Search Results (23)

Determining the mechanical properties of a composite material represents an important stage in its design and is generally a complicated operation. These values are influenced by the topology and geometry of the resulting composite and the values of the elastic constants of the components. Due to the importance of this subject and the increasing use of composite materials, different calculation methods have been developed over the last fifty years. Some of the methods are theoretical, with results that are difficult to apply in practice due to difficulties related to numerical calculation. In the current paper, using theoretical results offered by the homogenization theory, values of engineering elastic constants are obtained. The finite element method (FEM) is used to determine the stress and strain field required in these calculations; this is an extremely powerful and verified calculation tool for the case of a material with any type of structure and geometry. In order to minimize errors, the paper proposes the method of least squares, a mathematical method that provides the best estimate for the set of values obtained by calculating FEM. It is useful to consider as many load cases as possible to obtain the best estimates. The elastic constants for a transversely isotropic material (composite reinforced with cylindrical fibers) are thus determined for a real case. Full article

In this study, the physical properties of garlic just before collection were investigated, and garlic-collecting conditions are presented as basic data of design factors that can be utilized during the development of garlic collectors. The physical properties were subdivided into geometrical properties and mechanical properties, and the ecotype of garlic was divided into CSG (cold-season garlic) and WSG (warm-season garlic). Geometrical properties were compared between CSG and WSG by measuring the average weight, length, width, number of kernels, volume, and density of each cultivar, and WSG showed higher geometrical properties in all geometrical properties. In addition, there was garlic on the incomplete side of WSG, and shape non-uniformity was higher than that of CSG. There was no significant difference in the average Poisson’s ratio of mechanical properties. In the case of the modulus of elasticity, Namdo cultivars showed the lowest value at 15.52 MPa. The average allowable compressive stress measured using Hooke’s law was the lowest in the Uiseong cultivar (204.33 kPa) and the highest in the Danyang cultivar (376.42 kPa). The static friction coefficients among the four different materials by cultivar exhibited a commonality of being highest in aluminum and generally lowest in plastic. It is expected that the design of the garlic collector will be carried out in consideration of garlic when developing it using up-to-date physical properties of garlic just before collection. Full article

Slate typically possesses a pronounced layered structure and tends to soften when exposed to water, leading to numerous detrimental effects on the construction of related underground projects. In this study, X-ray diffraction (XRD) analysis was first performed to investigate the mineral composition of the typical slate from Changsha, China. Then, uniaxial and triaxial compression tests under varying bedding angles (i.e., 0°, 30°, 45°, 60°, and 90°) and moisture levels (i.e., dry state, natural state, and saturated state) were conducted to explore the anisotropy characteristics and susceptibility to water-induced softening of the slate. The results reveal that: (1) The exposure of slate to water exacerbates the deterioration of its layered structure, making it more prone to shear failure along the bedding planes. Furthermore, the energy released during shear-slip damage is reduced, which is macroscopically manifested by the decrease in slate brittleness and the increase in plasticity. (2) The slate’s compressive strength, elastic modulus, and cohesion vary in a U-shaped pattern with the increase in bedding angles. However, Poisson’s ratio and internal friction angle are slightly affected by the bedding angle and water content, which do not exhibit a clear variation pattern. (3) In addition, the formulations for strength and stiffness predictions of slate were also discussed in this study. The results show that the modified Hoek–Brown criterion characterizes the uniaxial and triaxial compressive strengths of slate more accurately, and the generalized Hooke’s Law more effectively predicts the elastic modulus. Full article

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer. Full article

Microforce plates are indispensable tools for quantitatively evaluating the behavior of small objects such as tiny insects or microdroplets. The two main measurement principles for microforce plates are: the formation of strain gauges on the beam that supports the plate and the measurement of the deformation of the plate using an external displacement meter. The latter method is characterized by its ease of fabrication and durability as strain concentration is not required. To enhance the sensitivity of the latter type of force plates with a planar structure, thinner plates are generally desired. However, brittle material force plates that are both thin and large and can be fabricated easily have not yet been developed. In this study, a force plate consisting of a thin glass plate with a planar spiral spring structure and a laser displacement meter placed under the plate center is proposed. The plate deforms downward when a force is exerted vertically on its surface, resulting in the determination of the applied force using Hooke’s law. The force plate structure is easily fabricated by laser processing combined with the microelectromechanical system (MEMS) process. The fabricated force plate has a radius and thickness of 10 mm and 25 µm, respectively, with four supporting spiral beams of sub-millimeter width. A fabricated force plate featuring a sub-N/m spring constant achieves a resolution of approximately 0.01 µN. Full article

With improvements in lubrication and material strength, the power transmitted by plastic gears has increased significantly. To develop high-performance transmission systems, it is necessary to gain deep insights into the dynamic characteristics of plastic gears. However, because plastics are viscoelastic materials, they do not obey Hooke’s law, which is the basis of traditional gear dynamic models. In this study, a refined dynamic model for an epoxy gear pair considering material viscoelasticity and extended tooth contact is established, and the differences in the dynamic responses between an epoxy and a steel gear pair are compared with respect to the dynamic meshing force and dynamic transmission error. The results show that: (1) the plastic gear can restrain the meshing impact, it has a generally lower dynamic meshing force than steel gear pair; (2) the position accuracy is the weak point of plastic gears, and this is significantly affected by the rotation speed; (3) the way to indirectly evaluate the dynamic meshing force by measuring the dynamic transmission error, which is often used for metal gears and is less effective for plastic gears. Full article

The aim of this paper is to present some important practical cases in the analysis of the creep response of unidirectional fiber-reinforced composites. Some of the currently used models are described: the micromechanical model, homogenization technics, the Mori–Tanaka method, and the finite element method (FEM). Each method was analyzed to determine its advantages and disadvantages. Regarding the accuracy of the obtained results, comparisons are made with experimental tests. The methods presented here are applied to carbon-fiber-reinforced composites, but these considerations can also be applied to other types of composite materials. Full article

The incorporation of bioactive ceramic into polyether ether ketone (PEEK) was expected to improve the bioinertia and hydrophobicity of pure PEEK, further facilitating osseointegration and bone ingrowth. However, the addition of bioceramic also changes the anisotropy of mechanical properties and failure mechanism of composite. Therefore, three-dimensional printed (3D-printed) PEEK/hydroxyapatite (HA) composite filaments with differing proportions (HA content: 10–30 wt%) were prepared using physical mixture and melting extrusion processes. The tensile elastic modulus and tensile strength of composite filaments were tested experimentally. These microscopic models, with multiple diameter variations and differing dispersity of HA particles, were built to estimate mechanical properties using finite element analysis. Based on a generalized version of Hooke’s Law, the influence of diameter variation and particle clustering on the elastic modulus was evaluated. The mathematical relationship between the elastic modulus and volume fraction of the bioceramic was established using the Halpin–Tsai model. The results showed that with an increase in HA content from 10 wt% to 30 wt%, the elastic modulus of the composite increased from 2.36 GPa to 2.79 GPa, tensile strength decreased from 95 MPa to 74 MPa, and fracture elongation decreased from 63% to 23%, presenting brittle fracture failure. When the dispersion of particles was uniform, the elastic modulus was less affected by diameter variation, but the modulus anisotropic coefficient was greatly affected by the composition ratio, particle diameter, and dispersity. Hence, 3D-printed PEEK/HA composite filaments can meet the strength requirements of human bone, and understanding the influence of mechanical anisotropy plays a very important role in the design, manufacture, and clinical application of medical implants. Full article

During the mining process of the near-vertical seam, there will be movement and collapse of the “roof side” rock layer and the “overlying coal seam,” as well as the emergence of the “floor side” rock layer roof which is more complicated than the inclined and gently inclined coal seams, which causes problems with slippage or overturning damage. With the increase of the inclination of the coal seam, the impact of the destruction of the immediate roof on the stope and roadway gradually becomes prominent, while the impact of the destruction of the basic roof on the stope and the roadway gradually weakens. The destruction of the immediate roof of the near-vertical coal seam will cause a large area of coal and rock mass to suddenly rush to the working face and the two lanes, resulting in rapid deformation of the roadway, overturning of equipment, overturning of personnel, and even severe rock pressure disaster accidents, all of which pose a serious threat to coal mine safety and production. It is necessary to carry out research on the mechanical response mechanism of the immediate roof of near-upright coal seams, to analyse the weighting process of steeply inclined thick coal seam sub-level mining. A four fixed support plate model and top three clamped edges simply supported plate model for roof stress distribution are established before the first weighting of the roof during the upper and lower level mining process. The bottom three clamped edges simply supported plate model and two adjacent edges clamped on the edge of a simply supported plate model are established for roof stress distribution before periodic weighting of the roof during the upper and lower level mining process. The Galerkin method is used to make an approximate solution of deflection equation under the effect of sheet normal stress, and then roof failure criterion is established based on the maximum tensile stress strength criterion and generalized Hooke law. This paper utilizes FLAC^3D finite element numerical simulation software, considering the characteristics of steeply inclined thick coal seam sub-level mining. It undertakes orthogonal numerical simulation experiment in three levels with different depths, coal seam angles, lateral pressure coefficient, and orientation of maximum horizontal principal stress, and translates roof stress of corresponding 9 simulation experiment into steeply inclined roof normal stress. We conclude that the distribution law of normal stress along dip and dip direction of a roof under the circumstance of different advancing distances and different sub-levels. The caving pace of first weight and periodical weight were counted under the effect of the roof uniform normal stress. It can better predict the weighting situation of the working face and ensure the safe, efficient, and sustainable mining of coal mines. Full article

The behaviors of functionally graded (FG) engineering structures are influenced by various parameters, such as the boundary temperature, the angular velocity, variations in the thickness, the weight of the structure, and the loading state. The thermo-elastic characteristics of FG rotating circular disks under the loading of contact forces were investigated. Hooke’s law in plane stress problems was applied to derive a pair of partial differential equations and a finite volume method was developed due to the complexity of the governing equations. The thermo-elastic characteristics of the FG rotating disks were investigated according to the variations in their outer boundary temperature and angular velocity. The increase in the outer boundary temperature caused crack generation at the inner surface of the circular disk and on the opposite side to the loading point. The increase in the angular velocity caused unstable thermo-elastic behaviors near the area of the outer boundary surface, especially at $0.7<\left(\mathrm{r}-\mathrm{a}\right)/\left(\mathrm{b}-\mathrm{a}\right)$< 0.9, and may have led to crack generation at the outer surface of the rotating disk. These results may be applied to the design of functionally graded circular cutters or grinding disks undergoing contact forces to produce proper and reliable thermo-elastic characteristics for practical applications. Full article

Ultra-high-performance concrete (UHPC) is an advanced concrete with superior mechanical strength, ductility and durability properties. However, the influence of steel fiber on its constitutive laws and the specimen geometric dimension effect on its strength had not been paid enough attention. To investigate the effect of steel fibers on the properties of UHPC, specimens with different fiber volume contents and fiber types were tested. Meanwhile, the mechanical properties of UHPC at different ages from 3 days to 28 days were conducted. Moreover, specimens with various geometric dimensions were also prepared to study the effect of specimen geometric dimensions (dog-bone-shaped, prism and cylinder specimens) on the properties of UHPC. The results indicated that elastic modulus, tensile peak stress and the corresponding strain increased as the fiber volume content and curing age increased. Specimens with hooked-end fibers exhibited better tensile performance than those with straight fibers. Furthermore, different geometric dimensions of specimens significantly influenced the tensile properties of UHPC. Based on the experimental results, conversion factors were suggested for the transformation of strength obtained from specimens with different geometric dimensions to reference specimens. In addition, both compressive and tensile constitutive laws were proposed to generate the stress–strain relationship of UHPC. Full article

Due to the complexity of landing environments, precision guidance and high-precision control technology have become key to the rope-hook recovery of shipborne unmanned aerial vehicles (UAVs). The recovery process was divided into three stages and a reasonable guidance strategy had been designed for them, respectively. This study separated the guidance and control issues into an outer guidance loop and an inner control loop. The inner loop (attitude control loop) controled the UAV to follow the acceleration commands generated by the outer loop (trajectory tracking loop). The inner loop of the longitudinal controller and the lateral controller were designed based on active disturbance rejection control (ADRC), which has strong anti-interference ability. In the last phase, the outer loop of the longitudinal controller switched from a total energy control system (TECS), which greatly decoupled the altitude channel and speed channel, to the proportional navigation (PN) guidance law, while the outer loop of lateral controller switches from the proportional control law based on the L₁ guidance law, which can reduce the tracking error and deviation, to the PN guidance law, which considerably enhances the tracking precision. Finally, the simulation data and flight test data show that the controller has strong robustness and good tracking precision, which ensures safe rope-hook recovery. Full article

This paper aims to consider approximation-estimation tests for decision-making by machine-learning methods, and integral-estimation tests are defined, which is a generalization for the continuous case. Approximation-estimation tests are measurable sampling functions (statistics) that estimate the approximation error of monotonically increasing number sequences in different classes of functions. These tests make it possible to determine the Markov moments of a qualitative change in the increase in such sequences, from linear to nonlinear type. If these sequences are trajectories of discrete quasi-deterministic random processes, then moments of change in the nature of their growth and qualitative change in the process match up. For example, in cluster analysis, approximation-estimation tests are a formal generalization of the “elbow method” heuristic. In solid mechanics, they can be used to determine the proportionality limit for the stress strain curve (boundaries of application of Hooke’s law). In molecular biology methods, approximation-estimation tests make it possible to determine the beginning of the exponential phase and the transition to the plateau phase for the curves of fluorescence accumulation of the real-time polymerase chain reaction, etc. Full article

With the typical composite roof roadway and roof fall accidents in the Guizhou Province of China as the research background, the expression of damage parameters of composite roof was deduced according to Weibull statistical distribution, generalized Hooke’s law and Mises yield criterion, and the influence of shape and scale parameters of Weibull on damage characteristic was discussed. Based on the infinite slab theory, the expressions of deflection and layer separation of each layer of the composite roof were obtained, the critical load expression of each delamination was determined, and the influence of roadway width, overlying strata load, elastic modulus, shape parameters and scale parameters on the stability of composite roof was explored. The research shows that the bolt support can effectively reduce the layer separation between the composite roofs and enhance the stability of the composite roof. On this basis, it is proposed that for the surrounding rock control problem of roadways with composite roof, the active support technology with bolts as the core should be adopted. Full article

The process of heat exchange between two fluids of different temperatures and separated by a solid wall occurs in many engineering applications. Log mean temperature difference and effectiveness-NTU methods are widely used to assist in the design of heat exchangers. However, the two methods focus on overall analysis and cannot show the local temperature distributions. This paper obtains the mathematical solutions to the temperature profiles in an ideal counterflow heat exchanger. The aim of this research is to explain the phenomenon called the “entropy generation paradox”, which indicates a discrepancy between effectiveness and optimal entropy generation. The theoretical analysis reveals that the temperature curves are exponential functions when the heat capacity rates of the two streams are different; otherwise, the curves are linear functions. A heat exchanger is demonstrated to draw the temperature profiles under different working conditions. Local entropy generation rates are determined by the ratio of local stream temperatures in the form of a hook function. To realize a certain heat duty, there are many stream flow rate couples, and each couple results in a different entropy generation profile and obtains a corresponding total entropy generation. The helical steam generator of a high-temperature gas-cooled reactor is analyzed in this article and the principle of equipartition of entropy generation is confirmed. This principle indicates that, among the many working conditions to achieve a certain heat duty, a heat exchanger characterized by a nearly constant entropy production gives the best second law efficiency possible in order to achieve the best energy conversion. Full article