Extension of the Linear Matching Method to frame structures made from a material that exhibits softening

This paper considers the problem of evaluating the maximum load that an elastic–plastic frame structure can withstand when material or element softening is present. Here we propose an extension of the Linear Matching Method to take into account material softening. The technique has two major steps: reduction of the total potential energy to obtain the solution of a linear problem and scaling of the resulting mechanism of deformation to maximize the load. Two procedures are evaluated for the second of these steps; a direct approach which simply examines how the solution evolves along a radial path in degree of freedom space, and an incremental method which takes into account how the solution might evolve along paths away from this radial line. It is demonstrated that the incremental approach is more robust and provides stable solutions for high and low levels of softening, but numerical instabilities in the procedure can occur for intermediate degrees of softening.     

Traction problem in electro-elasticity and bifurcation theory

This paper is the first of a series of two. It will deal with the problem of static traction problem with minor deformations for a material which is governed by the electrostriction phenomenon. Two approaches to this problem will be described. We can consider either the equilibrium equations which are naturally non-linear, or the equations after linearization. The linearization of equations must be done near a natural state. Locally, under some conditions, we can establish the existence and the uniqueness of the solutions. We use the local theorem of implicit functions. The problem can be approached more globally. If we consider the non-linear equations, we can use a natural principle of these equations: the independence of the choice of the observer, also known as objectivity property. This property makes it possible for us to take into account an action of the rotations group of the Euclidean space, and consequently to take into account all the trivial solutions. It is then possible to prove within the space of all configurations the existence of the non-linear equations solutions and to find their number.This work presents a thorough and detailed approach to a non-linear theory, the geometric arguments of which make it possible for us to prove the existence of all the solutions and to study their stability in the aggregate; this last aspect will be developed in the second paper. Not only can this theory anticipate the eventual existence of a stable solution, it can also anticipate that an unstable solution in terms of the elasticity can, thanks to the effect of an electric field, become stable in terms of the electro-elasticity.     

Closed solutions of boundary-value problems of coupled thermoelasticity

Coupled equations of thermoelasticity take into account the effect of nonuniform heating on the medium deformation and that of the dilatation rate on the temperature distribution. As a rule, the coupling coefficients are small and it is assumed, sometimes without proper justification, that the effect of the dilatation rate on the heat conduction process can be neglected. The aim of the present paper is to construct analytical solutions of some model boundary-value problems for a thermoelastic bounded body and to determine the body characteristic dimensions and the medium thermomechanical moduli forwhich it is necessary to take into account that the temperature and displacement fields are coupled. We consider some models constructed on the basis of the Fourier heat conduction law and the generalized Cattaneo-Jeffreys law in which the heat flux inertia is taken into account. The solution is constructed as an expansion in a biorthogonal system of eigenfunctions of the nonself-adjoint operator pencil generated by the coupled equations of motion and heat conduction. For the model problem, we choose a special class of boundary conditions that allows us to exactly determine the pencil eigenvalues.     

Rolling contact of a rigid sphere/sliding of a spherical indenter upon a viscoelastic half-space containing an ellipsoidal inhomogeneity

In this paper, the frictionless rolling contact problem between a rigid sphere and a viscoelastic half-space containing one elastic inhomogeneity is solved. The problem is equivalent to the frictionless sliding of a spherical tip over a viscoelastic body. The inhomogeneity may be of spherical or ellipsoidal shape, the later being of any orientation relatively to the contact surface. The model presented here is three dimensional and based on semi-analytical methods. In order to take into account the viscoelastic aspect of the problem, contact equations are discretized in the spatial and temporal dimensions. The frictionless rolling of the sphere, assumed rigid here for the sake of simplicity, is taken into account by translating the subsurface viscoelastic fields related to the contact problem. Eshelby's formalism is applied at each step of the temporal discretization to account for the effect of the inhomogeneity on the contact pressure distribution, subsurface stresses, rolling friction and the resulting torque. A Conjugate Gradient Method and the Fast Fourier Transforms are used to reduce the computation cost. The model is validated by a finite element model of a rigid sphere rolling upon a homogeneous vciscoelastic half-space, as well as through comparison with reference solutions from the literature. A parametric analysis of the effect of elastic properties and geometrical features of the inhomogeneity is performed. Transient and steady-state solutions are obtained. Numerical results about the contact pressure distribution, the deformed surface geometry, the apparent friction coefficient as well as subsurface stresses are presented, with or without heterogeneous inclusion.     

Rayleigh Surface Waves on a Kelvin-Voigt Viscoelastic Half-Space

In this paper we consider the propagation of Rayleigh surface waves in an exponentially graded half-space made of an isotropic Kelvin-Voigt viscoelastic material. Here we take into account the effect of the viscoelastic dissipation energy upon the corresponding wave solutions. As a consequence we introduce the damped in time wave solutions and then we treat the Rayleigh surface wave problem in terms of such solutions. The explicit form of the secular equation is obtained in terms of the wave speed and the viscoelastic inhomogeneous profile. Furthermore, we use numerical methods and computations to solve the secular equation for some special homogeneous materials. The results sustain the idea, existent in literature on the argument, that there is possible to have more than one surface wave for the Rayleigh wave problem.     

Well-posedness of characteristic symmetric hyperbolic systems

We consider the initial-boundary-value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the well-posedness in Hadamard's sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary.     

有阻尼体系的时域边界元法

针对时域边界元方法的特点，提出了一种新的阻尼模型（称为比例时耗阻尼），并成功地应用于时域边界元方法中．这是在时域边界元方法中首次考虑阻尼这一影响结构动力响应的重要因素，为时域边界元在实际工程中的应用解决了一个难题．通过对简单问题的分析和计算，验证了本文模型的正确性．     

Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes

This paper presents an efficient procedure for analyzing naturally curved and twisted beams with general cross-sectional shapes. The hypothesis concerning the cross-sectional shapes of the beams is abandoned in this analysis, and relatively general equations are derived for the analysis of such a structure. Solving directly such equations for various boundary conditions, which take into account the effects of torsion-related warping as well as transverse shear deformations, can yield the solutions to the problem. The solutions can be used to calculate various internal forces, stresses, strains and displacements of the beams. The present theory will be used to investigate the stresses and displacements of a cantilevered curved beam subjected to action of arbitrary load. The numerical results are very close to the FEM results.     

The unilateral contact buckling problem of continuous beams in the presence of initial geometric imperfections: An analytical approach based on the theory of elastic stability

An analytical method for the treatment of the elastic buckling problem of continuous beams with intermediate unilateral constraints is presented, which is based on the fundamental theory of elastic stability. The study focuses on the unilateral contact buckling problem of beams in the presence of initial geometric imperfections. The mathematical Euler approach, based on the fundamental solution of the boundary value problem of the buckling of continuous beams, is appropriately modified in order to take into account the unilateral contact conditions. Furthermore, in order the obtained analytical solutions to be applicable for practical design cases, the actual strength of the cross-section of the beam under combined compression and bending is considered. The implementation of the proposed method is demonstrated through a characteristic example.     

Stability of aneurysm solutions in a fluid-filled elastic membrane tube

When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a critical value. As inflation continues thebulge will grow until it reaches a maximum size after whichit will then propagate in both directions to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluidand it was shown that such bulging solutions are unstableunder pressure control. In this paper we extend this recentstudy by assuming that the inflation is by an inviscid fluidwhose inertia we take into account in the stability analysis.This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series ofstudies. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect.     

Aeroelastic analysis of swept pre-twisted wings

In this paper, aeroelastic modeling of aircraft wings with variations in sweep angle, taper ratio, and variable pre-twist angle along the span is considered. The wing structure is modeled as a classical beam with torsion and bending flexibility. The governing equations are derived based on Hamilton’s principle. Moreover, Peters’ finite state aerodynamic model which is modified to take into account the effects of the wing finite-span, the wing sweep angle, and the wing pre-twist angle, is used to simulate the aerodynamic loads on the wing. The coupled partially differential equations are discretized to a set of ordinary differential equations using Galerkin’s approach. By solving these equations the aeroelastic instability conditions are derived. The results are compared with some experimental and analytical results of previous published papers and good agreement is attained. Effects of the wing sweep angle, taper ratio, bending to torsional rigidity, and pre-twist angle on the flutter boundary in several cases are studied. Results show that these geometrical and physical parameters have considerable effects on the wing flutter boundary.     

Photoelastic coatings

While photoelastic-model analysis is an effective method to measure stresses, its practical use is limited to solving problems under well-defined loading conditions which can be successfully applied on a simulated basis to the model. Further, model analysis does not take into account such conditions as hidden material defects, assembly stresses, residual stresses, inelastic behavior, and other parameters that are contributing factors to the structural integrity of a part or structure. On the other hand, with photoelastic coatings, the stress analysis is conducted on real parts operating under actual service conditions. The coating reveals the true surface strains occurring on a part, since most, if not all, of the contributing stress conditions mentioned above can be taken into account during testing. Photoelastic coatings are easy to apply and, with proper test planning, are very economical to use. Since a visible picture of the stress field is provided over the entire area coated, intelligent application of the technique can save many hours of testing time and provide quick solutions to design or service-failure problems.     

Waves in a solid medium with liquid-filled pores

The dynamic nonlinear theory of deformation of a two-phase medium, a solid with pores filled with a liquid, is developed. The variational principle is used to derive nonlinear equations that take into account the motions of the solid and liquid phases and the porosity variations. All types of nonlinearity, including nonlinear friction, are also taken into account. Formulas for the velocities of the linear and nonlinear waves and the absorption coefficient are derived. The one- and three-dimensional cases are considered. In the three-dimensional case, an equation describing the wave profile evolution is obtained as well as a nonlinear Schrödinger equation. Their solutions are analyzed; soliton-type solutions and solutions for narrow beams are obtained.     

Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics

In the present research two different whole vehicle multibody models are established respectively, including rigid and rigid-flexible coupling multibody vehicle models. The former is all composed by rigid bodies while in the later model, the flexible rear suspension is built based on the finite element method (FEM) and mode superposition method, in which the deformations of the components are considered. The ride simulations with different speeds are carried out on a 3D digitalized road, and the weighted root mean square (RMS) of accelerations on the seat surface, backrest and at the feet are calculated. The comparison between the responses of the rigid and rigid-flexible coupling multibody models shows that the flexibility of the vehicle parts significantly affects the accelerations at each position, and it is necessary to take the flexibility effects into account for the assessment of ride comfort.     

Control of a wheeled system taking into account its inertial properties

Mechanical wheeled systems (WS) such as a wheeled tractor, a motor car, a mobile robot, etc. are studied. The well-known trajectory problem, i.e., the problem of controlling the WS motion along a given trajectory, is considered. This problem was solved earlier in the framework of kinematic WS models. The present paper deals with general WS models that additionally take into account inertial properties such as the WS masses and/or moments of inertia. We establish that the WS are subjected to rather significant perturbing forces. A control law stabilizing the WS motion along a given trajectory is constructed.     

Solution of generalized coordinate for warping for naturally curved and twisted beams

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.     

Influence of the erection regime on the stress state of a viscoelastic arched structure erected by an additive technology under the force of gravity

We study the influence of gravity forces on additively constructed objects of a viscoelastic aging material (in a special case, of a purely elastic material) in the absence of additional surface loads and prestresses in the accreted material elements. It is shown that the stress-strain state of such objects crucially depends on how the process of their gradual formation evolves in time. The main tendencies whose interaction determines the process of deformation of these objects under a given formation regime are revealed and analyzed. The general reasoning is illustrated by the results of numerous numerical experiments performed in the framework of the model of linear mechanics of accreted bodies, which was developed by the authors for studying the essentially two-dimensional engineering problem on the erection of a heavy circular arched structure (a semicircular vault) on a smooth horizontal base by the method of layer-by-layer thickening of a blank structure previously erected on the base. This problem is used as an example in the detailed studies of the influence of the erection regime of a viscoelastic aging structure on the development of its stress state. We show that it is very important to take into account the influence of gravity forces during the entire process of erection of heavy objects rather than in their final configuration. It is conclusively shown that, without considering this influence, one can arrive at completely false conclusions about the current and resulting states of the erected structures such as overestimation of their strength and stability at the stage of formation and of their bearing capacity in their operation. The possibilities of efficient control of the stress state of the considered arch structure by varying the rate of the additional material accretion to the structure are demonstrated.     

Modeling and motion simulation of a three-wheeled mobile robot with front wheel driven and steered taking into account wheels�� slip

The problem of modeling of dynamics of a three-wheeled mobile robot with front wheel driven and steered is analyzed in this paper. Kinematical structure and kinematics of the robot are described. A universal methodology of analytical modeling of robot??s dynamics is applied. This methodology takes into account wheel-ground contact conditions and wheels?? slip. Its essence is the use of a contact model of deformable tire with rigid ground and division of the robot??s dynamics model into parts connected with wheels, including tire model, and with the mobile platform. The tire model used in this paper results from empirical dependencies determined during investigations of car tires. Ground geometry and type are specified in the environment model. Tire-ground interface is characterized by coefficients of friction and rolling resistance. The robot model takes into account the presence of friction in kinematical pairs. The model of servomotors is included as well. The important part of this work is simulation research performed using Matlab/Simulink package. Simulation research includes solving of the forward and inverse dynamics problems as well as the tracking control task. During simulations, the robot was moving on concrete and on a piece of ice. The simulation research enabled verification of the elaborated solutions.     

Application of the Kantorovich-Galerkin Method for Solving Boundary Value Problems with Conditions on Moving Borders

The approximate Kantorovich-Galerkin method is considered for solving problems describing the vibrations of viscoelastic objects with conditions on moving boundaries and analyzing the resonance properties of these objects. The method makes it possible to take into account the effect of forces of environmental resistance on the system, flexural rigidity, and also boundary conditions with weak nonstationarity. The mathematical formulation of the problem involves a partial differential equation with respect to the desired displacement function and inhomogeneous boundary conditions. The Kantorovich-Galerkin method makes it possible to take into account the initial conditions, but they do not affect the resonance properties of linear systems, so in this case they are not taken into account. By introducing a new function into the problem, the boundary conditions are reduced to homogeneous ones. The solution is carried out in dimensionless variables to within a second order of smallness with respect to small parameters characterizing the velocity of the boundary motion and viscoelasticity. Using the Kantorovich-Galerkin method, an approximate solution of high accuracy of the problem of forced longitudinal vibrations of a viscoelastic rope of variable length, one end of which is wound on a drum, and the second is rigidly fixed, is found. The results obtained for the amplitude of oscillations corresponding to the nth dynamical mode are presented. The phenomenon of steady resonance and passage through resonance is investigated using numerical methods. A graphical dependence of the maximum amplitude of the rope oscillations as it passes through the resonance, depending on the coefficient characterizing the viscoelasticity of the object based on the Voigtmodel, is presented. The accuracy of the Kantorovich-Galerkin method is estimated.     

Equation of a layered packet with transverse shears and compression taken into account

The equations describing a layered packet with transverse shears and compression taken into account in all layers are constructed in this paper. The layer material is assumed to be elastic and transversely isotropic. The generalized Timoshenko kinematic hypotheses are used to take into account the transverse shears and compression. The equations in generalized forces, moments, and displacements are obtained, and the equations for characteristic functions in terms of which all variables describing the stress-strain state in the layered packet can be expressed are derived. The deformation problem for a three-layer beam is considered as an example.