Simulation of planar flexible multibody systems with clearance and lubricated revolute joints

Modeling of clearance joints plays an important role in the analysis and design of multibody mechanical systems. Based on the absolute nodal coordinate formulation (ANCF), a new computational methodology for modeling and analysis of planar flexible multibody systems with clearance and lubricated revolute joints is presented. A planar absolute nodal coordinate formulation based on the locking-free shear deformable beam element is implemented to discretize the flexible bodies. A continuous contact-impact model is used to evaluate the contact force, in which energy dissipation in the form of hysteresis damping is considered. A force transition model from hydrodynamic lubrication forces to dry contact forces is introduced to ensure continuity in the joint reaction force. A comprehensive study with different lubrication force models has also been carried out. The generalized-α method is used to solve the equations of motion and several efficient methods are incorporated in the proposed model. Finally, the methodology is validated by two numerical examples.     

A new pedestrian-following model for aircraft boarding and numerical tests

The purpose of this paper is to develop a new pedestrian-following model based on the properties of the aircraft boarding process. The passengers’ motion trail, the number of interfaces, the total aircraft boarding time, the wasted time that is resulted by the interfaces and the effective aircraft boarding time are investigated in detail. The numerical results illustrate that the new model can qualitatively describe some dynamic properties of the aircraft boarding process.     

A new analytical model for the elastic–plastic behaviour of spot welded joints subjected to orthogonal load

An analytical procedure for the evaluation of the elastic–plastic stiffness behaviour of spot welded joints is presented. The procedure is based on a new model of spot weld region: a circular plate having variable thickness with a central rigid nugget, which is resolved using an original analytical method.The closed-form solution allows to describe the displacement of a rigid nugget when an axial orthogonal load is applied on the plate while plasticity and large deflections are present. The goal is to reach a reliable spot weld region model which can be used as the basis to develop a spot weld element in FE analysis even when plasticity and large deflections are in effect.The procedure is as completely original as no other can be found in the technical literature, and it has been applied to some examples of plates usually employed for spot weld analysis. The analytical results obtained by using the new general relations precisely match those obtained modelling spot weld area by FEA.     

A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

We propose a theoretical model for spatial variations of the temperature variance σ~2( z, r)( z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection(RBC).Adapting the "attached-eddy" model of shear flow to the plumes of RBC, we derived an equation for σ~2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z/λ_(th), where λ_(th) is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr, but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.     

A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems

By introducing a new parametric transformation and a suitable nonlinear frequency expansion, the modified Lindstedt–Poincaré method is extended to derive analytical approximations for limit cycles in three-dimensional nonlinear autonomous dynamical systems. By considering two typical examples, it can be seen that the results of the present method are in good agreement with those obtained numerically even if the control parameter is moderately large. Moreover, the present prediction is considerably more accurate than some published results obtained by the multiple time scales method and the normal form method.     

A new method for solving Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.     

A new drag model for TFM simulation of gas–solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas–solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with experimental data than those of the Gidaspow drag model did.     

Bifurcation and stability analysis in predator–prey model with a stage-structure for predator

A predator–prey system with Holling type II functional response and stage-structure for predator is presented. The stability and Hopf bifurcation of this model are studied by analyzing the associated characteristic transcendental equation. Further, an explicit formula for determining the stability and the direction of periodic solutions bifurcating from positive equilibrium is derived by the normal form theory and center manifold argument. Some numerical simulations are also given to illustrate our results.     

A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems

This paper discusses the synchronization and anti-synchronization of new uncertain unified chaotic systems (UUCS). Based on the idea of active control, a novel active Pinning control strategy is presented, which only needs a state of new UUCS. The proposed controller can achieve synchronization between a response system and a drive system, and ensure the synchronized robust stability of new UUCS. Numerical simulations of new UUCS show that the controller can make chaotic systems achieve synchronization or anti-synchronization in a quite short period and both are of good robust stability.     

A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap

A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner.If two firms are competitors(copartners),the default inten- sity of one firm will decrease(increase)abruptly when the other firm defaults.As time goes on,the impact will decrease gradually until extinct.In this model,the joint distri- bution and marginal distributions of default times are derived by employing the change of measure,and the fair swap premium of a credit default swap(CDS)can be valued.     

BEM–FEM coupling for the analysis of flexible propellers in non-uniform flows and validation with full-scale measurements

The first part of the paper presents a partitioned fluid–structure interaction (FSI) coupling for the non-uniform flow hydro-elastic analysis of highly flexible propellers in cavitating and non-cavitating conditions. The chosen fluid model is a potential flow solved with a boundary element method (BEM). The structural sub-problem has been modelled with a finite element method (FEM). In the present method, the fully partitioned framework allows one to use another flow or structural solver. An important feature of the present method is the time periodic way of solving the FSI problem. In a time periodic coupling, the coupling iterations are not performed per time step but on a periodic level, which is necessary for the present BEM–FEM coupling, but can also offer an improved convergence rate compared to a time step coupled method. Thus, it allows to solve the structural problem in the frequency domain, meaning that any transients, which slow down the convergence process, are not computed. As proposed in the method, the structural equations of motion can be solved in modal space, which allows for a model reduction by involving only a limited number of mode shapes.The second part of the paper includes a validation study on full-scale. For the full-scale validation study a purposely designed composite propeller with a diameter of 1 m has been manufactured. Also an underwater measurement set-up including a stereo camera system, remote control of the optics and illumination system has been developed. The propeller design and the underwater measurement set-up are described in the paper. During sea trials blade deflections have been measured in three different positions. A comparison between measured and calculated torque shows that the measured torque is much larger than computed. This is attributed to the differences between effective and nominal wakefields, where the latter one has been used for the calculations. To correct for the differences between measured and computed torque the calculated pressures have been amplified accordingly. In that way the deformations which have been computed with the BEM–FEM coupling for non-uniform flows became very similar to the measured results.     

A three-invariant cap model with isotropic–kinematic hardening rule and associated plasticity for granular materials

In this paper, a three-invariant cap model is developed for the isotropic–kinematic hardening and associated plasticity of granular materials. The model is based on the concepts of elasticity and plasticity theories together with an associated flow rule and a work hardening law for plastic deformations of granulars. The hardening rule is defined by its decomposition into the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters. The model assessment and procedure for determination of material parameters are described. Finally, the applicability of proposed plasticity model is demonstrated in numerical simulation of several triaxial and confining pressure tests on different granular materials, including: wheat, rape, synthetic granulate and sand.     

A new unified constitutive model with short- and long-range back stress for lead-free solders of Sn–3Ag–0.5Cu and Sn–0.7Cu

A series of tensile tests of Sn–3Ag–0.5Cu and Sn–0.7Cu lead-free solders were investigated at various strain rates from 1 × 10⁻⁴ s⁻¹ to 1 × 10⁻² s⁻¹ and over a wide temperature range from 25 ^oC to 150 ^oC. Two-step strain rate jump tests, three-step short term creep tests with stress jump, and uniaxial ratcheting tests were also conducted. Based on the test data, a new constitutive model was proposed with a simple formulation and only eight material constants which can be easily obtained. The model employs two carefully defined back stress components to simulate the loading/unloading asymmetry phenomenon in uniaxial ratcheting tests. Different evolution rules of short-range back stress were given for loading and unloading stage, which provides the model ability to simulate the asymmetry in hysteresis loops. The proposed model presents good simulation of uniaxial tensile tests, strain rate jump tests, short term creep tests with stress jump, and uniaxial ratcheting tests.     

A new method for computing turbulence in compressible laminar-turbulent transition and boundary layers--PSE＋DNS

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers is proposed. It is especially useful for computation of laminar-turbulent transition and turbulence starting from small-amplitude disturbances. The laminar stage, up to the beginning of the breakdown in laminar-turbulent transition, is computed by parabolized stability equations (PSE). The direct numerical simulation (DNS) method is used to compute the transition process and turbulent flow, for which the inflow condition is provided by using the disturbances obtained by PSE method up to that stage. In the two test cases incfuding a subsonic and a supersonic boundary layer, the transition locations and the turbulent flow obtained with this method agree well with those obtained by using only DNS method for the whole process. The computational cost of the proposed method is much less than using only DNS method.     

A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint

The end shear restraint, which is an un-classical type of end support, has a significant effect on the behavior of elastic composite beams. The principal aim of this paper is to present a numerical model for studying the effect of end shear restraint on static and free vibration behavior of elastic composite beams with various end conditions. The elastic composite beam, considered in this study, is composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The three types of end conditions considered in this study are simple, fixed and free supports. The numerical model is based on the combination of transfer matrix and analog beam methods. The field transfer matrices for the element of the elastic composite beam are derived. The present model is applied to the beam systems with and without end shear restraint and the static response and natural frequencies are calculated. the effect of shear stiffness between the upper slab and lower beam is also demonstrated.     

A Representation Theorem for Material Tensors of?Weakly-Textured Polycrystals and?Its Applications in?Elasticity

Material tensors pertaining to polycrystalline aggregates should manifest also the influence of crystallographic texture on the material properties in question. In this paper we make use of tensors which form bases of irreducible representations of the rotation group and prove a representation theorem by which a given material tensor of a weakly-textured polycrystal is expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a set of undetermined material parameters. Once the irreducible basis tensors that appear in the formula are determined, the representation formula, which is valid for all texture and crystal symmetries, will delineate quantitatively the effect of crystallographic texture on the material tensor in question. We present an integral formula and an orthonormalization process which serve as the basis for a procedure to determine explicitly the irreducible basis tensors required in the representation formula. For applications we determine a set of irreducible basis tensors for the elasticity tensor and a set for fourth-order tensors that define constitutive equations in incompressible elasticity and Hill’s quadratic yield functions in plasticity. We show that orientation averaging of a tensor can be done easily if we have in hand a set of irreducible basis tensors for the decomposition of the tensor in question. As illustration we derive a formula, which is valid for all texture and crystal symmetries, for the elasticity tensor under the Voigt model.     

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio is proposed. Effects of thermo-oxidative aging and viscoelastic Poisson’s ratio are considered in this comprehensive constitutive equation with two sets of reduced time system coping with the time and temperature dependence. In order to simulate the single and combined effects of aging and viscoelastic Poisson’s ratio, constitutive equation is rewritten into an incremental form and implemented in the user subroutine UMAT at the platform of finite element code ABAQUS. Detailed procedure for acquiring the parameters in constitutive equation is introduced and conducted for the subsequent applied analysis. Two typical loading cases during the service life of solid rocket motor and four sets of combined constitutive models are simulated. Von Mises strain and stress distribution and their changes versus time are utilized as the main analysis index. The results show that the effects of aging and viscoelastic Poisson’s ratio or their combinations will improve or decrease the level and change the distribution of Von Mises strain and stress in varying degrees.     

A helicopter’s formation flying model in the low airspace with two telegraph poles and electrical wire

In this paper, we develop a helicopter??s formation flying model with telegraph poles and electrical wire to study each helicopter??s flying behavior in the low airspace. The numerical results show that the proposed model can qualitatively describe the influences of the telegraph poles and electrical wire on the helicopter??s formation flying behavior in the low airspace and that the effects will be related to each helicopter??s initial conditions.