Showing papers in "Applied Mathematics and Mechanics-english Edition in 2006"
TL;DR: Support vector machine (SVM) was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method (FORM) and the Monte Carlo simulation (MCS).
Abstract: Support vector machine (SVM) was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method (FORM) and the Monte Carlo simulation (MCS). As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e., SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method (RSM) and the artificial neural network (ANN), which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the “curse of dimensionality”. The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis (usually finite element analysis), and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.
103 citations
TL;DR: In this article, a thermal post-buckling analysis of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented.
Abstract: Analysis of thermal post-buckling of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrical nonlinear governing equations including seven basic unknown functions for functionally graded beams subjected to mechanical and thermal loads were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko beams with fixed-fixed edges were obtained. Characteristic curves of the buckling deformation of the beam varying with thermal load and the power law index are plotted. The effects of material gradient property on the buckling deformation and critical temperature of beam were discussed in details. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the transversely non-uniform characteristic of materials.
75 citations
TL;DR: The singular hybrid boundary node method (SHBNM) as mentioned in this paper was proposed for solving three-dimensional problems in linear elasticity, which represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation.
Abstract: The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
40 citations
TL;DR: In this paper, the viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model.
Abstract: The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study is reported while a perturbation analysis is presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region is compared with that of asymptotic analysis and a good degree of agreement is observed.
31 citations
TL;DR: In this article, an analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time, in the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced.
Abstract: An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers (e.g., the coefficient of thermal consolidation, elastic modulus) on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the thermo-osmosis effect has an obvious influence on thermal responses.
31 citations
TL;DR: In this paper, a catastrophe model of tunnel rockburst was established, and the computation expression of the earthquake energy released by tunnel rockbursts was given, where the conditions of rockburst occurrence were relative to rock's ratio of elastic modulus to descendent modulus and crack growth degree of rocks.
Abstract: Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock’s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.
27 citations
TL;DR: In this article, the propagation of symmetric and skew symmetric wave modes in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated.
Abstract: The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.
27 citations
TL;DR: This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping and revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one.
Abstract: Flexible insect wings deform passively under the periodic loading during flapping flight. The wing flexibility is considered as one of the specific mechanisms on improving insect flight performance. The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet. A viscoelastic constitutive relation model was established based on the stress relaxation experiment of a dragonfly wing (in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping. It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one. The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.
27 citations
TL;DR: In this article, a new droplet collision and coalescence model was presented, a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collisions outcome.
Abstract: A new droplet collision and coalescence model was presented, a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence, numerical simulations were carried out for model validation. Results show that the model presented is mesh-independent and less time consuming, it can not only maintains the system momentum conservation perfectly, but not susceptible to initial droplet size distribution as well.
27 citations
TL;DR: A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied, and some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed.
Abstract: A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings.
27 citations
TL;DR: In this article, the authors employed the Newtonian method to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid and analyzed the order magnitudes of relevant physical parameters to establish a foundation on the further study of the model.
Abstract: The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3:1, 2:1 and 1:1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3:1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.
TL;DR: In this article, the stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing and different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory.
Abstract: Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.
TL;DR: A novel knowledge-based fuzzy neural network (KBFNN) for fault diagnosis is presented and has those merits of shorter training time and higher right diagnostic level compared to general fuzzy neural networks.
Abstract: A novel knowledge-based fuzzy neural network (KBFNN) for fault diagnosis is presented. Crude rules were extracted and the corresponding dependent factors and antecedent coverage factors were calculated firstly from the diagnostic sample based on rough sets theory. Then the number of rules was used to construct partially the structure of a fuzzy neural network and those factors were implemented as initial weights, with fuzzy output parameters being optimized by genetic algorithm. Such fuzzy neural network was called KBFNN. This KBFNN was utilized to identify typical faults of rotating machinery. Diagnostic results show that it has those merits of shorter training time and higher right diagnostic level compared to general fuzzy neural networks.
TL;DR: In this article, the authors defined the damage division of end area of control fissure and established calculation methods of timed-Poisson's ratio and timed-Young's modulus in damage mechanics theory.
Abstract: Hitherto, perilous rock is the weakest topic in disasters studies. Specially, damage of control fissure under loads is one key technique in study of develop mechanism of perilous rock. Damage division of end area of control fissure was defined by authors, then calculation methods of timed-Poisson’s ratio and timed-Young’s modulus were established in damage mechanics theory. Further, the authors set up damage constitutive equation of control fissure, which founds important basis to numerical simulation for control fissure to develop.
TL;DR: In this article, the incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities, and numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure.
Abstract: The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.
TL;DR: In this paper, the generalized variable principle of magnetoelectroelastic solids was derived to Hamiltonian system and the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem.
Abstract: By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic industion, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.
TL;DR: The dynamic modeling and simulation of an N- Flexible-link and N-flexible-joint robot is reported and the approach of assumed modes is adopted to describe the deformation of the flexible-link.
Abstract: The dynamic modeling and simulation of an N-flexible-link and N-flexible-joint robot is reported. Each flexible joint is modeled as a linearly elastic torsional spring and the approach of assumed modes is adopted to describe the deformation of the flexible-link. The complete governing equations of motion of the flexible-link-joint robots are derived via Kane’s method. An illustrative example is given to validate the algorithm presented and to show the effects of flexibility on the dynamics of robots.
TL;DR: In this paper, an efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem, which is based on the reduction procedure of the original system of PDEs describing coupled thermomic behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations.
Abstract: An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.
TL;DR: In this paper, the analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load by means of Airy stress function method.
Abstract: The analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load. A stress function involving unknown coefficients was constructed, and the general expressions of stress and displacement were obtained by means of Airy stress function method. Two types of the description for the fixed end boundary condition were considered. The introduced unknown coefficients in stress function were determined by using the boundary conditions. The analytical solutions for stresses and displacements were finally obtained. Numerical tests show that the analytical solutions agree with the FEM results. The analytical solution supplies a classical example for the elasticity theory.
TL;DR: Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system.
Abstract: The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered in this paper The mathematical model of the airship attitude is a multi-input/multi-output uncertain nonlinear system Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties Using the input/output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output The controller is easy to compute and complement Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system
TL;DR: In this article, the authors proposed a method to calculate velocities of solid phase and liquid phase in debris flow through solution to general equations, which is suitable for both viscous debris flow and thin debris flow.
Abstract: Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham’s rheology equation of liquid phase and Bagnold’s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.
TL;DR: In this paper, the implicit relations were given and a common fixed point theorem was proved for two mappings satisfying implicit relation functions on two compact metric spaces, and a further fixed-point theorem was shown for mappings with implicit relation function on two continuous metric spaces.
Abstract: First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.
TL;DR: In this article, a dynamic model of subtropical high based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF (empirical orthogonal function) temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamic model parameters optimization search.
Abstract: Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF (empirical orthogonal function) temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.
TL;DR: A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm based on the definition of a Roe’s type matrix.
Abstract: A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe’s type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe’s scheme.
TL;DR: In this article, the dynamic behavior of two parallel symmetry cracks in magneto-electroelastic composites under harmonic anti-plane shear waves is studied by Schmidt method, which can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces.
Abstract: The dynamic behavior of two parallel symmetry cracks in magneto-electroelastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezom agnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed.
TL;DR: Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system was accurately obtained as mentioned in this paper.
Abstract: Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.
TL;DR: In this article, the stress intensity factors of a rotating thick-walled cylinder with a radial crack along the internal bore along with the change of crack depths and the ratio of outer radius to inner radius were studied.
Abstract: The equation of stress intensity factors(SIF) of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.
TL;DR: In this paper, a spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5.
Abstract: Spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that, during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance, when they became larger, leads to remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.
TL;DR: In this article, the large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach.
Abstract: The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. This kind of substitution can transform the basic equation, an integral differential equation into nonlinear algebraic ones, thus simplify computational process. Compared with present results, it indicates that the large deflection problem solved by using pseudolinear analysis can lead to simple and precise results.
TL;DR: In this paper, the response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated using a numerical inversion technique.
Abstract: The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.