Archive of Applied Mechanics最新文献

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.

This study investigates the static response, instability, and buckling behavior of porous nanoplates subjected to electrostatic fields using the non-local strain gradient theory. The nanoplate is modeled with a non-uniform porosity distribution and boundary radial load. Dimensionless governing equations are derived by introducing scaled parameters such as the applied load, voltage, and length-scale factors. The static deformation and stability are analyzed using both analytical and numerical approaches, namely, the Galerkin mode summation and finite element methods. A derivation-based analytical technique is also proposed to determine the pull-in instability voltage and buckling load. The main advantage of this technique lies in its simplicity and high accuracy in predicting instability and critical parameters compared with existing analytical procedures. Comparisons between analytical and numerical results demonstrate good agreement, confirming the reliability of the formulations.

The parametric study provides detailed insights into the influence of porosity ratio, non-local parameter, and length-scale parameter on stiffness, pull-in instability voltage, and buckling load. Results show that both the pull-in instability voltage and buckling load vary almost linearly with porosity. Increasing the length-scale parameter enhances stiffness and stability, while increasing the non-local parameter reduces them. Specifically, when the porosity ratio increases from 0.05 to 0.3, the pull-in instability voltage decreases by about 20%, and the buckling load is reduced by nearly 56%, demonstrating the strong influence of porosity on the electromechanical stability of porous nanoplates.

Functionally graded materials (FGM) which are made from ceramic and metals are popular due to their mechanical and thermal resistance. These materials are prone to cracking and fracture, particularly are ceramic phase because of the brittleness. The weight function (WF) method, which is a powerful method in the field of fracture mechanics, is employed to analyze the fracture behavior of plates made of FGMs. To this end, WF coefficients were determined to calculate stress intensity factors (SIF) in plates made of FGM. The modified (J_{k})-integral and a validated finite element method (FEM) code in ABAQUS were used to calculate the reference SIFs and WF coefficients. In the next step, SIFs in cracked FGM plates were analyzed using the developed WF approach and then compared with results directly calculated by the FEM method. Various variables were studied, such as crack length, crack angle, and material distribution along the geometry. The relative differences between the predicted results by the WF method and FEM were found to be acceptable. It was concluded that the WF method successfully determines SIFs for this case. Additionally, it was demonstrated that using more terms in the WF method leads to more accurate results and less difference between the FEM and the WF methods.

The main purpose of this work is to present a new trigonometric shear deformation theory (TSDT) in conjunction with the strain-based approach for developing a four-node quadrilateral high-order plate bending finite element with five degrees of freedom per node for bending and buckling analysis of sigmoid functionally graded porous (S-FGP) plates. In this context, a novel shear function is introduced within the framework of a five-unknown high-order shear deformation theory, where the shear strain variation across the plate thickness is nonlinear, with zero transverse shear stress on the upper and lower surfaces. Therefore, the introduction of shear correction factors is not required. The sigmoid law distribution is considered for modeling the material characteristics of plates, which vary gradually in the thickness direction. To describe the internal pores of plates, three porosity distribution types in terms of cosine functions are adopted: symmetrical center-enhanced distribution, bottom-enhanced distribution, and top-enhanced distribution. Comparative studies with published higher-order analytical and numerical models demonstrate the simplicity and efficiency of the proposed model in predicting S-FGP plates under complex mechanical conditions. Moreover, numerical applications of S-FGP plates are conducted to evaluate the impacts of loading type, boundary conditions, porosity coefficient, material index, and geometric parameters on the bending and stability behaviors. In summary, this study provides key insights that enhance the comprehension of the mechanical behavior of porous sigmoid functionally graded plate structures.

This study presents a comprehensive analysis of elastodiffusive behavior in a nonsimple, isotropic solid cylinder subjected to transient thermal excitation. The governing framework integrates nonlocal thermoelasticity with memory-dependent diffusion, capturing the lagging effects of heat and mass transport through multi-phase-lag models and kernel-based formulations. Constitutive relations are developed to incorporate spatial nonlocality and temporal memory, yielding coupled field equations that describe the distributions of temperature, displacement, chemical potential, and stress. The model is solved in the Laplace domain using analytical techniques, and numerical inversion is performed via the Durbin method enhanced by the ε-algorithm for improved convergence. Parametric studies reveal the influence of kernel functions, nonlocal parameters, propagation velocity, and discrepancy factors on the spatial profiles of thermoelastic quantities. Results demonstrate that increasing nonlocality and memory sensitivity leads to smoother field distributions, reduced stress concentrations, and enhanced thermal uniformity. The novelty lies in combining nonlocal elasticity and phase-lag transport in cylindrical geometry, offering a unified, memory-sensitive model for coupled thermo-elasto-diffusion. These findings provide valuable insights into the design of microstructured, memory-sensitive materials under coupled thermal and mechanical loading.

Understanding the time-dependent deformation behavior of concrete under mild thermal conditions is critical for ensuring the long-term performance of underground structures. This study proposes a novel three-dimensional fractional-order creep model that accounts for both viscoelastic and viscoplastic deformation mechanisms while incorporating thermal effects. The model leverages the advantages of fractional calculus to capture the multiscale and memory-dependent characteristics of concrete. It is extended from a one-dimensional to a three-dimensional form through stress–strain tensor decomposition and the integration of Perzyna’s viscoplastic flow theory. The parameter analysis is conducted to link the parameter values with concrete microstructure. A series of triaxial stepwise loading creep tests were conducted on C30 concrete specimens at temperatures ranging from 25 to 100 °C under a constant confining pressure. The experimental data were used to calibrate and validate the model via parameter identification using the least-squares method. The model demonstrates strong agreement with experimental data across various temperature and stress conditions, accurately reproducing transient, steady-state, and accelerating creep phases. Furthermore, temperature-dependent expressions for the elastic shear modulus, viscoelastic modulus, and viscoplastic viscosity were established, enabling the prediction of concrete creep behavior under different thermal environments. The proposed model provides a robust theoretical basis and practical guidance for the long-term durability design of concrete support systems in mild-temperature underground engineering applications.

This study focuses on the bending behavior of carbon nanotubes modeled as Timoshenko nano-beams under various boundary and loading conditions, which have not been previously examined within the framework of doublet mechanics. The sixth-order differential equation derived from equilibrium equations is solved analytically using the displacement field in doublet mechanics. The analyzes reveal paradoxes in some bending solutions, which have not been reported before. For example, the scale parameter effect disappears in clamped–clamped beams subjected to uniform load and in cantilever beams with a point load at the free end. Additionally, cantilever beams under uniform load exhibit unexpected stiffening behavior, which differs from that of clamped-pinned cases. To resolve these inconsistencies, a new analytical solution is developed based on variationally consistent boundary conditions, highlighting the originality of the developed approach. This approach reinstates the anticipated scale-dependent softening across all boundary conditions examined. Furthermore, a novel macro-stress expression has been identified and validated, thereby extending the previous formulations documented in the literature. The effects of the scale parameter, slenderness ratio, and boundary conditions on bending behavior are thoroughly examined. The results indicate that the influence of the scale parameter is most pronounced for the clamped–clamped, clamped-pinned, and clamped-free nano-beams, respectively. The proposed framework elucidates existing paradoxes and advances the application of doublet mechanics as a reliable analytical approach for nano-scale structural design.

This study presents a high-fidelity modelling and vibration analysis framework for a 600 MW turbo-generator stator end winding, integrating composite materials theory and discrete element methods. The double-layered winding is modelled as a conical shell model with ring and stringer stiffeners representing supporting components. Natural and forced vibration equations are derived using the Rayleigh–Ritz method with an enhanced Fourier series, enabling accurate simulation of complex elastic boundary conditions. The model is extended to optimize the stator-winding characteristic equation, yielding a semi-analytical solution for spring stiffness configuration. Key innovations include the analytical derivation of modal parameters, a rigorously formulated frequency response function, and the introduction of Rayleigh damping and excitation force potential energy. Multidimensional displacement response analysis demonstrates strong agreement with finite element results, validating the proposed equivalent digital mechanism model’s accuracy and robustness.