Showing papers in "International Journal of Non-linear Mechanics in 2004"
TL;DR: The steady two-dimensional stagnation point flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation point, has been studied in this paper.
Abstract: The steady two-dimensional stagnation point flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation point, has been studied in this paper. The resulting equations of non-linear ordinary coupled differential equations are solved numerically using the Keller–box method. The results obtained for velocity, microrotation and skin friction are shown in tables and graphs. Comparison with the recent results of Mahapatra and Gupta {Heat Mass Transfer 38 (2002) 517} for the corresponding problem of a viscous fluid ( K =0) has been done and it has been shown that the results are in excellent agreement.
288 citations
TL;DR: In this article, the authors analyzed Stokes and Couette flows produced by an oscillatory motion of a wall under conditions where the no-slip assumption between the wall and the fluid is no longer valid.
Abstract: Stokes and Couette flows produced by an oscillatory motion of a wall are analyzed under conditions where the no-slip assumption between the wall and the fluid is no longer valid. The motion of the wall is assumed to have a generic sinusoidal behavior. The exact solutions include both steady periodic and transient velocity profiles. It is found that slip conditions between the wall and the fluid produces lower amplitudes of oscillations in the flow near the oscillating wall than when no-slip assumption is utilized. Further, the relative velocity between the fluid layer at the wall and the speed of the wall is found to overshoot at a specific oscillating slip parameter or vibrational Reynolds number at certain times. In addition, it is found that wall slip reduces the transient velocity for Stokes flow while minimum transient effects for Couette flow is achieved only for large and small values of the wall slip coefficient and the gap thickness, respectively. The time needed to reach to steady periodic Stokes flow due to sine oscillations is greater than that for cosine oscillations with both wall slip and no-slip conditions.
140 citations
TL;DR: An on-line adaptive tracking technique, based on the least-square estimation, to identify the system parameters and their changes of non-linear hysteretic structures and demonstrate the application and effectiveness of the proposed technique in detecting the structural damages.
Abstract: System identification and damage detection based on vibration data have received considerable attention recently because of their importance to structural health monitoring. Various technical approaches have been proposed in the literature; however, the on-line identification of the changes of parameters for non-linear structures due to damages is still a challenging problem. In this paper, we propose an on-line adaptive tracking technique, based on the least-square estimation, to identify the system parameters and their changes of non-linear hysteretic structures. The method proposed is capable of tracking abrupt or slow changes of the system parameters from which the damage event and the severity of the structural damage can be detected and evaluated. Simulation results for tracking the parametric changes of non-linear hysteretic structures are presented to demonstrate the application and effectiveness of the proposed technique in detecting the structural damages.
133 citations
TL;DR: In this paper, a theory for the equilibrium response of magnetoelastic membranes under pressure and applied magnetic fields is formulated on the basis of three-dimensional magneto-elasticity.
Abstract: A theory for the equilibrium response of magnetoelastic membranes under pressure and applied magnetic fields is formulated on the basis of three-dimensional magnetoelasticity. A variational principle admitted by the three-dimensional theory is used to generate a model for membranes regarded as thin three-dimensional bodies. Minimum energy considerations in the presence of applied magnetic fields are used to motivate a direct theory of magnetoelastic membranes which does not require information about bulk properties. The theory is applicable to conventional elastomers magnetized through infusion with uniformly dispersed ferrous particles.
115 citations
TL;DR: In this paper, it was shown that the vibrational resonances caused by a biharmonical external force with two different frequencies are conjugate, and these resonances occur as either the low and high frequency is varied.
Abstract: Using a bistable oscillator described by a Duffing equation as an example, resonances caused by a biharmonical external force with two different frequencies (the so-called vibrational resonances) are considered. It is shown that, in the case of a weakly damped oscillator, these resonances are conjugate; they occur as either the low and high frequency is varied. In addition, the resonances occur as the amplitude of the high-frequency excitation is varied. It is also shown that the high-frequency action induces the change in the number of stable steady states; these bifurcations are also conjugate, and are the cause of the seeming resonance in an overdamped oscillator.
113 citations
TL;DR: In this paper, the effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiasial loading paths.
Abstract: The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.
106 citations
TL;DR: In this paper, the balance laws of a single continuum with mass diffusion overcomes the difficulties inherent in the theory of mixtures in specifying boundary conditions, and a natural boundary condition based upon the continuity of the chemical potential is derived by the use of a variational approach, based on maximizing the rate of dissipation.
Abstract: This paper is concerned with the modeling of slow diffusion of a fluid into a swelling solid undergoing large deformation. Both the stress in the solid as well as the diffusion rates are predicted. The approach presented here, based on the balance laws of a single continuum with mass diffusion, overcomes the difficulties inherent in the theory of mixtures in specifying boundary conditions. A “natural” boundary condition based upon the continuity of the chemical potential is derived by the use of a variational approach, based on maximizing the rate of dissipation. It is shown that, in the absence of inertial effects, the differential equations resulting from the use of mixture theory can be recast into a form that is identical to the equations obtained in our approach. The boundary value problem of the steady flow of a solvent through a gum rubber membrane is solved and the results show excellent agreement with the experimental data of Paul and Ebra-Lima (J. Appl. Polym. Sci. 14 (1970) 2201) for a variety of solvents.
103 citations
TL;DR: In this paper, an analysis of the steady two-dimensional stagnation point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point is made.
Abstract: An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B′ model), a boundary layer is formed when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases with increase in the elasticity of the fluid. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the velocity of the free stream and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. It is found that temperature at a point decreases with increase in the elasticity of the fluid.
101 citations
TL;DR: It is shown that the calculation of the free response of a single-degree-of-freedom (SDOF) mass-hysteresis-spring system is amenable to an exact solution and appears to be an inherent property of the system pointing to the need for developing further analysis methods.
Abstract: Many machine elements in common engineering use exhibit the characteristic of “hysteresis springs”. Plain and rolling element bearings that are widely used in motion guidance of machine tools are typical examples. The study of the non-linear dynamics caused by such elements becomes imperative if we wish to achieve accurate control of such machines. This paper outlines the properties of rate-independent hysteresis and shows that the calculation of the free response of a single-degree-of-freedom (SDOF) mass-hysteresis-spring system is amenable to an exact solution. The more important issue of forced response is not so, requiring other methods of treatment. We consider the approximate describing function method and compare its results with exact numerical simulations. Agreement is good for small excitation amplitudes, where the system approximates to a linear mass-spring-damper system, and for very large amplitudes, where some sort of mass-line is approached. Intermediate values however, show high sensitivity to amplitude variations, and no regular solution is obtained by either approach. This appears thus to be an inherent property of the system pointing to the need for developing further analysis methods.
99 citations
TL;DR: In this paper, the Restoring Force Method is used for the non-parametric identification of non-linear systems, and a general procedure is presented for the direct identification of the state equation of complex nonlinear systems.
Abstract: Building on the basic idea behind the Restoring Force Method for the non-parametric identification of non-linear systems, a general procedure is presented for the direct identification of the state equation of complex non-linear systems. No information about the system mass is required, and only the applied excitation(s) and resulting acceleration are needed to implement the procedure. Arbitrary non-linear phenomena spanning the range from polynomial non-linearities to the noisy Duffing–van der Pol oscillator (involving product-type non-linearities and multiple excitations) or hysteretic behavior such as the Bouc–Wen model can be handled without difficulty. In the case of polynomial-type non-linearities, the approach yields virtually exact results for sufficiently rich excitations. For other types of non-linearities, the approach yields the optimum (in least-squares sense) representation in non-parametric form of the dominant interaction forces induced by the motion of the system. Several examples involving synthetic data corresponding to a variety of highly non-linear phenomena are presented to demonstrate the utility as well as the range of validity of the proposed approach.
97 citations
TL;DR: In this article, the homotopy analysis method is employed to control the convergence of approximation series and adjust convergence regions when necessary, unlike other analytic techniques, this approach provides us with a convenient way to adjust convergence region when necessary.
Abstract: A new analytic approximate technique for non-linear problems, namely the homotopy analysis method, is employed to propose an approach for free oscillations of self-excited systems. Different from perturbation methods on this topic, this approach does not depend upon any small/large parameters at all and therefore is valid for free oscillations of all self-excited systems. Besides, unlike other analytic techniques, this approach provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. Two examples are employed to illustrate the validity and flexibility of this approach.
TL;DR: In this article, an expansion theorem of Steklov is used to obtain exact solutions for flows satisfying no-slip boundary conditions, and steady state solutions are also obtained for t→∞.
Abstract: This paper deals with some unsteady unidirectional transient flows of an Oldroyd-B fluid in unbounded domains which geometrically are axisymmetric pipe-like. An expansion theorem of Steklov is used to obtain exact solutions for flows satisfying no-slip boundary conditions. The well known solutions for a Navier–Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limiting cases of our solutions. The steady state solutions are also obtained for t→∞.
TL;DR: In this paper, an exact solution of an oscillatory flow is constructed in a rotating fluid under the influence of an uniform transverse magnetic field, where the fluid is considered as second-grade (non-Newtonian).
Abstract: An exact solution of an oscillatory flow is constructed in a rotating fluid under the influence of an uniform transverse magnetic field. The fluid is considered as second-grade (non-Newtonian). The influence of Hall currents and material parameters of the second-grade fluid is investigated. The hydromagnetic flow is generated in the uniformly rotating fluid bounded between two rigid non-conducting parallel plates by small amplitude oscillations of the upper plate. The exact solutions of the steady and unsteady velocity fields are constructed. It is found that the steady solution depends on the Hall parameter but is independent of the material parameter of the fluid. The unsteady part of the solution depends upon both (Hall and material) parameters. Attention is focused upon the physical nature of the solution, and the structure of the various kinds of boundary layers is examined. Several results of physical interest have been deduced in limiting cases.
TL;DR: In this article, the boundary layer flow of a viscoelastic fluid of the second-grade type over a rigid continuous plate moving through an otherwise quiescent fluid with constant velocity U is studied.
Abstract: The boundary layer flow of a viscoelastic fluid of the second-grade type over a rigid continuous plate moving through an otherwise quiescent fluid with constant velocity U is studied. Assuming the flow to be laminar and two-dimensional, local similarity solution is found with fluid's elasticity and plate's withdrawal speed as the main variables. Results are presented for velocity profiles, boundary layer thickness, wall skin friction coefficient and fluid entrainment in terms of the local Deborah number. A marked formation of boundary layer is predicted, even at low Reynolds numbers, provided the Deborah number is sufficiently large. The boundary layer thickness and the wall skin friction coefficient are found to scale with fluid's elasticity—both decreasing the higher the fluid's elasticity. The amount of fluid entrained is also predicted to decrease whenever a fluid exhibits elastic behavior.
TL;DR: In this article, the authors constructed exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid, which are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient.
Abstract: Exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid are constructed The flows are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient Expressions for velocity, flux and skin friction are obtained for both large and small times It is found that large and small times solutions are dependent on the coefficient of viscoelasticity The solutions corresponding to Newtonian fluids can be easily obtained from those for fluids of second order by letting the viscoelastic parameter to be zero
TL;DR: In this article, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC) are presented.
Abstract: In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.
TL;DR: In this paper, approximate analytical solutions to large-amplitude oscillations of a general, inclusive of odd and non-odd nonlinearity, conservative single-degree-of-freedom system are presented.
Abstract: This paper presents new, approximate analytical solutions to large-amplitude oscillations of a general, inclusive of odd and non-odd non-linearity, conservative single-degree-of-freedom system. Based on the original general non-linear oscillating system, two new systems with odd non-linearity are to be addressed. Building on the approximate analytical solutions of odd non-linear systems developed by the authors earlier, we construct the new approximate analytical solutions to the original general non-linear system by combinatory piecing of the approximate solutions corresponding to, respectively, the two new systems introduced. These approximate solutions are valid for small as well as large amplitudes of oscillation for which the perturbation method either provides inaccurate solutions or is inapplicable. Two examples with excellent approximate analytical solutions are presented to illustrate the great accuracy and simplicity of the new formulation.
TL;DR: In this paper, the authors examined the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) and reported that the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite.
Abstract: Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained from a series of biaxial tests that were conducted with different proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full field surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He–Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement field, Δu(x,y) and Δv(x,y). From these, the incremental inplane surface strains Δex, Δey and Δγxy are obtained by numerical differentiation. The present paper, which is the first in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.
TL;DR: In this article, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations, for the velocity field (f′,f,g), which are solved numerically by using a fourth-order Runge-Kutta integration scheme.
Abstract: Hydromagnetic flow between two horizontal plates in a rotating system, where the lower is a stretching sheet and the upper is a porous solid plate (in the presence of a magnetic field), is analyzed. The equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. These basic non-linear differential equations, for the velocity field (f′,f,g), are solved numerically by using a fourth-order Runge–Kutta integration scheme. The numerical results thus obtained are validated by the analytical results (for small R) obtained by the perturbation technique and presented through graphs. Also, the effects of the non-dimensional parameters R, λ, M2 and K2 on the velocity field are discussed, and it is shown that for large K2, the coriolis force and the magnetic field that act against the pressure gradient cause reverse flow.
TL;DR: In this article, the numerical path integration method, based on Gauss-Legendre integration scheme, is applied to a Duffing oscillator subject to both sinusoidal and white noise excitations.
Abstract: The numerical path integration method, based on Gauss–Legendre integration scheme, is applied to a Duffing oscillator subject to both sinusoidal and white noise excitations. The response of the system is a Markov process with one of the drift coefficients being periodic. It is a non-homogeneous Markov process that does not have a stationary probability distribution. When applying the numerical procedure, the values of transition probability density at the Gaussian–Legendre quadrature points need only be calculated for time steps of the first period of the sinusoidal excitation, and they can be saved for use in all subsequent periods. The numerical procedure is capable of capturing the evolution of the probability density from an initial distribution to one that is changing and rotating periodically in the phase space.
TL;DR: In this paper, an analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid past a stretching sheet in the presence of a transverse magnetic field.
Abstract: An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field. In heat transfer, two cases are considered: 1. The sheet with prescribed surface temperature (PST case); and 2. The sheet with prescribed wall heat flux (PHF case). The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k 1 , Schmidt number Sc , and Prandtl number Pr on flow, heat and mass transfer characteristics.
TL;DR: In this paper, a panel forced by a supersonic unsteady flow is numerically investigated using a finite difference method, a Galerkin approach, and proper orthogonal decomposition (POD).
Abstract: A panel forced by a supersonic unsteady flow is numerically investigated using a finite difference method, a Galerkin approach, and proper orthogonal decomposition (POD). The aeroelastic model investigated is based on piston theory for modeling the flow-induced forces, and von Karman plate theory for modeling the panel. Structural non-linearity is considered, and it is due to the non-linear coupling between bending and stretching. Several novel facets of behavior are explored, and key aspects of using a Galerkin method for modeling the dynamics of the panel exhibiting limit cycle oscillations and chaos are investigated. It is shown that multiple limit cycles may co-exist, and they are both symmetric and asymmetric. Furthermore, the level of spatial coherence in the dynamics is estimated by means of POD. Reduced order models for the dynamics are constructed. The sensitivity to initial conditions of the non-linear aeroelastic system in the chaotic regime limits the capability of the reduced order models to identically model the time histories of the system. However, various global characteristics of the dynamics, such as the main attractor governing the dynamics, are accurately predicted by the reduced order models. For the case of limit cycle oscillations and stable buckling, the reduced order models are shown to be accurate and robust to parameter variations.
TL;DR: In this article, the authors re-examined Stokes' first problem for Maxwell fluids using integral transform methods and several forms of the exact solution are presented, and pointed out a recent case in the literature where this solution has been stated incorrectly.
Abstract: Stokes’ first problem for Maxwell fluids is re-examined using integral transform methods and several forms of the exact solution are presented. In the process, we call attention to, and correct, a recent case in the literature where this solution has been stated incorrectly. In addition, we note a number of analytical results and give several velocity profile plots. Finally, connections are drawn to other areas of research.
TL;DR: In this paper, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach, which includes the effects of shear deformation, in-plane and rotary inertia.
Abstract: Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.
TL;DR: In this article, the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness nonlinearity, were studied.
Abstract: We study the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness non-linearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (non-linear normal modes—NNMs), as well as, asynchronous periodic motions (elliptic orbits—EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets ‘captured’ in the neighborhood of a damped NNM before ‘escaping’ and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive non-linear energy pumping phenomena from the linear to the non-linear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions.
TL;DR: In this paper, a general inelastic framework for the derivation of general three-dimensional thermomechanical constitutive laws for materials undergoing phase transformations is proposed, which is based on the generalized plasticity theory and on some basic elements from the theory of continuum damage mechanics.
Abstract: In this work, a general inelastic framework for the derivation of general three-dimensional thermomechanical constitutive laws for materials undergoing phase transformations is proposed. The proposed framework is based on the generalized plasticity theory and on some basic elements from the theory of continuum damage mechanics. More specifically, a new elaborate formulation of generalized plasticity theory capable of accommodating the multiple and interacting loading mechanisms, which occur during the phase transformations, is developed. Furthermore, the stiffness variations occurring during phase transformations are taken into account by the proposed framework. For this purpose, the free energy is decomposed into elastic and inelastic parts, not in a conventional way, but in one which resembles the elastic-damage cases. Also, a rate-dependent version of the theory is provided. The concepts presented are applied for the derivation of a three-dimensional thermomechanical constitutive model for Shape Memory Alloy materials. Numerical simulations to show qualitatively the ability of the model to capture the behavior of the shape memory alloys are also presented. Furthermore, the model has been fitted to actual experimental results from the literature.
TL;DR: In this article, a micro-mechanical material model of woven fabric composite material is developed to simulate failure, which is based on repeated unit cell approach to simulate fiber reorientation.
Abstract: A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.
TL;DR: In this paper, the complete Lie group classification of a non-linear wave equation is obtained in the case of a hyperelastic homogeneous bar with variable cross-section, and the reduced equations are obtained for the same case.
Abstract: In this paper the complete Lie group classification of a non-linear wave equation is obtained. Optimal systems and reduced equations are achieved in the case of a hyperelastic homogeneous bar with variable cross section.
TL;DR: In this article, a global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph.
Abstract: A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.
TL;DR: In this article, an infinite porous plate exhibiting non-torsional oscillation of a given frequency was used to study the effect of material parameters on the flow and several limiting cases were deduced.
Abstract: A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.