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A damage model for carbon–carbon orthotropic composite materials is introduced with a special attention to the thermo-mechanical effects. The internal variables of damage are identified from tension–compression tests according to each fiber direction and from shear tests in each orthotropy plane. The influence of the temperature is taken into account from typical experimental stress–strain curves given for different values of the temperature. The finite element model was implemented in ABAQUS® using an implicit time incremental scheme. Finally, a significant numerical simulation of a thermo-mechanical loading with damage is presented.  相似文献   

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We consider a dissipative model recently proposed by M. Frémond to describe the evolution of damage in elastic materials. The corresponding PDEs system consists of an elliptic equation for the displacements with a degenerating elastic coefficient coupled with a variational dissipative inclusion governing the evolution of damage. We prove a local-in-time existence and uniqueness result for an associated initial and boundary value problem, namely considering the evolution in some subinterval where the damage is not complete. The existence result is obtained by a truncation technique combined with suitable a priori estimates. Finally, we give an analogous local-in-time existence and uniqueness result for the case in which we introduce viscosity into the relation for macroscopic displacements such that the macroscopic equilibrium equation is of parabolic type.Received: 31 July 2002, Accepted: 9 August 2003, Published online: 21 November 2003Correspondence to: E. Bonetti  相似文献   

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Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.  相似文献   

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A Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given. The procedure is utilized to analyze the effect of non-conservative autonomous and non-autonomous (pulsating) forces acting on a linearly damped Beck’s column involving geometrical nonlinearities. The linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach. Critical scenarios for the autonomous and non-autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. A comparison between critical and post-critical continuous and discrete model is performed adopting two control parameters, namely the amplitudes of the static and dynamic components of the forces, playing the role of detuning and bifurcation parameters, respectively.  相似文献   

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A temporal–spatial pseudospectral (TSP) method is proposed for the high-accuracy solutions of time-periodic unsteady fluid flow and heat transfer problems. In this method, both the spatial and temporal derivative terms in the governing equations are computed by pseudospectral method. The spatial derivatives are computed through Chebyshev and Lagrange polynomials while the time derivatives are computed by Fourier series. The TSP method is capable of directly finding out the periodic state solutions without the necessity to resolve the initial transient state solutions, hence holds high computational efficiency and high numerical accuracy properties for the time-periodic problems. This method is validated by three 2D benchmark problems: the time-periodic incompressible flow with exact solutions; the natural convection in enclosure with time-periodic temperature on one sidewall, and on both sidewalls. The TSP results fit well the exact solutions or the benchmark solutions and the TSP accuracy is much higher than the time marching spatial pseudospectral accuracy. Some time-dependent fluid flow and heat transfer characteristic parameters are analysed. The proposed TSP method could be further extended to more complex time-periodic unsteady fluid flow and heat transfer problems where high-accuracy results are required.  相似文献   

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The two-equation `low Reynolds number' k-? model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Prt in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 104?4. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.  相似文献   

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The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.  相似文献   

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The aim of this work is to critically assess the new model for porous, nonlinear viscous solids incorporating void shape effects proposed in Part I, by comparing its predictions with the results of some numerical micromechanical simulations. Two kinds of simulations are performed. First, the gauge surface of spheroidal representative volume elements, as considered in Part I, is determined for various values of the porosity, the aspect ratio of the void and the Norton exponent. This is done through minimization of the macroscopic viscous potential over a family of trial velocity fields especially adapted to the spheroidal geometry, which was proposed by Lee and Mear. Such simulations allow not only for satisfactory validation of the approximate analytical gauge surface proposed, but also for adjustment of the heuristic coefficients involved in the evolution equation for the void shape parameter. Second, the evolution in time of cylindrical cells subjected to various mechanical loads is determined by the finite element method. The quasi-periodicity of this new geometry is intended to approximately represent interactions between neighbouring voids. These simulations also reveal very good agreement between model predictions and numerical calculations, provided that the effect of the new geometry considered is accounted for by using a non-unity value for the analog of Tvergaard's famous “q1” parameter for porous plastic solids.  相似文献   

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Car-following models are proposed to describe the jamming transition in traffic flow on a highway. In this paper, a new car-following model considering the driver’s forecast effect is investigated to describe the traffic jam. The nature of the model is studied using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow and the time-dependent Ginzburg–Landau (TDGL) equation is derived to describe the traffic flow near the critical point. It is also shown that the modified Korteweg-de Veris (mKdV) equation is derived to describe the traffic jam. The connection between the TDGL and the mKdV equations is given.  相似文献   

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Zhai  Cong  Wu  Weitiao 《Nonlinear dynamics》2018,93(4):2185-2199
Nonlinear Dynamics - In this paper, we propose an extension of the optimal velocity car-following model to consider explicitly the timid and aggressive driving behavior as well as the traffic jerk....  相似文献   

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In this paper, we use car-following theory to propose a model with consideration of multi-telegraph poles and electrical wires to describe a single helicopter’s flying behavior in the low airspace with a parallel electrical wire network. The numerical results show that the proposed model can describe the qualitative effects of the parallel electrical wire network on the evolutions of a helicopter’s speed, safe distances for the telegraph poles and electrical wires and safe sphere. These results can help us to better understand the helicopter’s flying behavior in the low airspace with a parallel electrical wire network.  相似文献   

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An analytical model for damaged woven fabric composites is developed using the theory of advanced mechanics of materials. The analysis is based on Castigliano’s second theorem and utilizes a damaged mosaic model laminate. Three damage modes (i.e., transverse yarn cracking, interface debonding, and sliding with friction at the interface) are considered. Only one independent interfacial parameter, the friction coefficient between warp and fill yarns, is introduced in the analysis. A closed-form formula is provided for estimating effective Young’s modulus of damaged woven laminates. A parametric study of some 192 sample cases of two different composite systems (i.e., glass fiber/epoxy and ceramic fiber/ceramic) is conducted to illustrate the application and significance of the newly derived analytical model. The numerical values of the effective Young’s modulus for the special case involving only transverse yarn cracking (the first damage mode) estimated by the present mechanics-of-materials model agree fairly well with those predicted by an elasticity-based model [Int. J. Solids Struct. 38 (2001) 855]. For the general case involving all three damage modes simultaneously, the present model reveals the complex nature of Young’s modulus reduction in a quantitative manner, which differs from existing models.  相似文献   

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Based on Biot’s theory, the dynamic 2.5-D Green’s function for a saturated porous medium is obtained using the Fourier transform and the potential decomposition methods. The 2.5-D Green’s function corresponds to the solutions for the following two problems: the point force applied to the solid skeleton, and the dilatation source applied within the pore fluid. By performing the Fourier transform on the governing equations for the 3-D Green’s function, the governing differential equations for the two parts of the 2.5-D Green’s function are established and then solved to obtain the dynamic 2.5-D Green’s function. The derived 2.5-D Green’s function for saturated porous media is verified through comparison with the existing solution for 2.5-D Green’s function for the elastodynamic case and the closed-form 3-D Green’s function for saturated porous media. It is further demonstrated that a simple form 2-D Green’s function for saturated porous media can be been obtained using the potential decomposition method.  相似文献   

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Based on an extended lattice hydrodynamic model considering the delay of the driver’s response in sensing headway, we get the time-dependent Ginzburg–Landau (for short, TDGL) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method. The corresponding solutions are obtained. Numerical simulation is carried out to examine the performance of the model and the results show coincidence with the analysis results.  相似文献   

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