In the paper, nonlinear dynamic analysis of a circular plate composed of functionally graded material (FGM) is presented. Considering a transverse shear deformation and geometric nonlinearity, the von Karman geometric relation of the FGM circular plate is established. Based on the theory of the first-order shear deformation, a new set of equilibrium equations is developed by the principle of minimum total energy. Applying the finite difference method and Newmark scheme, the nonlinear transient problem is solved by the iterative method. To validate the presented method, the transient problem of the FGM circular plate is compared with those of the existed literature, and good agreement is observed. The effects of the volume fraction index, boundary conditions, mechanical load and the ratio of thickness to radius on the nonlinear transient problem of the FGM circular plate are investigated.

Enhancement of a heat transfer rate of mixed convection flow in a three-dimensional vertical channel with insertion of a moving slender block is investigated numerically. A slender block is installed along the direction of the channel flow, and the movement of the slender block is in periodic motion and transverse to the channel flow. The interaction between the moving block and the channel flow destroys and suppresses the velocity and thermal boundary layers on the heat surface periodically. Various ratios of the Richardson numbers (Gr/Re2) are simulated. The results show that under a higher velocity of the channel flow and a lower magnitude of Gr/Re2, the enhancement of heat transfer rate is better. Oppositely, under a lower velocity of the channel flow and a higher magnitude of Gr/Re2, the effect of natural convection driven by the buoyancy force is stronger and it is unfavorable to the heat transfer. A counter effect of the heat transfer rate is observed. These phenomena which are seldom analyzed before by numerical simulation are carried out in this study.

In this paper, we studied the peristaltic flow and heat transfer of an incompressible, electrically conducting Bingham Non-Newtonian fluid in an eccentric uniform annulus in the presence of external uniform magnetic field with slip velocity and temperature jump at the wall conditions. The viscous and Joule dissipations are taken into account. The inner tube is rigid and moving with a constant axial velocity, while the outer tube has a sinusoidal wave traveling down its wall. Under zero Reynolds number condition with the long wavelength approximation, the axial velocity and the stream function are obtained analytically. A numerical solution for the governing partial differential equation of energy is performed in order to analyze the temperature distribution. The effects of all parameters of the problem are numerically discussed and graphically explained.

In this paper, a new algorithm is developed based on the homogenization method integrating with the newly developed Hybrid Treffe FEM (HT-FEM) and Hybrid Fundamental Solution based FEM (HFS-FEM). The algorithm can be used to evaluate effective elastic properties of heterogeneous composites. The representative volume element (RVE) of fiber reinforced composites with periodic boundary conditions is introduced and used in our numerical analysis. The proposed algorithm is assessed through two numerical examples with different mesh density and element geometry and used to investigate the effect of fiber volume fraction, fiber shape and configuration on the effective properties of composites. It is found that the proposed algorithm is insensitive to element geometry and mesh density compared with the traditional FEM (e.g. ABAQUS). The numerical results indicate that the HT-FEM and HFS-FEM are promising in micromechanical modeling of heterogeneous materials containing inclusions of various shapes and distributions. They are potential to be used for future application in multiscale simulation.

Many engineering problems are governed by partial differential equations which can be solved by analytical as well as numerical methods, and examples include the plasticity problem of a geotechnical system, seepage problem and elasticity problem. Although the governing differential equations can be solved by either iterative finite difference method or finite element, there are however limitations to these methods in some special cases which will be discussed in the present paper. The solutions of these governing differential equations can all be viewed as the stationary value of a functional. Using an approximate solution as the initial solution, the stationary value of the functional can be obtained easily by modern global optimization method. Through the comparisons between analytical solutions and fine mesh finite element analysis, the use of global optimization method will be demonstrated to be equivalent to the solutions of the governing partial differential equations. The use of global optimization method can be an alternative to the finite difference/ finite element method in solving an engineering problem, and it is particularly attractive when an approximate solution is available or can be estimated easily.

This paper proposes a three-phase constitutive model for estimating the elastic moduli and strength of granular composite. The three-phase granular composite material containing aggregate (inclusion), matrix, and aggregate/matrix interface were investigated in this study. It was observed that significant improvement in predictive capability for three-phase granular composite materials can be achieved by using the proposed method. By using micromechanics and adopting the double-inclusion concept initiated by Hori and Nemat-Nasser and the two-phase model introduced by Yang et al.; the predicted elastic moduli for three-phase granular composite materials were evaluated. Moreover, analytical formulas were obtained to predict the strengths of three-phase granular composite materials. The potential of the proposed framework was also explored by comparing the analytical predictions in this study with other analytical methods as well as experimental data of other studies.

This study investigates the influences of constant compensations which are produced by capillary or constant flow pump on the dynamic characteristics of a circular worktable supported by a closed-type hydrostatic thrust bearing. The dynamic behaviors of this worktable are analyzed by using Runge-Kutta method to solve the coupled motion equation of worktable and pressure equations of hydrostatic film flow. For various supply pressure parameters, external loads, and varieties of design parameters, the dynamic responses of worktable subjected to both external excitations of harmonic force and step force are simulated, respectively. The results reveal the influences of both constant compensations on the dynamic characteristics of hydrostatic bearing by the different responses of worktable and make the appropriate parameters of design can be found for the worktable-bearing system. The accomplishments of this study will help the designers who deal with the hydrostatic- bearing compensated by constant restrictions to select the design parameters to approach the optimum condition.

This paper is concerned with two-dimensional (r, θ) thermoelastic dynamic responses of a long functionally graded hollow cylinder subjected to asysmmetrical thermal and mechanical loads. The material properties, except the Poisson's ratio, are assumed to be temperature independent and vary exponentially and continuously in the radial direction. By means of finite difference method and Newmark method, the motion governing equations of the long FGM hollow cylinder are solved. Comparisons between this paper's results and the corresponding analytical results validate the proposed solution. In addition, the effects of the volume fraction, temperature boundary conditions on the hollow cylinder's deformations and stresses distributions are examined, and many other valuable thermoelastic dynamic characteristics are revealed.

This paper investigates the suitability of auxetic materials for load-bearing circular plates. It is herein shown that the optimal Poisson's ratio for minimizing the bending stresses is strongly dependent on the final deformed shape, load distribution, and the type of edge supports. Specifically, the use of auxetic material for circular plates is recommended when (a) the plate is bent into a spherical or spherical-like cap, (b) a point load is applied to the center of the plate regardless of the edge conditions, and (c) a uniform load is applied on a simply-supported plate. However, auxetic materials are disadvantaged when a flat plate is to be bent into a saddle-like shell. The optimal Poisson's ratios concept recommended in this paper is useful for providing an added design consideration. In most cases, the use of auxetic materials for laterally loaded circular plates is more advantageous compared to the use of materials with conventional Poisson's ratio, with other factors fixed. This is achieved through materials-based stress re-distribution in addition to the common practices of dimensioning-based stress redistribution and materials strengthening.

This paper reports the results of a series of full-scale drilled shaft load tests subjected to combined axial and lateral loading and lateral loading only. The tested shafts, 1.4m in diameter, were embedded 37m in sandy silt. All tested shafts were installed using reverse circulation method. The test results indicated, given the same lateral loading, 63% of pile head displacement resulted from combined load corresponded with the case of lateral loading only. The test results were compared to the numerical results of the software LPILE as well as the analytical solutions proposed by the senior author and his co-workers. The analytical results of the pile bending moments along shaft showed better results than that of LPILE.

The linear problem of large deflection of a clamped and layered piezoelectric circular plate under initial tension due to lateral pressure is solved. Von Karman plate theory for large deflection is extended to a symmetrically laminated case including a piezoelectric layer. The thus derived nonlinear governing equations are simplified by neglecting the arising nonlinear terms, yielding a modified Bessel equation or a standard Bessel equation for the lateral slope. These equations are solved analytically by imposing boundary conditions for the clamped edge. For a 3-layered nearly monolithic plate with a low applied voltage upon the piezoelectric layer, the results are in a good agreement with those available in literature for a single-layered plate under pure mechanical loading, thus validates the present approach. Typical 3-layered piezoelectric plates are then implemented and the results show that, piezoelectric effect seems to be apparent only up to a moderate initial tension. For a relatively high pretension, the effect of initial tension appears to be dominant, yielding nearly the same results for the structural responses, regardless of the piezoelectric effect, i.e., the magnitude of voltage applied upon the piezo-electric layer.

By the approaches of the theory of complex functions, dynamic problem concerning mode I semi-infinite crack propagation was studied. Analytical solutions are very easily obtained by application of the measures of self-similar functions. The problems researched can be changed into Riemann-Hilbert problems and analytical solutions to semi-infinite crack under the condition of impulse loads and increasing loads Pt located at the origin of the coordinates, respectively, are attained.

We used the generalized differential quadrature (GDQ) method to compute the transient responses of thermal stresses and center deflection amplitude in the magnetostrictive functionally graded material (FGM) square plate under rapid heating acting at its lower surface. We obtained the GDQ solutions in the three-layer of magnetostrictive FGM plates subjected to four simply supported edges. We presented the transient responses of thermal stress and center deflection amplitude of magnetostrictive FGM plates with/without velocity feedback control, respectively, under the effects of the ratio of length to thickness, the power law index, the temperature of environment and the applied heat flux.

By application of the theory of complex variable functions, asymmetrical dynamic propagation problem on the edges of mode III interface crack subjected to superimpose loads was studied. Analytical solutions of the stresses displacements and dynamic stress intensity factors are obtained by means of self- similar functions. The problems researched can be facilely transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple according to this measure. After those solutions are utilized by superposition theorem, the solutions of arbitrarily complex problems can be gained.

In the present study, the effect of the number of stages of Tesla Micro-Valve (TMV), as well as the dependency of Reynolds number, Re, on the valve performance has been analyzed. For this purpose, different layouts include one to four-stage with different sizes are investigated numerically. The main criterion for evaluation of valves performance is diodicity, Di. Unsteady and steady flow in valve have been simulated and compared. It is shown that although there are some difference but the trend is similar for both responses. Finally, 2-D and steady state computations of the fluid flow have been utilized that reveal a strong dependence of Di on Re and pressure drop, ΔP. The results showed that the maximum Di of the two-stage microvalve is approximately 1.45 times of that of one-stage. Additional stages increase the complexity, and they do not change Di appreciably. It is concluded that two-stage layout of Tesla type valve is the best option. Also, the two-stage valve performance for three different sizes is compared with Nozzle-Diffuser type Micro-Valve (NDMV). Comparisons, which are performed based on calculation Di in applicable range of Re, showed that Di as a function of Re is independent of the valve size. Also, the superiority of the Tesla type valve at higher Re and its weakness at lower Re is observed.

Based on the researches on the temperature and microstructures dependent fracture strength and temperature dependent thermal shock resistance, the new thermal shock resistance models for ultra-high-temperature ceramics were proposed. The effect of density on the fracture strength of material was investigated. A damage term was introduced to reveal the effects of uncertain factors on fracture strength. The roles of residual stress and microstructure sizes at different initial thermal shock temperatures in the thermal shock resistance were studied using the models. The study showed that the models can reveal the relationships among the residual stress, microstructure sizes and the temperature dependent thermal shock resistance well. The better thermal shock resistance is found for ultra-high-temperature ceramics having small SiC grains and relatively large micro-cracks around SiC grains. Large enhancement in thermal shock resistance can be achieved through our studies.

The influence of annealing temperature in the course of mechanical-thermal treatment on the steady-state creep of metals is discussed and modeled. The synthesis theory of irrecoverable deformation is taken as a mathematical apparatus. Results obtained in terms of the generalized synthetic theory give good agreements with experimental data.

This paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring con-nection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

This paper presents a static and linear dynamic model to simulate the performance of a Micro Gas Turbine (MGT). The static model is obtained using thermodynamic equations and maps of the components to determine off design performance of the MGT with constant output power. The linear dynamic model is developed using linearized static and dynamic nonlinear equations around an operating point as state-space model to predict the behaviour of the MGT in transient conditions. To validate the results of the static model, important information such as fuel flow, fuel to air ratio, and turbine inlet temperature are compared with the results of Aspen-HYSYS software during an increase in ambient temperature. In addition, static model results are compared with experimental data of the MGT test by previous studies. Also, the compressor equilibrium running line of the MGT is derived in constant ambient condition. In order to evaluate the linear dynamic model, the verification is performed using the results of nonlinear model of previous studies. The comparison between the results confirms the ability of proposed dynamic model to simulate a MGT while decreasing the computational effort and complexity of equations. Moreover, a comparison is carried out between static model results and steady state values predicted by dynamic model.