Archive of Applied Mechanics最新文献

This study investigates the propagation characteristics of Rayleigh-type surface waves in layered viscoelastic media, with a particular focus on the role of impedance boundary conditions. The effects of material gradation, viscoelastic damping, and geometric configuration on wave speed and dispersion behavior are comprehensively analyzed, providing insights into the complexities of wave dynamics in heterogeneous media. A combination of analytical formulations and robust numerical techniques is employed to investigate the dispersive and damping characteristics of Rayleigh-type waves. The analysis systematically examines the effects of affecting parameters, including layer thickness, material gradation profiles, and viscoelastic properties, under impedance boundary conditions, thereby assessing their individual and combined influence on wave propagation behavior. The study demonstrates a pronounced sensitivity of Rayleigh-type wave characteristics to both impedance contrasts and material gradation parameters, highlighting the complex interplay between structural inhomogeneity and viscoelastic dissipation. These results provide valuable insights into the behavior of surface waves in engineered layered systems as well as in heterogeneous natural media. This work presents a novel framework for analyzing Rayleigh-type wave behavior under realistic boundary conditions and heterogeneous media. The findings have significant implications for geophysical exploration, structural health monitoring, and the design of advanced materials. Moreover, the results provide a solid foundation for future investigations in applied mechanics and wave-based diagnostics in layered viscoelastic systems.

The hydrodynamic behavior of water waves interacting with a surface-piecing π-shaped breakwater over uneven seabed configurations is analyzed using the eigenfunction matching method (EMM). The continuous seabed is modeled by shelves separated by steps. By employing eigenfunctions with unknown coefficients, the conservations of mass and momentum for each step are formulated into a system of linear equations. The hydrodynamic forces and moment on a variable floating breakwater with and without barriers over variable bottom are formulated. In the absence of thin vertical barriers, the system simplifies to the case involving a floating breakwater over variable bottoms. To assess the accuracy of the proposed model, the computed results are compared with the existing data from the literature, demonstrating excellent agreement. The model is further applied to investigate wave diffraction characteristics. Reflection and transmission coefficients, as well as wave forces, are analyzed in relation to various geometric parameters. Numerical results indicated that the π-shaped floating breakwater significantly alters wave diffraction patterns and energy distribution. Additionally, the structure is shown to reduce excitation wave forces when subjected to incoming waves.

The element-free Galerkin method (EFGM), a meshless approach, was applied to the stress analysis of adhesively bonded single-lap joints and compared with finite element method (FEM) and analytical solutions. EFGM successfully reproduced the general stress distributions, including three-dimensional effects such as anticlastic bending, free-corner stresses, and out-of-plane components that are not captured by classical analytical models. Error analysis revealed that FEM consistently provided closer agreement with analytical solutions, while EFGM exhibited larger quantitative discrepancies, particularly in σ_y and τ_yz. The novelty of this work lies in applying EFGM to the three-dimensional stress analysis of adhesively bonded joints, with a systematic comparison against FEM and analytical solutions, including explicit error analysis and evaluation of out-of-plane stress components. These results demonstrate that, although less accurate quantitatively, EFGM provides valuable qualitative insight and remains attractive for problems involving complex geometries or large deformations where mesh generation for FEM is difficult.

Graphical abstract

Shear deformable beams modelled in accordance with the first-order Timoshenko theory in presence of multiple cracks are the object of this study. Contrarily to the Euler–Bernoulli theory, forced vibrations of the latter multi-cracked beam model have not been satisfactorily studied in the literature. The contribution to the above issue provided by this work consists, first, in the derivation of the “extended” mode shapes explicitly formulated, by means of a distributional approach, to include the effect of multiple cracks on bending and shear stiffness in presence of external proportional damping. Then, it is proved that the orthogonality property of the proposed mode shapes embedding the effect of multiple cracks is preserved and the relevant conditions are explicitly formulated. On this ground, forced vibrations of the multi-cracked beam are analysed by making use of modal superposition exploiting explicit expressions of the Impulse Response Function.

In this short review, the multiscale modeling of dissipative composites undergoing fully coupled thermomechanical processes is outlined through the models presented in a collection of recent works. The aim is to demonstrate the challenges and limitations of: (1) the multiscale approaches (full-field or mean-field techniques), (2) the computational approaches dealing with complex material systems, (3) the alternative methodologies dedicated to the analysis of composite structures, such as those founded on the data-driven modeling and the model order reduction techniques.

This paper focuses on explaining the presence of ice cover in the linear surface wave scattering and radiation by a circular cylinder submerged in a finite-depth ocean. The ice cover has the property that it behaves like a thin elastic plate. Under small-breadth structural oscillations, analytical expressions of the three-dimensional problem are derived in each flow region for the wave motion by an eigenfunction expansion method. However, the velocity potentials of the incident and scattered waves involve the Bessel and Hankel functions for each region. To get complete analytical solutions, we solve the obtained integral equations by the multi-term Galerkin method, where the ultra-spherical Gegenbauer polynomial is chosen as a basis function. This logical approach gives rapid convergence and provides six-figure delicacy in the results of hydrodynamic quantities. The hydrodynamic quantities acting on the rigid cylinder are shown graphically against the frequency. The study also highlights the significance of crucial parameters such as depth, radius of the cylinder, and flexural rigidity of the ice cover to design the breakwater. Based on the numerical results, it can be concluded that the present cylindrical breakwater design is quite capable of attenuating the wave forces and roll moment amplitudes.

In this study, fracture analysis of thermally induced cracks in porous functionally graded (PFG) structures is carried out using extended isogeometric analysis (XIGA) under the mechanical and thermomechanical loading conditions. Multiple porosity distribution functions (PDFs) are modeled in the FG structures, and appropriate enrichment functions are utilized to represent discontinuities along the crack face while effectively capturing the singular behavior at the crack tip. Firstly, three distinct porosity distribution types—right end enhanced (REE), left end enhanced (LEE) and symmetrically center enhanced (SCE)—are incorporated into the functionally graded (FG) structure. A power law function is employed to describe the variation of material properties along the structure’s length, facilitating a gradual transition from a metal-rich region to a ceramic-dominant composition. The influence of porosity is integrated into this power law through an additional porosity term. The equivalent properties of the PFG structure are estimated along its length for various PDFs. Subsequently, an adiabatic crack is modeled within the domain to investigate its effect on the fracture behavior of FG structure under thermomechanical load using XIGA. This study introduces a novel approach by analyzing a PFG structure with an adiabatic center crack, considering various porosity distributions (LEE, REE, and SCE) under both mechanical and thermomechanical loading. To verify the accuracy of the XIGA method, the results obtained for a non-porous FG structure are compared with the existing results available in the literature under mechanical and thermal load separately. The impact of various porosity distributions on the fracture behavior of FG structure is further explored for both mechanical load and thermomechanical loading scenarios. Additionally, the effects of power law index, porosity parameter, and crack length on the fracture behavior of PFG structure are examined.

This paper primarily introduces the Adomian Decomposition Method (ADM) and its extended method, the Laplace Adomian Decomposition Method (LADM). The study begins by deriving the governing equations for both uniform and non-uniform beams, using LADM to transform the partial differential equations into recursive algebraic equations. By applying boundary conditions, the natural frequencies and vibration modes of the beams are calculated. Compared to traditional ADM and Modified Adomian Decomposition Method (MADM), LADM demonstrates higher numerical accuracy and faster convergence. The results indicate that the mass, moment of inertia, and eccentric distance at the beam’s endpoints have a significant impact on the natural frequencies. Larger masses lead to lower first natural frequencies, while increasing eccentric distance causes other natural frequencies to rise. Structural rigidity and axial tension also influence the relative amplitude of beam’s modal shape and natural frequencies, greater rigidity results in smaller amplitudes, and higher axial tension increases frequencies. Additionally, the taper ratio has a noticeable effect on the natural frequencies of tapered beams. In exponentially decreasing beams, the first natural frequency increases with a higher taper ratio, while other frequencies decrease. Conversely, exponentially increasing beams exhibit the opposite trend. In conclusion, LADM proves to be an effective method for solving eigenvalue problems in beams, surpassing traditional methods in terms of computational efficiency and accuracy.

The thermal shock behavior of a high-temperature ceramic plate with indentation crack was studied. The analytical solution of temperature field is obtained by the standard method of separating variables. The total stress intensity factor at the front of semi-elliptical indentation crack is evaluated by thermal stress and residual stress intensity factors. The thermal stress intensity factors in the depth direction and the surface direction of the semi-elliptical indentation crack front were obtained by fitting the polynomial form of the thermal stress and crack geometry factor. The residual stress intensity factor was related to indentation load, crack shape and length, elastic modulus and hardness of the material. The graphs of the total stress intensity factor and the thermal stress intensity factor were obtained by calculating the analytical solutions using MATLAB. The results were compared. The results provide a theoretical basis for studying the thermal shock fracture of indentation crack. The thermal shock resistance is evaluated by the strength failure criterion and fracture toughness failure criterion.