Archive of Applied Mechanics最新文献

This study presents a sophisticated thermoelastic model that integrates dual-phase-lag theory, memory-dependent kernel operators, and two distinct temperature fields—thermodynamic and conductive. The framework accounts for microstructural effects and temperature-dependent internal heat sources within a spherical cavity, modeled using a non-Fourier heat conduction approach grounded in energy conservation. The resulting system of coupled partial differential equations captures the evolution of thermal and mechanical fields under nonequilibrium conditions. Exact analytical solutions are obtained via Laplace transformations, and the Dubner–Abate technique is employed for accurate numerical inversion to recover time-domain behavior. The model offers enhanced physical realism compared to classical and fractional approaches, effectively representing the delayed and spatially distributed propagation of heat. Numerical simulations highlight the influence of kernel structure, hysteresis, and temperature discrepancy on stress and temperature profiles. These findings demonstrate the model’s predictive capability for advanced applications in microelectronics, nano-engineered materials, biomedical systems, and smart structures. An appendix detailing the numerical scheme is included to support reproducibility.

This paper deals with the development and assessment of 1D micropolar beam models of different lattice core structures according to micropolar continuum theory. The deformation kinematics of the lattice beams are based on the equivalent single-layer Timoshenko beam theory. The discrete-to-continuum transformation, through strain energy equivalence of discrete unit cells and corresponding micropolar continuum, is applied to deduce the constitutive law. The strain energy of the discrete unit cell is written by treating each element as Euler–Bernoulli beam element. The four different types of lattice cores are considered in the present study. The principle of minimum potential energy is used to derive the equilibrium equation for the webcore 1D micropolar Timoshenko beam model. Furthermore, the successive approximations are employed in the micropolar continuum model to deduce the governing equations for the couple stress Timoshenko beam model and classical Timoshenko and Euler–Bernoulli beam models. The couple stress Timoshenko beam models are obtained by assuming the internal antisymmetric shear force (S_a) equal to zero and microrotation (ψ) equal to macrorotation (Ω) for all lattice cores. Fourier series-based analytical solutions are obtained for the static behaviour of the different beams under uniformly distributed, sinusoidal and point loads. The present analytical solutions are compared with those obtained through the finite element method (ABAQUS) using plane frame element and it has been found that the accuracy of the different beam models is highly sensitive to the geometric properties of lattice. Among different theories, the micropolar continuum Timoshenko beam theory yields promising results.

This paper introduces an analytical framework for examining the coupled bidirectional bending and torsional vibrations of non-symmetric, axially loaded thin-walled Timoshenko–Ehrenfest beams. By integrating axial loads, shear deformation, rotational inertia, and warping stiffness into the traditional Timoshenko–Ehrenfest beam theory, we enhance its ability to address complex bending-torsion interactions. Utilizing Hamilton’s principle, we derive five coupled differential equations and twelve boundary conditions to accurately describe the beam’s dynamic behavior. The normal mode method is used to derive closed-form expressions of frequency responses under arbitrary harmonic loads, and orthogonality conditions are established to obtain precise modal impulse and frequency response functions. Our framework provides accurate and computationally efficient solutions and examines the impact of axial loads on natural frequencies, offering practical guidance for engineering design. These findings contribute to the dynamic analysis of thin-walled Timoshenko–Ehrenfest beams, providing useful insights for engineers in designing and optimizing structures under complex loading conditions.

This study presents a semi-analytical method for analyzing the buckling behavior of nonlocal Timoshenko beams using Eringen’s nonlocal elasticity theory. The method combines the initial value method (IVM) with a segment-wise approximate transfer matrix (ATM) approach, enabling accurate and efficient computation of critical buckling loads under various boundary conditions. The IVM calculates displacements and stress resultants from initial conditions, while the ATM constructs the principal matrix required by the IVM through segment-wise integration, ensuring numerical stability. The IVM–ATM framework offers a practical alternative to traditional analytical and numerical methods, especially for size-dependent problems. The results show excellent agreement with existing solutions, validating the method’s accuracy. The method’s accuracy is further supported by detailed convergence analyses. Parametric studies highlight the effects of length-to-diameter ratio, nonlocal parameter, and boundary conditions on buckling behavior. The proposed method provides a reliable and efficient tool for nanoscale beam structures.

The cerebral microvasculature plays a key role in determining the blood perfusion and oxygen diffusion to surrounding tissue. Multiscale models have thus been developed to incorporate the effect of the microvasculature into overall brain function. Moreover, brain tissue poroelastic properties are also influenced by the microvasculature. This study aims to determine the pororelastic properties of brain tissue using multiscale modeling on microvasculature networks described by the following effective parametric tensors: blood flow permeability ({varvec{K}}), interstitial fluid flow permeability ({varvec{G}}), Biot’s coefficients for blood ({alpha }_{c}) and interstitial fluid ({alpha }_{t}), Young’s modulus (overline{E }), and Poisson’s ratio (overline{v }). The microvasculature networks are built from a morphometric data of brain capillary distribution, which is represented using 1D lines. To allow for solving the microscale cell equations using finite element method, the microvasculature is modified into 3D shapes. The modifications resulted in 15% increment of the microvasculature volume. Validation is then performed by comparing the permeability tensor ({varvec{K}}) obtained using Poiseuille’s and Stokes’ equations, which resulted in the value of ({varvec{K}}) obtained through solving Stokes’ equation to be about 70% less than through solving Poiseuille’s equation. Based on these results, the other effective parameters have been estimated by considering the microvasculature volume increment due to the geometry modification. The volume increment significantly affects the parameter ({alpha }_{c}) but not the other parameters. The effective parameters are then used in a benchmark simulation, which further demonstrates the model value in describing the effects of brain capillary morphology in cerebrovascular diseases.

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.