A new methodology via using an adaptive fuzzy algorithm to obtain solutions of “Two-dimensional Navier-Stokes equations” (2-D NSE) is presented in this investigation. The design objective is to find two fuzzy solutions to satisfy precisely the 2-D NSE frequently encountered in practical applications. In this study, a rough fuzzy solution is formulated with adjustable parameters firstly, and then, a set of adaptive laws for optimally tuning the free parameters in the consequent parts of the proposed fuzzy solutions are derived from minimizing an error cost function which is the square summation of approximation errors of boundary conditions, continuum equation and Navier-Stokes equations. In addition, elegant approximated error bounds between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors have also been proven. Furthermore, the error equations in mesh points can be proven to converge to zero for the 2-D NSE with two sufficient conditions.

A generalized dynamic model for an automotive drive train system was detailed to investigate its modal properties and dynamic behavior. The model's engine excitation, clutch, gearbox and disc brake were presented. Then, vibration modes were obtained and classified into clutch, transmission system, disc brake, bearing and combined modes. For each vibration mode, the kinetic and strain modal energies distributions were studied. The dynamic equations were resolved using the numerical Newmark method. The dynamic behavior of the bearings and transmission errors for the two gear stages were studied, and, the effect of the disc brake parameters on the transmission error was analyzed. Finally, a frequency sweep analysis was studied to investigate the system resonance problem.

The purpose of the Reliability-Based Design Optimization (RBDO) is to find the best compromise between safety and cost. Therefore, several methods, such as the Hybrid Method (HM) and the Optimum Safety Factor (OSF) method, are developed to achieve this purpose. However, these methods have been applied only on static cases and some special dynamic ones. But, in real mechanical applications, structures are subject to random vibrations and these vibrations can cause a fatigue damage. So, in this paper, we propose an extension of these methods in the case of structures under random vibrations and then demonstrate their efficiency. Also, a Robust Hybrid Method (RHM) is then developed to overcome the difficulties of the classical one. A numerical application is then used to present the advantages of the modified hybrid method for treating problem of structures subject to random vibration considering fatigue damage.

A new method, called Cloud of Points (COP) Reconstruction, is proposed in the present work to extend the meshfree method to simulate viscous flows. With the characters of viscous flows, the anisotropic COP structure is distributed in boundary layer. The proposed method can improve the anisotropic COP structure to isotropic COP structure and reduce the condition number of the least square coefficient matrix for conventional meshfree method. The values of the new reconstructed points are calculated by the Lagrange interpolation. The accuracy and the robustness of the presented meshfree solver are demonstrated on a number of standard test cases, including the functions with analytical gradients and the viscous flows past NACA0012 airfoil. The comparison of the simulation results with the experimental data and other numerical simulation data are also investigated.

The reflection of longitudinal micro-rotational wave at the viscoelastically supported boundary of micropolar half-space is studied in this paper. The viscoelastic boundary is described by spring-dashpot model with parallel or serial connection. Both the spring and the dashpot contribute to the displacements and micro-rotation and the boundary conditions include the force stress and couple stress components. From the boundary conditions, the amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained. Further, the energy flux ratios of the reflection waves to the incident wave are estimated. In order to validate the numerical results, the energy flux conservation with consideration of the energy dissipation of dashpot is used. Based on the numerical results, the influences of elastic parameters and viscous parameters are studied, respectively. It is found that the elastic parameters and the viscous parameters have evident influences on the amplitude ratio, the phase shift and the energy partition. The causes resulting in these deviations are related with the instantaneous elasticity of spring and the time-delay effects of dashpot.

In this paper, case wise studies have been made to investigate the possibility of propagation of Rayleigh-type wave in a composite structure comprised of two transversely-isotropic material layers with viscoelastic effect. The common interface between the layers is considered to be rigid whereas the base has been considered as rigid, stress-free and yielding in three different cases (Case-I, II and III). Closed-form of frequency equation and damped velocity equation has been established analytically for propagation of Rayleigh-type wave in a composite structure for all three cases. In special cases, frequency equations and damped velocity equations for the case of composite structure with rigid, stress-free and yielding base have been found in well-agreement to the established standard results pre-existing in the literature. Numerical and graphical computation of phase and damped velocity of Rayleigh-type wave propagating in the composite structure comprised of double transversely-isotropic viscoelastic Taylor sandstone material layers (Model-I) and double isotropic viscoelastic material layers (Model-II) have been carried out. Significant effect of anisotropy and width ratio of layers, dilatational and volume viscoelasticity associated with viscoelasticity of layer medium and yielding parameter associated with yielding base of composite structure on phase and damped velocities of Rayleigh-type wave for the considered models have been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the present problem.

Aero-engines usually contain a lot of pipes and cables which have an important influence on product performance and reliability. In this paper, a new pipe routing approach for aero-engines is proposed. First, an adaptive octree modeling method is presented according to the characteristics of the layout space. After considering three types of engineering constraints, the total length of pipelines, the total number of bends and the natural frequency of pipelines are modeled as the optimal objective. Then, a Modified Max-Min Ant System optimization algorithm (MMMAS), which uses layered node selection and dynamic update mechanism, is proposed for pipe routing. For branch pipelines, ant colony searches in groups and parallel to improve the solution quality and speed up the convergence greatly. Finally, numerical comparisons with other current approaches in literatures demonstrate the efficiency and effectiveness of the proposed approach. And a case study of pipe routing for aero-engines is conducted to validate this approach.

This paper deals with the implementation of an anisotropic plasticity constitutive equations exhibiting non-linear isotropic, kinematic hardening and coupled continuum ductile damage models. A fully implicit integration of the coupling constitutive equations is adopted and leads to two non-linear local scalar equations solved using the Newton method. The consistent local tangent modulus is obtained in a closed form by exact linearization of the algorithm. The numerical treatment of the proposed algorithm is implemented on ABAQUS using user interface material subroutines (UMAT and VUMAT). The performance of the present algorithm is assessed and bared out by numerical examples.

Existing studies reveal that the shape corners of hexagonal fiber affect the degree of constraint on the matrix material. However, none of these studies included the effect of orientation of hexagonal fibers. In this study, a computational micromechanics model of oriented hexagonal fibers in periodic unidirectional composite materials is established for the determination of effective orthotropic elastic properties of the composite. In the present numerical modeling, the representative unit composite cell including the matrix material and the single oriented hexagonal fiber or random oriented hexagonal fibers is solved by micro-scale finite element analysis with different stress loads and periodic displacement boundary conditions, which are applied along the cell boundary to meet the requirement of straight-line constraint during deformation of the cell. Subsequently, the effective elastic properties of the composite are evaluated for periodic regular packing and random packing using the homogenization approach for investigating the influence of unified orientation and random orientation of the hexagonal fibers on the overall elastic properties of the fiber-reinforced composites. The numerical results are verified by comparing with other available results.

Constitutive equations, based on continuum mechanics and representing behavior of a mixture of two elastic solids, can be used for modeling of materials such as particulate composites. In this study, the behavior of continuum of a mixture occupying half-space under axisymmetric loads is calculated using Fourier and Hankel transform methods. For this purpose, Love's strain functions are used and the general solution of problem under proper boundary conditions is presented. By applying the results obtained to the sinusoidal distributed vertical load and Boussinesq problems that require the use of Cartesian and cylindrical coordinate systems, displacement vectors, diffusive force vector and components of stress tensors are calculated. At the end of the study, the experimental results of a special particulate composite are used to check the accuracy of the solutions obtained.

Based on unstructured hybrid grid and dynamic overlapping grid technique, numerical simulations of Unsteady Reynolds Averaged Navier-Stokes equations were performed and investigation on isolated propeller aerodynamic characteristics and effects of propeller slipstream on turboprops were undertaken. The computational grid consisted of rotational subzone of propeller and stationary major-zone of aircraft, and walls criterion was used in the automatic hole-cutting procedure. Distance weight interpolation and tri-linear interpolation were developed to transfer information between the rotational and stationary subzones. The boundaries of overlapping grids were optimized for fixed axis rotation. The governing equations were solved by dual-time method and Lower Upper-Symmetric Gauss-Seidel method. The method and grid technique were verified by isolated propeller configuration and the computational results were in well agreement with the experimental data. The grid independence was studied to establish the numerical results. Finally, the flow around a turboprop case was simulated and the influence of propeller slipstream was presented by analyzing the surface pressure contours, profile pressure distribution, vorticity contours and profile streamline. It's indicated that the slipstream accelerates and rotates the free stream flow, changing the local angle of attack, enhancing the downwash effects, affecting the pressure distribution on wing and horizontal tail, as well as increasing the drag coefficient, pitching moment coefficient and the slope of lift coefficient.

The position determination for rock bolt support design based on rock stress distribution is important in ensuring full mobilization of rock bolt tensions during excavation process. The monitoring of the progressive rock stress variation in magnitude and orientation can play an important role in optimal installation of rock bolt. The aim of this paper is to determine the optimal positions for rock bolt installation by computing the progressive directional variation of rock stresses and plot the stress distribution in a two-dimensional stereographic projection to capture the stress transformation during excavation process. Finally, an algorithm based on stress transformation determination for optimal rock bolt installation is proposed.

Modal analysis is developed in this paper in order to study the dynamic characteristics of rotating segmented blades assembled with spar. Accordingly, a three dimensional finite element model was built using the three node triangular shell element DKT18, which has six degrees of freedom, to model the blade and the spar structures. This study covers the effect of rotation speed and geometrically nonlinear problems on the vibration characteristics of rotating blade with various pretwist angles. Likewise, the effect of the spar in the blade is taken into consideration. The equation of motion for the finite element model is derived by using Hamilton's principle, while the resulting nonlinear equilibrium equation is solved by applying the Newmark method combined with the Newton Raphson schema. Results show that the natural frequencies increase by taking account of the spar, they are also proportional to the angular rotation speed and influenced by geometric nonlinearity and pretwist angle.

Most topology optimization methods seek optimal topologies that satisfy a minimum compliance with a pre-specified volume constraint in the design domain. However, practical designs often include various functional constraints and the optimal solid volume ratios are unknown a priori, which implies a gap between topology optimization methods and practical designs in industries. This paper studies the performance-based topology optimization (PTO) problem that searches for the optimal topology with minimum compliance to satisfy the pre-specified functional constraints without a pre-specified volume constraint. A novel element-based evolutionary switching method (ESM), which can automatically adjust solid volume ratio and material distribution, is developed and implemented using the commercial finite element software ABAQUS. The effects of displacement constraints on the optimal topologies are investigated, and the differences between PTO problems and the topology optimization problem which has a volume constraint are discussed. Numerical examples demonstrate that the optimal topologies are mainly determined by the load pattern and locally changed with respect to the location of the active displacement constraints. In addition, the displacement constraints to a large extent control the solid volume ratio of optimal topologies according to the allowable displacements in PTO problems. Finally, the proposed ESM could provide conservative solutions to the topology optimization with multiple displacement constraints problems.

A numerical coupled thermoplasticity multiscale procedure for small strain analysis is developed in the finite element environment. It is suitable for simulation of thermo-mechanical behavior and overall response of metallic materials, using standard approximation method based on the concept of representative volume element (RVE). The local level isothermal analysis that models the micro-scale, is fully coupled to the global level non-isothermal analysis. The global macro-scale tangent stiffness operator is obtained using numerical differentiation procedure using the forward difference scheme. The numerical procedure is developed for two-dimensional problems, using Abaqus user-defined subroutines. Applicability of the proposed framework is presented on several representative examples.

Numerical investigation of the strong interplay between a cavity and a store under supersonic inflow condition is conducted by using Improved Delayed Detach-Eddy Simulation (IDDES). Pressure fluctuations in the cavity are analyzed with smooth pseudo Winger-Vile distribution method and the time-frequency features are obtained. The effects of fluctuating flow inside the cavity on the aerodynamic loads of the store are also studied. It was shown that when the store is falling through the shear layer, the self-sustained oscillation loop is destroyed and the cavity tone vanishes. Vortex structures concentrate in the back of the cavity, as a result the noise levels at the rear of the cavity increase. After the store falls out of the cavity, the oblique shock wave formed at store's head interferences with the shear layer, which changes the cavity tone frequencies. The forces and moments acting on the store fluctuate strongly influenced by highly unsteady flow-field. Affected by oblique shock and the impact of shear layer, the store's pitch up angle keeps rising up and reaches to 24° at its maximum.

With good combustion characteristics, hydrogen has been developing as a clean alternative fuel of engines. This study is to develop a diesel/hydrogen dual fuel engine. The hydrogen was added at inlet port in a 4-cylinder direct injection turbocharged diesel engine with an EGR (Exhaust Gas Recirculation) system to investigate engine performance and exhaust pollutant. The measured items are composed of the gas pressure of cylinder, crank angle, consumption rate of diesel, consumption rate of hydrogen, air flow rate, emissions (HC, CO2, NOX, and Smoke), and so on. The authors analyze how the addition of hydrogen with EGR system influences the engine performance and emissions. The diesel/hydrogen dual fuel turbocharged engine can increase the brake thermal efficiency with a greater decrease in emissions compared with the turbocharged diesel engine. Furthermore, the authors little altered the engine structure to get the positive effect of energy saving and pollutant decreasing.

An inverse energy method for the identification of the structural force in high frequency ranges from radiated noise measurements is presented in this paper. The radiation of acoustic energy of the structure coupled to an acoustic cavity is treated using an energetic method called the simplified energy method. The main novelty of this paper consists in using the same energy method to solve inverse structural problem. It consists of localization and quantification of the vibration source through the knowledge of acoustic energy density. Numerical test cases with different measurement points are used for validation purpose. The numerical results show that the proposed method has an excellent performance in detecting the structural force with a few acoustical measurements.

A family of structure-dependent integration methods has been proposed by Gui et al. for time integration. Although it has desirable numerical properties, such as unconditional stability, explicit formulation and second-order accuracy, it has some adverse properties, such as a poor capability to capture structural nonlinearity, an overshoot in a high frequency steady- state response and a weak instability in the high frequency response of nonzero initial conditions. The causes of these adverse properties are explored. A poor capability to capture structural nonlinearity may originate from the convergence rate of 1 in velocity error. This family method has an overshoot in a high frequency steady-state response and this overshoot can be eliminated by adding a load-dependent term into the displacement difference equation. It is also analytically verified that the family method generally has no weak instability. However, the special member with λ = 4, i.e., CR explicit method, is shown to have a weak instability. Thus, it must be prohibited from practical applications although many applications of this method were found in the literature.

In this study, wave propagation in beams is studied using different beam theories like Euler-Bernoulli, Timoshenko and Reddy beam theories. Dispersion curves obtained for these beam theories are compared with the exact plane elasticity solutions. It is obtained that, there are two branches for Reddy beam theory similar to the Timoshenko beam theory. However, one branch is obtained for Euler-Bernoulli beam theory. The effects of in-plane load on Timoshenko and Reddy beam theories are examined and dispersion curves of the Timoshenko and Reddy beams are compared with exact plane elasticity solution. In Timoshenko beam theory, qualitative difference between the two spectrums has been lost with in-plane loads for some wave numbers.