Mechanics of Solids最新文献

Anomalous guided waves appearing at a non-semisimple degeneracy of the fundamental matrix are observed and analyzed in the framework of the Cauchy sextic formalism. The non-semisimple degeneracy condition is explicitly constructed for the most general case of Lamb waves propagating in a traction-free layer with arbitrary elastic anisotropy. A new type of dispersion equation and the corresponding dispersion solution are obtained. The connection with surface waves of the non-Rayleigh type is discussed.

This study presents coupled flexural-torsional buckling analysis of the thin-walled columns with nonsymmetric open cross-sections in dimensionless and exact man- ner. Transfer matrix method coupled with iterative eigenvalue solution procedure is used to calculate nondimensional buckling loads of the thin-walled columns. For all end conditions considered, closed-form solutions are also presented for the comparison. The related tables show that, to some extent, all results are in good agreement. However, the closed-form solutions available in literature do not completely capture the buckling loads obtained using the transfer matrix method for fixed-fixed, fixed-pinned, and fixed-free end conditions. Therefore, there is a need to find new expressions for buckling parameter to calculate analytically buckling loads. This is carried out by using the Euler’s theory of columns for doubly symmetric cross sections. Through using these expressions, a good matching between the results obtained from the transfer matrix method and closed-form solutions is provided. On the other hand, as a case study, nondimensional solution procedure is applied to the optimization of critical buckling load of the columns. Nondimensionalization is a useful procedure for optimization such that it has led to a naturally scaled optimization model. Three column configurations with different numbers of segments in the longitudinal direction were considered and the maximum dimensionless critical buckling load without constraint violations is attained for the five-segmented column and it is 7.2, which represents 48.0415% gain.

This study developed a macroscopic finite element model of the human body wearing NIJ III body armor target against blunt impacts of DBP10 type 5.8 mm rifle bullets and a microscopic representative volume element (RVE) finite element model of myocardial tissue to conduct multiscale numerical simulations of myocardium under blunt impact effects. Experimental tests on the bullet penetration of ballistic panels were compared with numerical simulations to validate the effectiveness of the macroscopic finite element model. Uniaxial quasi-static compression tests on sheep hearts were carried out, and the constitutive parameters of cardiac muscle fibers and connective tissues in the microscopic RVE model of myocardial tissue were fitted using the inverse finite element method. The numerical simulation results indicate that in the macroscopic behind armor blunt trauma (BABT) numerical simulation, the maximum stress in the heart reached 373 kPa, with a maximum nominal strain of  0.19. The calculated injury score for the heart was 0, indicating no damage. In the microscopic RVE model of myocardial tissue, stress was mainly concentrated in the connective tissue, with cardiac muscle fibers generally exhibiting higher strains than the connective tissues. Localized areas of high pressure were observed in the connective tissue, which could compress capillaries in the connective tissue, potentially leading to minor bleeding as indicated by blood pressure values.

Two classical problems of the theory of elasticity are considered in the paper. The first is the Kelvin problem for an infinite space loaded with a concentrated force. The classical solution is singular and specifies an infinitely high displacement of the point of the force application which has no physical meaning. To obtain a physically consistent solution, the nonlocal theory of elasticity is used, which, in contrast to the classical theory, is based on the equations derived for an element of continuum that has small but finite dimensions, and allows one to obtain regular solutions for traditional singular problems. The equations of the nonlocal theory include an additional experimental constant, which has the dimension of length and cannot be determined for a space problem. Consequently, the second problem for an infinite plane loaded with two concentrated forces lying on the same straight line and acting in the opposite directions is considered. The classical solution of this problem is also singular and specifies an infinitely high elongation of the distance between the forces, irrespective of their magnitude. The solution of this problem is also obtained within the framework of the nonlocal theory of elasticity, which specifies a regular dependence of this distance on the forces magnitude. This solution also includes an additional constant which is determined experimentally for a plane problem.

Resonant sensors are extensively utilized in engineering applications owing to simple mechanical structure, high sensitivity, and reliable stability. To further enhance the performance of resonant sensors, a common approach in industrial production is reducing the size of components to increase sensitivity. However, the reduction in size leads to the weaker output signals, which increasing the difficulty of signal detection. To solve this problem, this paper proposed a cross-shaped resonator to enhance the output signal by increasing the electrode plate area. This approach was expected to alleviate the signal attenuation dilemma associated with miniaturization, thereby advancing sensor performance in various engineering applications. In the sensor design, the vibration characteristics analysis of the model as a continuous system was a key step in determining design parameters. The vibration equation of the continuous system for this structure was established and a comprehensive solution methodology was proposed. Furthermore, the natural frequency and amplitude-frequency characteristic curves of the system were investigated to ensure precise performance prediction. Using advanced micromachining techniques, we successfully fabricated a cross-shaped micro resonator. The subsequent experimental tests confirmed the theoretical correctness and practical feasibility of our design. The results provide valuable guidance and insights for optimizing the design and performance of resonant sensors.

The paper considers a non-classical optimization problem associated with the development of the production of new functionally graded materials. It is proposed to optimize the first natural frequency of oscillations by choosing the law of change in elastic moduli, and not the shape, as is done in most works devoted to optimization. This formulation of the problem becomes practically justified with the development of 3D printing and the production of FGM ceramics with specified properties. As an example, the problems of oscillations of a FGM rod and a FGM beam with spring boundary conditions at one of the ends are considered.

The paper presents outcomes of the study of short-timed shock action of the pulse electron beam on the aluminum obstacle. Analysis of the generation of the stress wave near the loaded surface based on the experimental data is provided. It is proved that wave generation in this case in contrast to the action of laser beam takes place inside material in the area governed by the depth of electrons invasion. Relaxation of the stress wave starts from the boarder of this area. It was established that strongly non-equilibrium processes are take place in this relaxation area causing dramatic change depending on the shock parameters of the velocity of the stress and strength waves compared theirs stationary values. It is underlined that relaxation process has solo-wave nature in spite of the high stress amplitude. Separation of the elastic and plastic stresses propagation takes place only after the end of relaxation process.

The mechanical properties of metamaterials with different cellular internal structures were experimentally studied when perforated along the normal by a rigid spherical striker. Auxetic and non-auxetic samples of metamaterials with a chiral structure of cells, respectively, in the form of concave or convex hexagons, were produced using a 3D printer from e-PLA plastic. Based on the penetration experiments, the properties of chiral auxetic and non-auxetic samples of the same mass were compared for the cases when there was air inside the cells and when the cells were filled with gelatin. The relative loss of kinetic energy of the striker when perforating gelatin-filled samples was significantly higher for the auxetic metamaterial than for the non-auxetic one. For unfilled (“air”) samples, the relative loss of kinetic energy was slightly higher for the nonauxetic.

In this article, the performance of mechanical resistance against failure of mechanical structures under bending load was studied by the use of a hybrid sandwich composite (Magnetorheological Elastomer (MRE) – honeycomb). Accordingly, a series of four-point bending mechanical tests were carried out. In addition, a comparison of the force-deflection responses, the values of the maximum forces supported by each sample before damage were determined. Through the additional effect of the MRE core, the hybrid sandwich composite samples presented the best performances in terms of energy absorption-dissipation, and thanks to the effect of the honeycomb part, the Hybrid sandwich composite samples presented the best performance in terms of mechanical strength. To validate the performance of these developed hybrid structures, the numerical results are compared with the corresponding experimental results.

In continuum mechanics (especially in hydroaeromechanics), methods of modeling flow (deformation) by characteristic numbers are widely used. The present study is devoted to the search for characteristic combinations of constitutive thermoelastic modules, geometric and thermomechanical parameters of the boundary value problem. Modeling the micropolar solids deformation by characteristic numbers is characterized by a sufficiently large number (13) of constitutive modules. The constitutive equations, the dynamic equations and the heat conduction equation for a semi-isotropic micropolar thermoelastic continuum are derived in a linear approximation. A dimensional analysis of the governing system of differential equations is carried out. A physically consistent sets (9 primary and several arbitrary) of dimensionless characteristic combinations of constitutive constants is proposed. The characteristic numbers for harmonic waves propagating along the axis of a stress free thermally insulated long cylindrical semi-isotropic thermoelastic waveguide are obtained and discussed.