Archive of Applied Mechanics最新文献

The primary objective of this paper is to identify periodic orbits for solar sails within the oblate Earth-Moon Circular Restricted Three-Body Problem (CR3BP). Incorporating solar acceleration into the Earth-Moon system modifies the governing orbital equations, transforming the traditional CR3BP from an autonomous to a non-autonomous system. As a result, the procedure for identifying periodic orbits diverges from the conventional autonomous CR3BP method. Thus, this paper introduces a novel methodology to identify new periodic Halo and Lyapunov orbits within the non-autonomous CR3BP. Our proposed approach comprises four hierarchical steps: first, a surface of section simulation (Poincaré map) is conducted to obtain an initial approximation of the orbital state vector within the autonomous CR3BP. Second, a periodic orbit correction algorithm is developed using the autonomous CR3BP equations to acquire precise initial conditions. In the third step, initial conditions for solar sail periodic orbits are derived by applying the initial conditions of autonomous CR3BP periodic orbits as inputs to the periodic orbit correction algorithm, which is now executed using non-autonomous CR3BP equations. In the final step, a family of orbits is generated by gradually increasing the sail's characteristic acceleration. Our work addresses limitations in previous studies that relied on initial guesses derived solely from the unperturbed autonomous CR3BP reported in earlier research, which often resulted in the missing of numerous solar sail periodic orbits in the non-autonomous system. This approach enables the discovery of new periodic orbits within the Earth-Moon system, accounting for perturbations from the oblate primaries, including zonal harmonic terms from ({j}_{2}) to ({j}_{6}). The methodology is validated through simulations of solar sail Lyapunov and Halo orbits, offering a comprehensive understanding of the Earth-Moon CR3BP under non-autonomous conditions.

Bistable laminates (BSLs) are prone to vibration and dynamical snap-through behavior (STB) under the action of external environment. To control them, active vibration control using smart material is a terrific choice because it can minimize the impact on the stable configuration and properties of bistable laminate. This paper focuses on the active vibration control of rectangular asymmetric and anti-symmetric cross-ply bistable laminates under impact loadings using piezoelectric macro-fiber composite (MFC) whose size and position of paste are optimized instead of pasting randomly or middle of the laminate. The bistable laminated structures are simply supported at four selected points, while all the edges of them are free. With the aid of energy principle, governing equations of vibration of the bistable laminated structure are acquired with regard to two principal curvatures. The accuracy and validation of present formulation are verified by comparison studies of stable configurations and snap-through voltage of MFC. Then, the positions and geometric dimensions of piezoelectric macro-fibers are optimized by using genetic algorithm. The active vibration control of the bistable laminated structures subjected to step loading, decreasing loading, increasing loading and sinusoidal loading is studied for various control gains, geometries and different simply supported points.

In this study, a general method is developed for the torsional vibration of non-circular-shaped nanorods with varying boundary conditions using second-order strain gradient theory. In most of the studies in the literature, the cross section of the rods is considered to be circular. The reason for this is that the use of warping function is inevitable when the cross section geometry is not circular. For circular cross sections after torsion, the warping is very small and is considered to be non-existent. For non-circular sections, cross section warping should be taken into account in mathematical calculations. The cross section geometry is different from circular in this study, and the boundary conditions are not rigid, contrary to most studies in the literature. In this paper, the second-order strain gradient theory and the most general solution method are discussed. In some specific cases, it is possible to transform the problem into many studies found in the literature. The correctness of the algorithm is tested by comparing the resulting solutions with closed solutions found in the literature. The influence of some variables on the torsional frequencies is illustrated by a series of graphical figures, and the superiority of the applied method is summarized.

This study presents a comprehensive bending analysis of carbon nanotube-reinforced (CNTR) sandwich plates with varying stacking sequences, utilizing a non-polynomial zigzag theory based on the secant function. The secant function implicitly accommodates higher-order bending deformation with lesser computational costs and encompassing the cross-sectional warping. Principle of virtual work in conjunction with Navier’s solution methodology is used to develop the governing differential equation for the plate and to propose the solution of the system of equation, respectively. The analysis considers transverse deflection, normal stresses, in-plane shear stress, and transverse shear stresses to capture the complex behavior of CNTR sandwich composite plate structures. Different parametric studies are performed, exploring the effects of various reinforcement distributions of carbon nanotubes (CNTs) within the CNTR sandwich plate face sheet layers mainly, UD and FG. The superimposition of non-polynomial shear deformation theory based on secant function with zigzag functions provides accurate and efficient solutions, addressing the intricate stress distribution and deformation characteristics of CNTR sandwich plate. The findings offer valuable insights for the optimal design and application of CNTR sandwich plates in engineering fields, ensuring enhanced performance and structural integrity.

In the present study, maximum principal stress (MPS) criterion is incorporated into the reinforced isotropic solid (RIS) model to investigate the fracture behavior of orthotropic materials. Cracks are assumed along and across to the fibers in the linear elastic fracture mechanics context. Our experimental observations have shown that in macro point of view cracks in orthotropic materials always occur and grow between the fibers in the isotropic matrix media of orthotropic materials. When the composites are subjected to the pure mode I of loading which is across the fibers, the fibers do not react to the applied load. It means that they do not have effects on load bearing. On the other hand, when the mixed mode I/II of loading is applied to the same material, the fibers play a significant role in load bearing. In the present research, these effects are proposed in the form of reinforcement isotropic solid (RIS) coefficients. Taking an analytical approach, RIS coefficients are embedded into the MPS formulation to obtain the new extended maximum principal stress criterion (EMPS) with high accuracy. For the case of cracks across to the fibers, the crack kinking phenomenon has also been used and proved that when the cracks collide with the fibers, they kink and propagate along the fibers. To validate the proposed criterion, center notch disk tension (CNDT) specimens as appropriate ones for mixed mode I/II fracture test of orthotropic materials are fabricated which can cover the different range of mixed mode I/II loadings. Critical forces range from 452 to 1554 N for cracks along the fibers and 730–2399 N for cracks across the fibers. The fracture limit curves in comparison with the obtained experimental data indicate the compatibility of this criterion with the nature of fracture of the orthotropic materials.

This paper provides a detailed examination of the anisotropic thermal conductivity of a two-phase layered composite material with an imperfect interface. The development of a closed-form solution focuses on using the variational asymptotic method (VAM). Highlighting the one-dimensional periodicity of the unit cell, the study includes reduced thermal conduction at the imperfect interface between the two layers of a laminate. In addition to the VAM approach, the research introduces the finite element method (FEM) for the one-dimensional periodicity of the unit cell, for the reduced thermal conduction at the imperfect interface. Validation of both the derived VAM-based closed-form analytical solutions and the FEM solutions, under identical imperfect interface conditions, has been conducted by comparing the results with those present in the literature. The results show satisfactory agreement. Furthermore, the VAM-based analytical solution is extended to unidirectional composites with similar imperfect interface conditions, predicting effective thermal conductivity. These predictions are validated against various literature models, showing significant agreement, especially with lower-bound models. As a practical application, the closed-form solution derived from VAM is used to investigate the influence of an imperfect interface on thermal conduction with changes in volume fraction, providing valuable insights for practical applications.

The notch-induced anomalous growth of short fatigue cracks is investigated by the variational approach to fracture. The phase-field framework is extended to model the notch-induced anomalous growth of short cracks in metal components. The phase-field model is based on (1) the variational principle of fractures in elastic–plastic solids, (2) an elastic-perfectly plastic constitutive model and (3) a fatigue degradation function, with damage driven by plastic work. The notch-induced anomalous growth observed in experiments is reproduced by the present model. Our study suggests that the notch-induced anomalous growth of short fatigue cracks can be correlated with the growth of long fatigue cracks with the unified phase-field model. Furthermore, the plastic work done in the plastic zone ahead of a crack tip can be considered as the unified driving force dominating both the notch-induced anomalous growth of short fatigue cracks and the growth of long fatigue cracks.

To understand the shear characteristics of particles more comprehensively, the shear behavior of rigid particles, deformable particles, and breakable particles is investigated in this work. The rigid particles are modeled by the spheropolygon-based DEM. The deformable spheropolygon-based discrete element method is employed to study the shear behavior of deformable and breakable particles. Firstly, the influence of different circularization radii on rigid particles is studied. It is found that with a larger circularization radius, the edges and corners of the particles become less pronounced, and the particle shape approaches a circle, resulting in a smaller shear force. Secondly, the shear characteristics of breakable particles are examined. The experimental results indicate that particle fragmentation primarily occurs during the early stages of the shear process. Additionally, under high tensile strength, the impact of particle fragmentation on the mechanical properties of granular materials can be disregarded. Lastly, a comparison of shear forces is conducted among rigid, deformable, and brittle particles. The results show that particles assumed to be rigid generate the highest shear forces. On the contrary, deformable particles undergo deformation during shear, while brittle particles experience breakage, leading to a relatively loose packing and consequently less shear force.

In this study, we address the challenge of hidden damages in FRP composites, such as delamination, matrix cracking, and fibre breakage resulting from transverse low-velocity impact (LVI)—damages often elusive on the surface. Our methodology operates at the meso-scale, depicting laminates as stacked homogenized plies incorporating interfaces. To capture the mechanical behaviour and damages, we extend an existing nonlinear mean-field debonding model (NMFDM), accommodating asymmetric matrix plasticity (AAMP), fibre–matrix interface debonding failure, and in-plane progressive failure. In a key enhancement, we introduce a strain rate term to the AAMP model, addressing strain rate effects associated with LVI loading. Additionally, we incorporate a novel strain-driven 3D failure criteria, offering a more precise assessment of progressive failure subjected to LVI loading. The interfaces between plies are modelled using surface-based cohesive behaviour to capture interaction phenomena. To validate the developed NMFDM, we conduct impact simulations at various energies on a UD composite laminate consisting of AS4/8552 carbon fibre and epoxy matrix. These simulations showcase the predictive capability and accuracy of the NMFDM in capturing the intricate behaviour and damage progression of UD composites subjected to LVI.

The model of ice surface softening is represented by a system of three one-dimensional partial differential parabolic equations, taking into account the spatial inhomogeneity. Using one-mode and adiabatic approximations, an analytical soliton solution of a one-dimensional Ginzburg–Landau differential equation for the spatial normal distribution of shear strain to the ice surface is obtained. The analytical form of the numerical procedure for solving the equations, including initial and boundary conditions, is written on the basis of an explicit two-layer difference scheme. The distributions of time and stationary values of static friction force, kinetic friction force and temperature are constructed. Two cases were considered: 1) the upper and lower surfaces move with equal velocities in opposite directions; 2) the upper surface moves along the stationary lower surface. The dependencies of stress, strain and temperature on the coordinate in the normal direction to the surface are determined for different time series. It is shown that a stationary distribution of friction forces and temperature along the thickness of the near-surface ice layer is established with time. The values of the kinetic and static friction forces in the near-surface ice layer increase monotonically with distance from the friction surfaces, while the coordinate dependence of the temperature has a nonmonotonic appearance. The stationary values of the static friction force in the near-surface ice layer decrease with increasing temperature of the friction surfaces, indicating that the surface transforms to a more liquid-like state, while the coordinate dependence has a monotonically increasing form.