefficients. The solution in the Laplace domain is expressed in terms of modified Bessel and Neumann functions of arbitrary order. The inverse transformation is carried out in a form free from contour integrals and is represented as a rapidly converging double series of cylindrical functions. It is established that, for large wave numbers, the limiting phase velocity of this mode coincides with the Rayleigh wave speed.

To improve stress–strain prediction accuracy for dense vulcanized rubber, this study develops a constitutive modeling fitting framework incorporating bulk modulus (K) effects (i.e., a nearly incompressible formulation). Six classical phenomenological hyperelastic models—Three-Term Mooney-Rivlin (MR_T), Yeoh, Yeoh_Revised (Yeoh_R), Gent-Gent (GGent), Ogden, and Lopez-Pamies—are comparatively evaluated within this framework. Systematic assessment via the goodness-of-fit (R²) metric quantifies model performance across three deformation modes (simple tension, planar tension, and equibiaxial tension) for multiple rubber materials, including HNBR, FPM, silicone rubber, and the Treloar dataset. The framework is further extended to highly compressible rubber-like materials (e.g., foams/hydrogels). Key results demonstrate: (i) Significant R² improvement for comprehensive tensile stress predictions in dense vulcanized rubber; (ii) Pronounced enhancement of equibiaxial tensile stress accuracy for generalized Mooney-Rivlin models (e.g., MR_T, Yeoh_R); (iii) Critical dependence of the Ogden model on parameter initialization to ensure physical relevance and mitigate sensitivity; (iv) Limited applicability to highly compressible materials with strong model-specific performance variation; (v) Essential requirement for comprehensive experimental validation, particularly high-precision bulk modulus (K) characterization. This work provides quantitative selection criteria for phenomenological constitutive models in FEA, incorporating the calculation of shear modulus (G) to enable more reliable assessment of rubber material behavior in engineering applications.

The Theory of Porous Media (TPM) with an embedded phase-field approach to fracture provides an elegant opportunity to study complex flow phenomena in fractured porous materials in a unified single-domain approach. On this basis, the interactive flow behaviour between free flow and porous-media flow is studied using the example of flow through a thin porous plate containing a rectangular channel. By considering different boundary conditions and investigating the flow behaviour for a range of hydraulic conductivities, our study is designed to reveal insights into phenomena which are relevant for various sub-surface geo-engineered applications. Furthermore, we show that the applied macroscopic single-domain approach is able to reveal local flow effects near the porous interface (channel walls), namely the so-called velocity profile inversion phenomenon. Moreover, we introduce a geometrically motivated estimation of the length-scale parameter (epsilon ) used in phase-field approaches, which is directly related to the roughness of the fracture surface. Thus, values for (epsilon ) are proposed for microfluidic devices and different rock types. Furthermore, we apply fully three-dimensional simulations to evaluate the influence of the thickness of thin porous plates on the overall flow resistance, which is typically relevant in microfluidic devices. In a combined numerical–experimental study, we compare results from representative microfluidic experiments and simulations and confirmed the choice of (epsilon ) to correctly predict the flow transition across the porous interface.

In recent years, extensive studies on carbon nanotubes-reinforced composites (CNTRC) focus on the uniform-thickness structures and free vibration. However, there is few researches on the vibro-acoustic behaviors of CNTRC structures with variable thickness. Accordingly, this paper constructs a variable thickness double-functionally graded (DFG) sandwich curved plates reinforced by CNTs. The Mori–Tanaka model and mixture rule are used to evaluate the effective elastic modulus of the composite structures. The thermal–mechanical dynamic equation is established using the Hamilton’s principle and solved via Navier’s method combined with the fluid–solid coupling conditions to determine the natural frequency and sound insulation. In calculation, the variable thickness parameters, gradient indices of FG materials, CNT distribution forms, curvature and temperature variations on the vibro-acoustic behaviors are examined. The obtained results show that the curvature of curved plates can significantly increase the vibration frequency and optimize sound insulation characteristics. The coupling effect of material softening and thermal stress under temperature field has a strong suppression effect on vibration frequency, while the nonuniform parameters of variable thickness and the change rate of thickness positively correlate with the vibro-acoustic performances.