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In order to improve the resistances to delamination, damage tolerance, some in-plane and out-of-plane properties of composite materials, a through-thickness reinforcement must be provided. This through-thickness reinforcement is achieved by stitching multi-axial warp knit (MWK) fabrics used as preforms for the fabrication of composite materials. The MWK fabrics are constructed with layers of insertion fiber bundles in the warp, weft and bias directions. In order to correlate the microstructure of a preform with the elastic properties of stitched MWK composite, the analytical model for stitched MKW composite is developed. The overall geometry and geometric parameters of a representative volume are determined from the photomicrographs of cross sections of the fabricated composite specimens. The various elastic properties of MWK fabric composites are predicted as functions of various geometric parameters using an averaging method. The experimental results are compared with the predicted results in order to validate the suggested model. It is found that the predicted elastic properties are in reasonably good agreement with the experimental values.

In this paper, the oblique penetration and perforation process has been analyzed in three stages.

In the first and second stages, the entering of projectile nose into the target and the tunneling process have been considered, respectively. The calculation of force in these stages is based on spherical cavity expansion method. In both of these stages, the friction coefficient has been considered to vary with velocity changes during the process. At the end of each time step, the velocity components are readily determined by solving the equations of motion. The plug formation is modeled in the third stage, where the residual velocity is calculated by the application of energy balance.

In summary, a new approach has been developed to determine the residual velocity, the exit angle, and the depth of penetration of projectiles with spherical nose into the targets, for both cases of oblique and normal striking. The predicted results from this analytical model are in good agreement with experimental and analytical results from other researchers.

With the increase of the complexity of circuits, fast estimation can provide some vital information for optimal layout decisions. Fast congestion prediction plays an important role in the physical layout of VLSI design. In this paper, we present a probabilistic estimation approach with via minimization constraints. Our model is more realistic than previous models. It has more flexibility for wires to have more usage area to bypass congested regions and blockages. The experiment on routing benchmarks demonstrates the effectiveness of our approach.

Dimensions of metal–oxide–semiconductor field effect transistor (MOSFET) have been scaled down for decades to maintain the performance. So, as a result of aggressive scaling, gate oxide thickness approaches its manufacturing and physically limiting value of less than 2 nm in nano regime. Under such circumstances, gate leakage (tunneling) current has become a critical problem in nano domain as compared to subthreshold leakage current. Consequently, accurate quantitative understanding of gate tunneling leakage current is very important especially in context of low power VLSI application. In this work, gate tunneling currents have been modeled including the inevitable nano scale effects for a MOSFET having different high-k dielectric spacer such as SiO₂, Si₃N₄, Al₂O₃, HfO₂. The gate current model is compared and contrasted with santaurus simulation results and reported experimental result to verify the accuracy of the model. The agreement found was good, thus validating the developed analytical model. It is observed that neglecting nano scale effects may lead to large error in the calculated gate current. It is found in the results that gate leakage current decreases with the increase of dielectric constant of the gate spacer. Further, it is also reported that the spacer materials impact the threshold voltage, on current, off current, drain induced barrier lowering, and subthreshold slope of the device.

Parallel-rule firing approaches have been proposed to improve the performance of production systems. However, few models have been developed to measure the performance of parallel-rule firing approaches. There are three approaches to evaluating system performance, namely, analytical modeling, simulation, and system prototyping or implementation. Analytical modeling has its advantage in being cost effective and providing a powerful tool for studying various aspects of system performance by varying system parameters. Since analytical modeling has been very successfully used in evaluating database system performance, we develop such a model for parallel production systems, where rule firing is modeled as a transaction. Both resource contention and data contention are modeled in detail and the performance of locking, timestamp and optimistic approaches is analyzed. We show that significant speedup can be gained in parallel rule execution. Our main contribution is in the insights into parallel-rule firing provided by parametric modeling.

In this study, with the consideration of pore size distribution and tortuosity of capillaries, the analytical model for gas diffusivity of porous nanofibers is derived based on fractal theory. The proposed fractal model for the normalized gas diffusivity (D_e/D₀) is found to be a function of the porosity, the area fractal dimensions of pore and the fractal dimension of tortuous capillaries. It is found that the normalized gas diffusivity decreases with increasing of the tortuosity fractal dimension. However, the normalized gas diffusivity is positively correlated with the porosity. The prediction of the proposed fractal model for porous nanofibers with porosity less than 0.75 is highly consistent with the experimental and analytical results found in the literature. The model predictions are compared with the previously reported experimental data, and are in good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. Every parameter of the proposed formula of calculating the normalized gas diffusivity has clear physical meaning. The proposed fractal model can reveal the physical mechanisms of gas diffusion in porous nanofibers.

The effective thermal conductivity of porous media is of steady interest in the design of new materials. In this study, an analytical model for dimensionless effective thermal conductivity of media embedded with fracture networks of the power law length distributions is proposed. It is found that the proposed dimensionless effective thermal conductivity is a function of micro-structural parameters of media, such as the porosity $(\varphi )$ and fracture orientation (dip $𝜃$ and azimuth $\phi$). The present results show that the dimensionless effective thermal conductivity of the media increases with the increase in the ratio $(k_s/k_f)$ and the power law exponent $\alpha$ at $k_s/k_f<1$. Inversely, when $k_s/k_f>1$, it decreases with the increase in the power law exponent $\alpha$. In addition, the dimensionless effective thermal conductivity is gradually independent of the orientation as the ratio $k_s/k_f>1$. The present model may provide a significant insight into the mechanism of heat transfer in the media embedded with fracture networks of power law length distributions.

This paper presents an analytical model of the origin of nonlinear crosstalk induced by the XPM-SMZI (Cross-Phase Modulation-Symmetric Mach–Zehnder Interferometric) phenomenon occurring in the TWSOA (Traveling Wave Semiconductor Optical Amplifier). We analyze the variation of nonlinear crosstalk with increasing logic levels and length of the input bit sequence. The investigation shows that alteration in high and low logic of bit sequence engenders changes in cross-phase modulation occurring in TWSOA and hence brings nonlinear crosstalk into the picture. The performance is evaluated on 4×4 switching interconnect with a TWSOA cavity length of 500$\mu$m, a width of 3$\mu$m, and a height of 0.8nm with 0.15A injection current in SMZI configuration operating at 10Gbps. The performance of the switch is also tested by comparing various combinations of bit logic inputs. The degradation is observed in the quality of service with an increase in the number of ‘1’s in bit sequence. The Extinction Ratio (ER) also deteriorates when a logic ‘1’s appears at consecutive places. This impairment in ER can be controlled by bias conditions of TWSOA. The promising crosstalk of $-30$dB has been achieved and is further validated by comparing with previously reported techniques.

Fluid sloshing in a rigid circular cylindrical tank is investigated; the tank is resting on soil foundation and is excited by horizontal seismic accelerations. A rigid annular baffle is connected to the inner wall of the storage tank to reduce liquid sloshing. By using the fluid subdomain method, the convective velocity potential is derived. An equivalent model with mass-spring oscillators is proposed to describe the sloshing motions of the contained liquid. Then, by means of the least square method, a complex polynomial fraction is employed to fit the dynamic impedance of the soil. A nested lumped parameter model is established to model the effect of the soil foundation. The substructure method allows to obtain the soil–tank–liquid coupled model. The equation of motion of the coupled system is solved by the Newmark-$\beta$ method. A comparison between the present sloshing results and those published in the literature shows an excellent agreement. The effects of the soil parameters, the baffle position and its size on the dynamic behavior of the soil–tank–liquid system are discussed in detail. The results demonstrate that the soil properties and the baffle parameters can have a remarkable influence on liquid sloshing. The novelty of this research is that an analytical model for the soil–tank–liquid–baffle coupled system is derived for the first time and it allows to study the dynamics and sloshing response of the system with accuracy and low computational cost.

Flexible suspension bridges are susceptible to aerodynamic instability phenomena. In this paper, the torsional divergence is addressed in terms of underlying mechanism, 3D and turbulence effects. A 3D generalized analytical model is first established by reasonable simplification of the model. Comparisons among results from different models are performed. The mechanisms of symmetric and asymmetric torsional divergence are explored. Finally, the 3D and turbulence effects are investigated. The results show that the proposed 3D generalized model is feasible for estimating the critical wind speed of asymmetric torsional divergence, and its computational accuracy is higher than the method provided by the code. The effects of turbulence on torsional divergence are multifaceted: the buffeting response due to wind fluctuations can significantly reduce the aerostatic stability of the bridge, resulting in a much lower critical wind speed than that in a smooth flow; the threshold of divergence is ambiguous and the instability is intermittent; further, the left and right quarter span sections largely vibrate in opposite directions during asymmetric torsional divergence.

Establishing a concise and accurate analytical model is the key to developing a feasible progressive collapse design for engineering practice. However, existing models either focused on an individual force mechanism or required complicated computer programming. Among existing machine learning (ML) techniques, multi-gene genetic programming (MGGP) can be trained to obtain explicit formulas for engineering problems. In this study, a comprehensive database was established by data collection, Latin hypercube sampling and structural design, and was used to train the mathematical model for quantifying progressive collapse resistance of reinforced concrete (RC) beam-column substructures under middle column removal scenarios. Further, an energy-based error index was proposed to validate the accuracy of the MGGP model among others. The research outcomes can provide references for the development of simplified analytical models for calculating the progressive collapse progress of RC frame structures, and promote the development of the practical design method.

In spite of earlier experimental and modeling studies, the relative role of the intra-abdominal pressure (IAP) in spine mechanics has remained controversial. This study employs simple analytical and finite element (FE) models of the spine and its surrounding structures to investigate the contribution of IAP to spinal loading and stability. The analytical model includes the abdominal cavity surrounded by muscles, lumbar spine, rib cage and pelvic ring. The intra-abdominal cavity and its surrounding muscles are represented by a thin deformable cylindrical membrane. Muscle activation levels are simulated by changing the Young's modulus of the membrane in the direction of muscle fibers, yielding IAP values recorded under the partial Valsalva maneuver. In the FE model, the abdominal cavity is cylindrical and filled with a nearly incompressible fluid. The surrounding muscles are modeled as membrane elements with transverse isotropic material properties simulating their fiber orientation. Results indicate a good qualitative agreement between the analytical and FE models. Larger external force and/or higher levels of muscle activation generate higher IAP thereby increasing spinal stiffness. These effects are more pronounced for activation of muscles with more horizontally directed fibers, e.g., transverse abdominis (TA). The capacity of the abdominal muscles to indirectly unload and stabilize the spine by generating IAP depends mostly on their fiber orientation, and secondarily on their cross-section area.

Remanence enhancement has been calculated for a range of configurations, including 1D (one-dimensional), 2D and 3D arrays of hard magnetic grains, composites of hard and soft magnetic grains and triple-films. A linear relationship between the remanence M_r and the reduced domain wall width W/L has been derived analytically, which is consistent with available experimental and numerical data. For composite materials with a soft phase inserted among hard phases, the soft grain behaves like a massive inter-grain domain-wall and results in more effective remanence enhancement. In view of this, a unified formula is reached which can be applied to both composite and single phased magnets with in-plane random easy axis distribution.

An analytical model was developed to explore the effect of swirl action on the mean evolution of a near flow field of turbulent jet. The equations of motion for turbulent flow were integrated to obtain the theoretical model with the aid of boundary layer approximations and the concept of self-preservation of velocity profiles. Vortex breakdown at the core of the jet, a phenomenon associated with swirling jets, was taken into account through the axial velocity distribution. Axial velocity profiles were described in terms of Gaussian curves and azimuthal velocity profiles described in terms of sinusoidal curves. Expressions were obtained which describe the decay of axial and azimuthal maximum velocities and the growth of jet half width. The proposed model proves that the initial swirling degree significantly influences the time-averaged jet characteristics. Collected data from various sources, covering weak to moderate degrees of swirling, were used to verify the theoretical model. The simulated results for the decay of axial and swirling velocities and the jet spread agree closely with the existing experimental findings. Compared to a non-swirling jet, the growth of the jet width is considerably large, and velocity field is suppressed in a swirling jet, and also the core length becomes shorter.

An analytical model is used to investigate the resonant behavior in a semi-closed channel. The main integral quantities of the tidal wave are obtained by means of a linearized one-dimensional model as a function of three dimensionless parameters, representing cross-section convergence, friction and distance to the closed boundary. Arbitrary along-channel variations of width and depth are accounted for by using a multi-reach approach, whereby the main tidal dynamics are reconstructed by solving a set of linear equations satisfying the continuity conditions of water level and discharge at the junctions of the sub-reaches. We highlight the importance of depth variation in the momentum equation, which is not considered in the classical tidal theory. The model allows for a direct characterization of the resonant response and for the understanding of the relative importance of the controlling parameters, highlighting the role of convergence and friction. Subsequently, the analytical model is applied to the Bristol Channel and the Guadalquivir estuary. The proposed analytical relations provide direct insights into the tidal resonance in terms of tidal forcing, geometry and friction, which will be useful for the study of semi-closed tidal channels that experience relatively large tidal ranges at the closed end.

A simplified bridge model suitable for use in a parametric study of short-span skew highway bridges and bridges with stiffness eccentricity is presented. The proposed model is simple, yet it captures all essential features that affect the dynamic response of these bridges. Using this simplified model, formulas for computing earthquake response of the bridges are developed and parameters that significantly influence the dynamic response of the bridges are identified. The study indicates that the response of a given skew bridge depends not only on its deck aspect ratio, the stiffness eccentricity ratio, the skew angles, its natural frequencies, but also on the frequency ratio. In particular, the rotational to translational frequency ratio has a pronounced influence on the dynamic response of the bridge. It is found that skew bridges with high rotational to translational frequency ratios often exhibit less dependence on such parameters as deck aspect ratios, stiffness eccentricity ratios and skew angles.

Penetration of flat-ended cylindrical projectiles into thin laminated composite plates was investigated analytically and experimentally. An analytical modeling was carried out for thin laminated composite plates by developing a new function for deflection by computing Von Karman nonlinear strains and by using the principle of energy balance. During the perforation process, different regions were considered for the plate, such as fracture region, elastic deformation region, delamination region, and undeformed region. The energy absorbed by each region was measured in small time intervals. To validate this model, the ballistic experiment is performed on the thin laminated composite plate near and beyond ballistic limit velocity. The samples were made from plain woven glass/epoxy using a hand lay-up method. In addition to the initial velocity, the residual velocity of the projectile was also measured using two parallel laser curtains. A comparison drawn between analytical and experimental results demonstrated a good consistency in the residual velocity of the projectile. Finally, the distribution of strains along the plate thickness direction over time, the different amounts of absorbed energy of the failure modes, delamination radius, and energy are assessed at near and beyond ballistic limit velocity.

Tetrahedral lattice materials can be used as the core of a sandwich structure. The properties of tetrahedral lattice materials can be controlled by modifying their geometrical parameters and relative density. In this paper, a tetrahedral lattice structure deformation mechanism-based theoretical analysis model is established to predict the effective mechanical properties of the structure under compressive and shear loadings. The analytical solutions are subsequently verified by finite element analysis of a large-scale lattice material model. Based on the obtained results, the effects of the geometrical parameters, relative density, and shear deformation are discussed. At a specific relative density, as strut inclination angle increases: (1) the effective compressive modulus in the z-direction increases; (2) the effective compressive modulus in x- and y-directions, and the effective shear modulus in xy-, xz-, and yz-directions firstly increases but then decreases; (3) the effective Poisson’s ratios ${\nu }_{zx}$ and ${\nu }_{zy}$ increase, whereas, ${\nu }_{xz}$, ${\nu }_{yz}$, ${\nu }_{xy}$, and ${\nu }_{yx}$ decrease. With an increase in relative density, the effective compressive and shearing modulus increase, the effective Poisson’s ratios remain constant, ${\nu }_{xy}$ and ${\nu }_{yx}$ are always equal to 0 when the strut inclination angle is $45^{\circ }$. The effect of shear deformation on the effective mechanical properties increases as the slenderness ratio increases. The predicted effective properties enable the tetrahedral lattice unit cells to be treated as “material” in the design and analysis process.

The lining incorporating yielding elements has been proved to be the most effective solution for tunneling through severe squeezing ground. Unfortunately, there has not been a well-organized method to transfer its beneficial effects into the practical tunnel design. This study aims to provide an analytical model for predicting the behavior of yielding lining supported tunnel. The internal force analysis of the lining is first carried out to determine the optimal installation positions of the yielding elements. Second, the lining incorporating yielding elements is processed as a simplified shell using the equivalent deformation principle. The equation for calculating the elastic modulus of the simplified shell is presented. The analytical solutions for the tunnel displacement and lining pressure are provided in the viscoelastic Burgers rocks, where the installation delay of the lining and the tunnel face advancement effect are taken into account. The proposed analytical model is applied in the Saint Martin La Porte access adit of Lyon-Torino Base tunnel, where the yielding lining was employed. The analytical result provides a good prediction of the time-dependent tunnel convergences in the Saint Martin La Porte access adit. Finally, a comprehensive parametric investigation is performed, including the influences of installation time of yielding lining, yield stress and length of yielding elements. Some inspiring results for the tunnel design are provided.

Shear stress concentrations may promote damage and failure processes. Quantities of studies have focused on the direct shear loading test, while the analytical model has not yet been studied in depth. Aiming to fill the knowledge gap, the theoretical and numerical analyses of the shear stress distribution in the shear band were investigated. In order to reflect the variation in the stress state, the differential element method was first used. The shear stress distribution equation was derived from the stress equilibrium, geometric and physical equations. The shear stress distribution was plotted, using the proposed equation. After that, the ratio of yield strength to crack initiation strength was calculated. The analytical model was analyzed with FDEM simulation, and the results were compared with those obtained from the laboratory tests. Using the elastoplastic theory, the damage evolution and process in rock were characterized from laboratory scale. The implication for underground engineering analysis was finally discussed with a case study of strain rockburst in hard rock. The analytical model and results could provide a fundamental basis for stability analysis in geotechnical engineering.