Computation of the stresses in a moving reference system in a half-space due to a traversing time-varying concentrated load

An analytical approach is employed to investigate the transient and steady-state stresses in an isotropic, homogeneous half-space subjected to moving concentrated loads with subsonic speeds. Applying the Stokes–Helmholtz resolution to the Navier’s equation of motion for the half-space results in a system of wavetype partial differential equations. Based on the new moving coordinate system, a modified system of partial differential equations is obtained. Applying a concurrent two-sided and one-sided Laplace transformation, this system is modified to a system of ordinary differential equations, the solutions of which are obtained with respect to boundary conditions. The transformed transient stresses can be inverted by the Cagniard–de Hoop method. Special properties of Laplace transformation yield the steady-state stresses through an analytical approach. Numerical examples are presented to illustrate the methodology. Final results revealed the importance of considering the stresses related to the initial stages of the loading.     

移动简谐力激励非线性无限长地基梁稳态响应

同时计入地基中的非线性弹性、黏性以及剪切作用的影响,研究移动集中简谐力作用下无限长地基梁稳态响应问题.假设基础非线性弹性为立方非线性.通过Adomian多项式分解方法和Fourier变换得到梁稳态响应的Green函数,再运用Fourier逆变换得到梁稳态响应近似解析解的积分表达式.最后对解析积分表达式应用留数定理得到复数域上的解.通过数值算例,考察了移动集中简谐力的频率和移动速度对无限长地基梁稳态响应的影响.另外,还通过算例对比研究了地基的非线性弹性系数和剪切系数对无限长地基梁稳态响应的影响.     

Thermo-elastic interactions in an infinite elastic solid due to distributed time-dependent heat sources in generalized thermo-elasticity III

The generalized theory of thermo-elasticity of Type III recently developed by Green and Naghdi is employed to study thermo-elastic interactions in a homogeneous isotropic unbounded solid having distributed instantaneous and continuous heat sources. The solutions are derived by using Laplace transform on time and then Fourier transform on space. It is found that the interactions consist of a wave travelling with the speed of dilatational wave and a diffusive part. The temperature and the deformation field are both continuous at the dilatational wave front while the stress field exhibits finite discontinuity at this location in case of instantaneous distributed heat sources. For continuous distributed heat sources, the thermal, deformation, and stress fields are however all continuous at the dilatational wave front. All the fields suffer exponential attenuation at the dilatational wave front and the attenuation is influenced by the thermo-elastic coupling and the thermal diffusivity of the medium. The results of the present analysis are compared to those derived by using other generalized thermo-elasticity theories such as L-S theory and G-L theory. The analysis reveals that G-N theory III eliminates some of the finite discontinuities and δ-function singularity in the deformation, temperature and stress fields derived by using other generalized thermo-elasticity theories in earlier investigations. Finally, numerical results applicable to a copper-like material are presented in order to illustrate the analytical result.     

Collapse load evaluation of structures with frictional contact supports under combined stresses

This paper extends classical limit analysis to structures for which some supports are subjected to “nonstandard” unilateral frictional contact with the ground. A typical and commonly adopted model is nonassociative Coulomb friction. For such cases, the use of the classical bound theorems is not possible. Moreover, simply solving the governing equations as a mixed complementarity problem (MCP) does not guarantee that the best bound has been calculated. We have therefore developed an approach that attempts to compute, in a single step, the critical (least) upper bound solution by formulating and solving an instance of the challenging class of optimization problems, known as a mathematical program with equilibrium constraints (MPEC). Two examples are provided to illustrate application of the proposed scheme, as well as to highlight some key features of such structures.     

弹性支撑梁在移动荷载作用下的响应分析

考虑弹性支撑刚度对弹性支撑梁固有频率及模态的影响,比较前二阶频率受弹性支撑刚度影响的规律及大小.选取二阶模态,利用模态叠加原理,研究弹性支撑梁在移动荷载和移动车辆作用下的动力响应.研究中,一阶模态考虑为简支梁一阶模态与弹性支撑梁的刚体平动相叠加,二阶模态考虑为简支梁二阶模态与弹性支撑梁的刚体转动相叠加.研究结果表明:考...     

A boundary element analysis of the linear elasto-static axisymmetric contact problem of an infinite layered medium with a homogeneous body

A boundary element method for analyzing the linear elasto-static frictionless axisymmetric contact problem of a multi-layered medium with a homogeneous body is presented in this work. In the present method, the boundary element method using Kelvin's fundamental solution is employed to deal with the homogeneous body, while a newly developed boundary integral approach for linear elasto-static axisymmetric problems is utilized to evaluate the distributions of the stresses and displacements of the multi-layered medium in contact status. With the newly developed boundary integral approach for the multi-layered problems, the element discretization is only needed in the contact area of the multi-layered medium regardless of the variations of layer thickness, and the singularities that occur in the common boundary element are thoroughly avoided. Some numerical tests are carried out to show the efficiency of the present method.     

3D scattering of waves by a cylindrical irregular cavity of infinite length in a homogeneous elastic medium

The three-dimensional (3D) wave field scattered by an irregular, cylindrical cavity of infinite length contained in a homogeneous elastic medium illuminated by a dilatational point load is obtained. This model is used to evaluate the effect of the cross-sectional geometry of the cavity on the waves propagating in its vicinity. It particularly highlights the identification of the normal modes excited both in the frequency and time domain. The solution is formulated using the boundary element method for a wide range of frequencies and spatially harmonic line loads, which are then synthesized to obtain the time responses. The 3D solution is obtained as a summation of two-dimensional responses for different axial wavenumbers.The responses in the frequency vs. axial-wavenumber domains are presented, allowing the recognition, identification, and physical interpretation of the variation of the wave field when five irregular cross-sections are used, namely a circle, an oval, a thin oval, a kidney and a boomerang.     

Working on a moving surface—a biomechanical analysis of musculoskeletal load due to ship motions in combination with work

Ship motions are recognized by fishermen as a cause of high musculoskeletal load, In the present study, the motions of a Swedish trawler at sea were registered over three degrees of freedom. Simultaneously, the working postures of a fisherman on board were registered in the sagittal plane during five different working siiuations: (1) standing erect in Mill conditions; (2) holding a load of 21 kg in still conditions; (3) standing erect during motion of the ship; (4) standing during motion of the ship, holding a load of 21 kg, and (5) repeatedly lifting and lowering a 21 kg load during motion of the ship. All registrations were sampled using a computer where data were processed in a two-dimensional, dynamic biomechanics model, developed for this particular purpose. Vertical and horizontal forces as well as moments were calculated for seven major joint systems of the body, as was compression at the L4/L5 vertebral level. In situation (3), ship motions were mainly counteracted by motions in the lower extremity and lumbar back, thus inducing increased strain in these parts of the body; other pans of the body were little affected. Holding a load considerably increased the load on most joints. Lifting the load further increased the musculo-skeletal strain and also increased the range of moments in each joint as well as the range of lumbar compression. Moment at the C7 vertebral level was relatively unaffected by ship motions and by handling external loads     

Radial displacements of an infinite liquid saturated porous medium with cylindrical cavity

This paper deals with radial displacement fields in solid and liquid parts of a liquid-saturated porous medium with cylindrical cavity subjected to an arbitrary time dependent force. The Laplace transform technique is used to solve the problem. A particular case of impulsive force is discussed and closed form solutions are obtained. As a special case, results of classical elasticity are derived.     

Computation of MHD flow due to moving boundaries

A non-iterative numerical scheme is presented which computes in a single iteration the steady, laminar flow of a viscous, incompressible, electrically conducting fluid caused by moving boundaries in the presence of a transverse magnetic field. It also eliminates the possible error induced by taking the value of numerical infinity (representing the unbounded domain of the flow) as a finite number. The scheme is based on implicit use of infinite series of exponentials for velocity components. The issue of convergence of these series is also discussed. An asymptotic solution valid for large values of M, the Hartmann number, and an approximate solution valid for any value of M are further developed. In particular, the case of axisymmetric magnetohydrodynamic (MHD) flow due to a stretching sheet has been dealt with in some detail. A comparison has been made of the merits of various techniques used in the paper and appropriate conclusions are drawn.     

Bending of an axisymmetrically loaded thin circular plate on a layered elastic half-space

The problem of interaction between an axisymmetrically loaded thin circular plate and a supporting elastic medium is reduced to that of solving an integral equation for the unknown normal contact pressure. The supporting medium is an isotropic elastic layer of constant thickness lying, with or without friction, on a semi-infinite isotropic elastic base or on a rigid base. For the solution of the resulting integral equation an effective numerical procedure is employed and some numerical results are presented.     

Optimal design of box-section sandwich beams subject to moving load

Minimum weight designs of sandwich beams subject to moving load are performed as a function of prescribed load index, where the stiffness and strength constraints are both considered. The dynamic properties of sandwich beams are detected and validated through finite element simulation. Five different topologies are optimized and compared. Numerical results show that the topology of a hollow tube with sandwich walls comprising a lattice tetrahedral truss core is the most weight efficient, whereas the topology of a hollow tube with monolithic walls and a foam-filled core is the heaviest. The failure mechanisms that govern the optimal designs are also evaluated. The optimal results exhibit great sensitivity to the load moving velocity when it approaches the critical velocity of the sandwich beams. The optimization for sandwich beams under three-point bending is implemented for comparison and special dynamic characteristics of sandwich beams subject to moving load are discovered.     

Analysis of an infinite multi-server queue with an optional service

This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 − θ), or the completion of the FES may immediately require a SOS with a probability θ (0 ? θ ? 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters.     

Nonlinear resonance responses of size-dependent functionally graded cylindrical microshells with thermal effect and elastic medium

The nonlinear resonance responses of functionally graded (FG) cylindrical microshells with the elastic medium is investigated by considering thermal and scale effects. First, using the modified couple stress theory, the nonlinear dynamics model for FG microshell are established. Then the reduced nonlinear differential equations are derived by Galerkin’s method and static condensation. Finally, subharmonic, superharmonic and primary resonances of FG cylindrical microshells are analyzed by a perturbation method. In addition, the bifurcation characteristics of the nonlinear dynamic responses are investigated by some numerical examples. The effects of key parameters (modal damping, excitation frequency, foundation medium, scale parameter and thermal effect) on the nonlinear resonance responses are also discussed by numerical simulation.

     

Dynamic response of double-FG porous beam system subjected to moving load

In this paper, the vibration response of the double-FG porous beam system (DFGPBS) acted by a moving load is investigated. The DFGPBS composed of two parallel FG porous beams with their material properties varying along both the axial and transverse directions, i.e., bi-directional FG material distribution, is taken into account. The porous imperfection is simulated by distributing the porosity along the beam thickness with even and uneven patterns. The governing equations of this bi-directional DFGPBS under a moving load are established with the aid of the Hamilton principle associated with the Timoshenko beam theory. The Ritz method is adopted to discrete the differential governing equations, which are solved by the Newmark-β approach. The validation of the present model is performed by comparing the numerical results with two previous works. Then, the parametric study is carried out to investigate the influences of bi-directional gradient indices, porosity volume fraction, boundary conditions, stiffness of elastic layer, and velocity of the moving load on the vibration response of bi-directional DFGPBSs excited by a moving load. It is demonstrated that the vibration response of the double-beam system subjected to moving loads can be governed by tailoring the distribution of the bi-directional FG materials. The present work can be used to guide the multi-functional design of a double-beam system under dynamic loadings.

     

An efficient algorithm for computation of stresses due to strain measurements

An efficient and accurate algorithm for computation of stresses corresponding to measurements of strains, in materials obeying the von Mises yield criterion and perfect plasticity, is presented. The relevant formulation and computer implementation is described. Through a numerical example the accuracy, efficiency and robustness of the algorithm is verified. The listing of the source code is added for completeness.     

Minimum mass design of elastic frames subjected to multiple load cases

For frames with stress- and displacement constraints subjected to multiple load cases the formulation is given that enables use of the unified optimization approach which combines finite element and linear programming. Sensitivity analysis is shown analytically for Timoshenko beam models with transformations for eccentricities. For a specific case of a portal frame for a crane a study is made of the influence of the given portal columns (boundary conditions), the relations to fully stressed designs, and the influence of slenderness, when displacement constraints are involved.     

Dynamic response of orthotropic curved bridge decks due to moving loads

The dynamic response of horizontally curved bridge decks simply supported along the radial edges under the action of the moving vehicle is investigated. The bridge deck is idealised as a number of finite strips with orthotropic elastic properties. The stiffness and mass matrix of an individual element were derived using a homogeneous differential equation of an orthotropic plate in polar co-ordinates. The vehicle is idealized as a sprung mass moving at a constant speed in a circular path parallel to the central line of the bridge. The unsprung mass of the vehicle is assumed to be always in contact with the bridge surface during its motion. Viscous damping is taken into account for both bridge and vehicle. Dynamic deflections and moments are presented for the mid-point of the bridge deck and the values have been compared with the available analytical solution.     

Analysis of an infinite buffer system with random server interruptions

An infinite buffer with general arrival process, synchronous transmission, one single output channel and random server interruptions is considered.As opposed to previous analyses the interruption process of the output line is kept rather general, i.e. the server is assumed to be in one of two states, “available” or “blocked”, where the sojourn time of the blocked state is arbitrarily distributed and the sojourn time of the available state has a density function which is a mixture of a finite number of geometric densities. For this general case the probability generating function of the buffer occupancy at various time instants is derived.The results of the study are applied to the case where the server interruptions are due to the presence of speech at the input of the transmission channel of an integrated voice-data system. Some considerable deviations from earlier results are found.     

Deformation and structural stability of layered plate microstructures subjected to thermal loading

We study the deformation and stability of gold-polysilicon MEMS plate microstructures fabricated by the MUMPS surface micromachining process and subjected to uniform temperature changes. We measured, using an interferometric microscope, full-field deformed shapes of a series of square and circular gold (0.5 /spl mu/m thick)/polysilicon (1.5 /spl mu/m thick) plate microstructures with characteristic lengths l (square side length and circle diameter) ranging from l=150 to 300 /spl mu/m. From these measurements we determined the pointwise and average curvature of the deformed plates. Although the curvature generally varies with position, the deformation response of the plates can be broadly characterized in terms of the spatial average curvature as a function of temperature change. In terms of this, three deformation regimes were observed: (i) linear thermoelastic response independent of plate size; (ii) geometrically nonlinear thermoelastic response that depends on plate size; and (iii) bifurcations in the curvature-temperature response that also depend on plate size. We modeled the deformation response both analytically and with the finite element method; in the former we assume spatially constant curvature, while in the latter, we relax this assumption. Good qualitative and quantitative agreement is obtained between predictions and measurements in all three deformation regimes, although the details of bifurcation are less accurately predicted than the linear and nonlinear response. This is attributed to their strong sensitivity to slight imperfections, which is discussed in some detail. Good agreement is also obtained between measurements and predictions of the spatial nonuniformity of the curvature across the plate. Although it is not the focus of this study, the predictions, when coupled with curvature measurements, can be used inversely to determine elastic and thermal expansion properties of the materials in a layered plate microstructure.