Archive of Applied Mechanics最新文献

Resin-mineral composite materials (RMC) have attracted much attention due to their excellent dynamic properties. However, the mechanical models related to RMC have not fully considered the complex interactions between components and interface transition zones (ITZ), and have also given less consideration to the influence of initial defects in the material, resulting in lower prediction accuracy of RMC mechanical models. To address the problem, based on composite sphere model, generalized autonomous method, and improved Mori–Tanaka method, the theoretical prediction model of RMC elastic modulus considering the influence of ITZ and pores is established in this study. Then, based on the micromechanical analysis method and combined with the theoretical data, the numerical prediction model of RMC elastic modulus considering the impact of pores and ITZ is founded. Furthermore, the influence of ITZ, pore, aggregate, and matrix parameters on the elastic modulus of RMC is investigated. The research results indicate that: (1) The error between the predicted RMC effective elastic modulus and the corresponding experimental values is within a reasonable range, indicating that the theoretical and numerical models proposed in this study are theoretically feasible. (2) ITZ and pore parameters have remarkable impact on the effective elastic modulus of RMC, indicating that it is indispensable to take into account ITZ and pores. (3) It is the elastic modulus of RMC that can be sensitive concerning the volume fraction and effective modulus of aggregate and matrix. The research results provide a theoretical basis for the design and application of RMC.

In cold regions, the water in rock fissures may freeze due to external temperature, leading to crack expansion and propagation, which induces rock damage. In this work, the rock fracture due to uniaxial expansion of tension cracks under freezing conditions was studied, and different pressures acting on the crack surfaces were analyzed from the fracture mechanics perspective. The corresponding physical model was also developed. Considering the physical and mechanical degradation, the damage to fracture toughness caused by freeze-thaw cycles was determined, and improvements were made to the existing brittle phase field finite element model (PFM). Numerical simulations and calculations were carried out at different stages throughout the entire freeze-thaw cycle to obtain the crack expansion morphological features at different stages. The results showed that hydrostatic pressure and freezing pressure are the primary loads driving the crack expansion, with freezing pressure playing a dominant role, whereas hydrostatic pressure contributes relatively little. The freezing period is the main stage of crack expansion governing the crack morphology. The thawing period accelerates the crack propagation rate, leading to rock failure. Also, the inclination angle of cracks may significantly influence rock failure. In general, rock failure results from different combinations of the initiation, expansion and connection of primary cracks under freeze-thaw action .

Large strain analysis is a challenging task, especially in fictitious or immersed boundary domain methods, since badly broken elements/cells can lead to an ill-conditioned global tangent stiffness matrix, resulting in convergence problems of the incremental/iterative solution approach. In this work, the finite cell method is employed as a fictitious domain approach, in conjunction with an eigenvalue stabilization technique, to ensure the stability of the solution procedure. Additionally, a remeshing strategy is applied to accommodate highly deformed configurations of the geometry. Radial basis functions and inverse distance weighting interpolation schemes are utilized to map the displacement gradient and internal variables between the old and new meshes during the remeshing process. For the first time, we demonstrate the effectiveness of the remeshing approach using various numerical examples in the context of finite strain elastoplasticity.

Bubble-based metamaterials have been extensively studied both theoretically and experimentally thanks to their simple geometry and their ability to manipulate acoustic waves. The latter is partly dependent on the structural characteristics of the metamaterial and partly dependent on the incident acoustic wave. Initially, the selection of specific structural characteristics is explained by presenting the Fourier transformations of the reflected waves for different arrangements of a bubbly meta-screen subject to Gaussian excitation. Next, the numerical study focuses on the changes induced to the response of a bubbly meta-screen, subject to different excitation pulses. For complex frequency excitation the bubbles delay to return to their equilibrium position for a couple of moments, hence the energy is stored in the system during those moments. This research provides a new strategy to actively control the response of a bubbly meta-screen and seeks to inspire future studies towards further optimization of the incident pulse based on the functionalities in need.

The present article contributes a new novel mathematical model influenced with the memory effect that endeavours to record the thermal responses inside a living tissue exposed to an oscillatory heat input on its outer surface. Heat transport inside the tissue is modelled with the hyperbolic equation involving three relaxation times. Analytical solutions of the significant field quantities—temperature, displacement and thermal stress are determined in the frequency domain by adopting the Laplace transform mechanism. Computational results are derived by inverting the field quantities from frequency domain to the physical domain. Memory influences are forecasted on the propagation of the thermo-mechanical waves inside the tissue by obtaining the influences of the kernel functions and time-delay quantity on the physical fields. Impact of the relaxation times is pronounced on the variances of the waves’ constituents. Graphical outcomes speculate that inclusion of the phase lags in heat transfer model supresses and stabilizes the speed of the waves. This study may support to the medical practitioners during thermal therapy and to develop the precised clinical equipment.

The crux of the present investigation is to come up with a mathematical model for the analysis of moving interfacial crack caused by SH-wave propagating in a composite strip featuring dissimilar orthotropic material. Wiener–Hopf methodology along with complex variable transform technique has been applied to determine the closed form analytical expression of SIF (stress intensity factor). Two different types of loading constraints, viz. NHL (non-harmonic loading) and HL (harmonic loading), on the edges of the crack have been studied. In addition to this, some special cases, viz. constant loading and stress free condition, following aforementioned loading constraints have also been taken into account for the moving crack in the considered composite strip. The limiting case for static condition leading to resonance-type phenomena has been presented for the subject under investigation. When computed numerically and depicted graphically, the profound impacts of distinct material and geometrical parameters on SIF for distinct loading constraints have also been manifested. The computational results bring out the fact that stress intensity factor falls off with rise in crack velocity when the edges of the crack are under NHL, whereas SIF shows reverse nature for HL.

The primary objective of this paper is to introduce innovative orthogonal power function series aimed at obtaining accurate nonlinear analytical solutions for axisymmetric circular thin plates. The main features of this paper are as follows: The deflection is expanded by the innovative orthogonal power function series. The Airy stress function, which satisfies the geometric deformation compatibility equation, responds to the nonlinear coupling relationships between the plate deflection and the in-plane force or displacement boundary conditions. The nonlinear algebraic equations are obtained by the energy variational method. Many comparisons are made with the results of related researchers. The present accurate solutions not only allow the problems to be solved perfectly and provide the most reliable basis for engineering design but also set new benchmarks for the verification of various nonlinear numerical and approximate analytical solutions. The developed methodology represents a significant improvement, providing better accuracy and computational efficiency compared to historical approaches. Therefore, the present method is more worthy of promotion.

This study presents an efficient and accurate method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures. The eigenequations for the surface waves in an ideal semi-infinite periodic structure and those eigenequations for the finite periodic structure within the bandgap are derived using the symplectic matrix. Based on these two eigenequations and the properties of the symplectic matrix, we show that the eigenfrequencies of the surface waves in an ideal semi-infinite periodic structure can be obtained using the eigenfrequencies within the bandgap of a finite periodic structure with different boundary conditions. The eigenfrequencies of the finite periodic structure can be calculated efficiently and accurately by the method combining the (2^{N}) algorithm and Wittrick–Williams algorithm. The proposed method is also extended to solve the surface waves in defective semi-infinite periodic structures. The accuracy and efficiency of the proposed method are demonstrated using several numerical examples.

Tall wind turbines are structures susceptible to high vibration levels, which may affect their optimal functioning and, ultimately, their overall structural stability. One alternative to minimize undesirable vibrations is to install vibration control devices. Various such devices are documented in the literature, with one noteworthy example being the tuned liquid column damper (TLCD), which is a vertical column filled with a liquid mounted at the top of the structure. When the main structure is dynamically excited, the appropriate TLCD vibrates out of phase with the structure, controlling its dynamic response. In this work, the nonlinear vibrations and control of a wind tower-nacelle-blade system subjected to an external harmonic force are studied. Nonlinear Euler–Bernoulli beam theory, together with the Rayleigh–Ritz method and Hamilton’s principle, are used to obtain a set of nonlinear equations of motion, which are, in turn, solved by the Runge–Kutta method. A TLCD device located at the top of the tower is used to control vibrations. First, the effect of blade rotation on the natural frequencies of the system is studied. Second, resonance curves are obtained to study the effect of blade rotation and the frequency of the external force on the nonlinear vibrations of the tower, and the effect of the TLCD on vibration control is also analyzed. This study provides valuable perspectives on the dynamics of offshore wind turbines, contributing to the development of wind energy systems that are more robust and adaptable.

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge–Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step, and thus, the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed s-sub-step implicit method with ( sle 6 ) can reach sth-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present s-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors’ previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms.