Mechanics of Solids最新文献

The impact contact of the plate by the rod exhibits different properties from the impact of the sphere. Upon impact, the excitation stress wave reflects back to the rod’s free end, while the bending wave propagates around the plate. Therefore, the wave propagation response in the rod significantly affects the whole impact response process. The mid-rod graded configuration can adjust the wave propagation response. Different graded rod types were designed and implemented. We constructed a variable coefficient wave equation to describe the wave propagation response in the rod. The Zener contact law was applied to model bending wave propagation in the plate for the contact boundary conditions. Subsequently, the Laplace transform was employed to solve the wave equation and give expressions such as the relationship between the displacement and the contact force. The effects of graded configuration and contact stiffness on wave propagation and impact contact response were investigated. Results show that the graded configuration can effectively adjust the wave propagation behavior of the rod and affect its rebound velocity, contact time, and energy conversion. These findings can be used to guide the design of heterogeneous impactors and to explore the mechanism of high-frequency oscillation of low-velocity impacts.

The transient impact response of piezoelectric structures in ultrafast heating condition is critical for lowering unwanted vibrations in the smart sensors/actuators energy harvester systems, whereas the experimental validated cubic-polynomial temperature-dependent material properties are still not considered on this topic. To address this issue, this paper aims to establish the Lord-Shulman (L-S) piezoelectric thermoelasticity model with the cubic-polynomial temperature-dependent material properties. To solve the nonlinear governing equations, the nonlinear time-domain finite element method is developed. The proposed model and numerical approach are applied to investigate transient thermo-electromechanical impact responses of two-dimensional orthotropic piezoelectric plate of crystal class mm2. Dimensionless results indicate that the cubic-polynomial temperature-dependent parameters greatly influence the nonlinear transient thermo-electromechanical responses, lifting the electrical energy harvesting capability and heat wave propagation in the orthotropic piezoelectric plate.

The hot deformation behavior of AA2099 Al-Li alloy was analyzed constitutively to model flow stress during thermo-mechanical processing. In order to obtain the true stress-strain curve data of AA2099 Al-Li alloy, isothermal uniaxial compression tests were carried out using a Gleeble 3800D thermo-mechanical simulator in the strain rate range of 0.01–10 s^–1 and deformation temperature range of 360 – 520°C. Based on the experimental data obtained here, three types of constitutive material models were developed: modified Johnson-Cook model, strain compensated Arrhenius model and microstructure-based model. For these three models, a modification was made to increase the prediction accuracy of high temperature flow stress. The prediction accuracy was estimated by means of the average absolute relative error and correlation coefficient, with 5.09% and 0.9928 for the modified Johnson-Cook model, 6.12% and 0.9820 for the strain compensated Arrhenius model, and, 1.58% and 0.9994 for the microstructure-based model. The flow stress predicted by the proposed microstructure-based model was in good consistent with the experimental results. This indicates that the proposed microstructure-based model can describe the hot deformation behavior of AA2099 Al-Li alloy very accurately. The developed constitutive material models are of great significance in the simulation and optimization of hot working processes of AA2099 Al-Li alloy.

Low-frequency vibration in fluid-conveying pipes remains a critical challenge in engineering applications. To address this issue, this paper designs a locally resonant double-layered pipe (LR-DLP) structure constructed by periodically inserting cylindrical ring units between two concentric pipes with different diameters. The proposed cylindrical ring unit incorporates a triple-layered cylindrical ring comprising an outer rubber layer, a middle metal layer, and an inner rubber layer. For torsional vibration analysis, a double-layered shaft torsional equivalent model (DLS-TEM) is established by equivalently representing cylindrical rings as a torsional spring-inertial disk-torsional spring system. While a double layered beam bending equivalent model (DLB-BEM) with radial spring-mass-radial spring system is established for bending vibration analysis. The differential equation governing bending vibration of fluid-conveying pipes are derived based on Hamilton’s variational principle. The Transfer Matrix Method (TMM) and Plane Wave Expansion (PWE) method are further developed for characterizing both torsional and flexural bandgaps in the LR-DLP structure, with particular emphasis on the flexural wave attenuation performance under fluid-conveying conditions within the inner pipe. Finite element numerical simulations are systematically performed in COMSOL Multiphysics for the finite-periodic locally resonant double-layered pipe (LR-DLP) structure. The results demonstrate excellent agreement with theoretical analysis in both torsional and flexural bandgap characteristics. Parametric studies reveal the influence of structural dimensions properties on bandgap characteristics, demonstrating the effectiveness of the proposed design in suppressing low-frequency vibrations.

A thermal shock problem in a semiconducting rod under modified Green-Lindsay theory of length l is discussed. The partial differential equations are simplified by applying the Laplace transformation technique. It is assumed that one end of the rod is subjected to a sudden heat source. The governing equations of a semiconducting medium are transformed using the Laplace transform, and analytical expressions for displacement, stress, carrier density, and temperature distribution are obtained. These transformed components are then inverted by the numerical inversion method and are presented graphically to show the results in different theories of thermoelasticity.

The Discrete Element Method (DEM) is a numerical technique proposed for solving mechanics problems of non-continuous media. However, applications of DEM in continuous media structures are relatively limited. In this manuscript, a modification of the torsional spring stiffness coefficient of the simply supported boundary contact element is proposed based on our previous work. Then, the plate DEM based on modifying the torsional spring stiffness coefficient is adopted to solve the load-bearing problems of cylindrical shells. This study aims to investigate the validity of using the plate DEM based on modification of the torsional spring stiffness coefficient for nonlinear large deformation analysis of shell-type structures. Compared to traditional methods, continuity of displacement and deformation coordination are not required for the plate DEM, and there is no need to assemble a stiffness matrix, so matrix non-convergence problems are evitable. To evaluate accuracy of the developed plate DEM, several popular benchmark problems of geometric nonlinearity for shells are solved by adopting the plate DEM. The results demonstrate that the proposed numerical method can obtain highly accurate solutions in the nonlinear large deformation numerical calculations of shells, which further confirms the feasibility of the plate discrete element method in solving the geometric nonlinear problems of plate and shell structures.

To mitigate the limitations associated with strength degradation in fatigue life prediction methodologies, a refined nonlinear cumulative damage model is proposed. This model constitutes an enhancement of the foundational Manson-Halford (M-H) theory by incorporating load interaction coefficients. These coefficients explicitly account for the complex interactions between successive loading cycles, a critical factor influencing damage evolution under variable amplitude loading. Validated under two-level loading conditions, the proposed model achieves superior predictive accuracy compared to the original M-H formulation: 80% of its predictions exhibit relative errors below 30%, significantly improving upon the M-H model’s 68% accuracy. The proposed model demonstrates greater conservatism, with 90% of predictions falling within a 1.5x lifetime factor and 98% within a 2x lifetime factor. This conservatism, arising from explicit consideration of load interactions and strength degradation, enhances design safety by mitigating premature failure risk while maintaining balanced error distributions to avoid excessive overdesign. Under multi-level loading spectra, the proposed model consistently yields lower relative prediction errors than its M-H model. Critically, the model maintains practical utility, requiring only standard fatigue test data for parameter determination and introducing no additional fitting parameters. Consequently, this enhanced nonlinear cumulative damage model offers a viable and improved engineering tool for predicting the fatigue life of metallic (steel and aluminum alloys) components under variable loading histories.

A quaternion solution of the problem on optimal rotation of a rigid body (spacecraft) from an arbitrary initial to a specified angular position with constraints on the control variables is presented. A combined quality functional has been used to optimize the control process. It combines in a given proportion the sum of time and control efforts spent on the rotation and the integral of the kinetic energy of rotation during the rotation. Based on L.S. Pontryagin’s maximum principle and quaternion models of controlled motion of a rigid body, a solution of the problem is obtained. The properties of optimal motion are disclosed in an analytical form. Formalized equations and calculation formulas are written to construct the optimal rotation program. Analytical equations and relations for finding optimal control are given. Key relations that determine the optimal values of the parameters of the rotation control algorithm are given. A constructive scheme for solving the boundary value problem of the maximum principle for arbitrary rotation conditions (initial and final positions and moments of inertia of the rigid body) is also given. In the case of a dynamically symmetric rigid body, a solution of the reorientation problem in closed form is obtained. A numerical example and the results of mathematical modeling, confirming the practical feasibility of the developed method for controlling the orientation of a spacecraft, are presented.

The study investigates the influence of the sliding effect between the contacting inner layers of the shell mold, as well as the external force impact of the supporting filler on its crack resistance. It is shown that the absence of friction between the layers reduces the crack resistance of the multilayer shell mold, while the presence of friction between the supporting filler and the shell mold increases it.

In this paper, for the first time, a solution is constructed to the dynamic contact problem of the time-harmonic effect of a deformable die on a layer of anisotropic composite material. It is assumed that the die occupies the region of the first quadrant and has a complex rheology, in particular, the linear theory of elasticity. The paper uses a universal modeling method developed by the authors, which makes it possible to apply the block element method to both differential and integral equations. The solutions of boundary value problems for deformable dies of complex rheology are constructed in the form of decompositions according to the solutions of boundary value problems for materials of simple rheology described, for example, by Helmholtz equations. This possibility was previously established for materials of a wide range of rheology by using Galerkin transformations. The solution of the two-dimensional Wiener-Hopf integral equation is obtained both in coordinate form and in Fourier transforms. This makes it particularly convenient to further study it using analytical or numerical methods using standard computer programs. They will make it possible to identify certain properties of composites used as structural materials in various engineering technologies dictated by types of anisotropies, as well as in issues of seismology in the study of seismicity in mountainous areas. The constructed integral representation of the solution of the contact problem, which makes it possible to identify terms describing the concentrations of contact stresses under the die, makes it possible to select the soles of deformable dies or the properties of the materials used to get rid of undesirable concentrations of contact stresses or enhance them. Since Vorovich resonances can occur during vibration in contact problems with a deformable die, systems of equations are constructed in the work that allow, when solved, to obtain a dispersion equation for finding resonant frequencies.