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The stability of a simple truss subjected to a single force, P, as shown in Fig. 8.1 was investigated by Mises [40] as a basic model to illustrate some of the buckling phenomena of structures. This model is known as the Mises truss. Buckling of the truss has also been studied by Von Karman and Kerr [54] and Huang and Vahidi [27]. In these studies, either the bending or the axial thrust was neglected. [ABSTRACT FROM AUTHOR]

The vibrations of conical shells are due to the inertial and external forces acting the transverse, circumferential and meridional directions of the cone. For small vibrations, the system is linear, thus, the effects of these three forces may be treated separately. It may be due to the mathematical dificulty, the transverse vibration, so far, is solved by numerical methods only, such as Rayleigh-Ritz method, Galerkin procedure, power series, matrix method, and the finite element method. A comprehensive literature review on the conical shell vibrations is provided in [8]. [ABSTRACT FROM AUTHOR]

The solutions of conical shells with linearly varying thickness presented in the last chapter have suggested a new approach to obtain asymptotic solutions of conical shells with constant thickness. One may assume that the two types of conical shells would behave alike if the ratios of thickness to the radius of the smaller end of the cone is very small. Under this assumption, asymptotic solutions of conical shells with constant thickness are obtained in this chapter. Two numerical examples are given for comparison with the present solutions: the semi-circular conical segment discussed in the last chapter and a complete cone. A solution of the latter is given in [12]. [ABSTRACT FROM AUTHOR]

The equilibrium equations for a surface element of a conical shell in the framework of generalized plane stress of linear theory of elasticity are given in [19]. These equations may be applied to linearly varying thickness as well as to constant thickness of conical shells. [ABSTRACT FROM AUTHOR]

The buckling of conical shells subjected to external loads is a classic problem in shell structures. Since the theoretical predications could not agree with the experimental results, a number of research works have been performed [44]. In the present study, an improvement is made by following the two suggestions in Chaps. 2 and 8: (1) treating the smaller end constraint properly and (2) taking the effect of the angle change into consideration. It is shown that with these improvements, the theoretical predictions are closer to the experimental results. [ABSTRACT FROM AUTHOR]

The so called edge-zone or boundary-layer solutions are widely used in large dediection problems of thin elastic plates [20,35,36] and shells [31,35], but little experimental work has been seen in the literature to verify these approximate solutions. The boundary-layer solutions for the buckling of a rectangular plate are shown in [36]. An experiment was performed for this simple problem. The agreement between the analytical and experimental results are excellent. [ABSTRACT FROM AUTHOR]

A two-bar truss subjected to lateral normal distributed loads as shown in Fig. 9.1 represents a double leaf miter-type gate used in navigation locks as shown in Fig. 9.2. The gate is subjected to hydraulic static pressure whose intensity depends on the level of depth. The gate is supported by horizontal girders. Both ends of the girder are hinged and flxed in space, and the center joint is also hinged but deformable along the central line. [ABSTRACT FROM AUTHOR]

The frame vibrations studied in Chaps. 3 to 5 are for in-plane vibrations. If a plane frame acted upon by a force or horizontal ground vibration in the perpendicular direction of the plane, the frame will experience out-of-plane vibrations as shown in a numerical example in [41]. [ABSTRACT FROM AUTHOR]

The effect of rotatory inertia and shear deformation on the vibration of the inclined bar with the end constraint studied in Chap. 2 is examined here. The basic equations are derived by the variation method. The present work may be considered as an extension of the investigation of that chapter; therefore, the same nomenclature are used herein with some specified additions. [ABSTRACT FROM AUTHOR]

The study of vibrations for the x-braced portal frames in the last chapter is extended to high-rise x-braced multi-story frames in this chapter. Frequencies for two- to five-story frames are given. Forced vibrations for three-story frames are analyzed. Investigations are also made for the effects of horizontal ground motion for three- to five-story frames. Comparison of the present approach with available frequencies of a three-story rectangular frame is made. [ABSTRACT FROM AUTHOR]

Because of devastation of structures due to earthquake and wind force, increasing attention has been paid to dynamic responses of braced structures [13, 22, 24, 45]. Extension of the formulation for vibrations of the two- and three-member frames of exact solutions in Chap. 3 to an x-braced portal frame is made in this chapter. [ABSTRACT FROM AUTHOR]

The model established for the vibration of the inclined bars in the last chapter now is applied to two- and three-bar frames with inclined members. [ABSTRACT FROM AUTHOR]

Considered are the vibrations of inclined bars with the bottom end flxed in space and the top end having a constraint which requires that this end can move only in the vertical direction. [ABSTRACT FROM AUTHOR]

There are two basic methods to analyze the continuum elastic structural mechanics: One is by applying Newton's law of motion to a free body element of a structure; the other is by the energy method or calculus of variations [23]*. Two examples of vibration of a bar are used in this chapter to illustrate these two methods as a review. [ABSTRACT FROM AUTHOR]

The Non Smooth Contact Dynamics method (NSCD) deals with frictional unilateral contact between rigid or deformable bodies. It was originated around 1984 by J.J. Moreau as the Contact Dynamics method (CD). It was extended as the (NSCD) method by M. Jean to deal with more general applications, such as nite element modelling. Numerical applications of the CD method for granular materials are currently customized in C language by J.J. Moreau. The NSCD method has been implemented by M. Jean in a now obsolete fortran77 general purpose software. F. Dubois is the author of a completely remodelled new version LMGC90 written in fortran90, open to research scientists for further developments and applications. This is an open source software governed by a Cecill license (i.e. GPL). In the NSCD method the basic laws such as Coulomb's law and the inelastic shock law are described as non smooth laws in terms of multimappings. The dynamical equation is discretized according to a low order implicit algorithm. The main unknowns are the relative velocities between contactors at some overlapping moments with the time steps (leap frog technique) and the mean reaction impulses during the time step. Assuming provisional values for contacts neighbouring of a given contact, values of the reactions for this given contact are obtained discussing the intersection of the graphs of affine mappings. Values of the reactions are updated, and all contacts are processed successively as long as necessary to obtain a satisfactory convergence. This may be described as a non linear block Gauss Seidel method. The LMGC90 software is dedicated to applications with a large number of 2D or 3D contactors. It is a modular software written in fortran90 with an object oriented organisation: [ABSTRACT FROM AUTHOR]

Discomfort problems due to the noise emittence of braking systems in trains have suggested recently several mechanical analyses. This paper gives some of our results obtained from the numerical modelling of TGV brakes in relation with some experimental data. The numerical discussion is based upon the Coulomb's law of contact with a constant coefficient of friction. A dynamic stability analysis enables us to show the loss of stability by flutter of the steady sliding response of the pad on the brake disks. We will present the numerical calculation of the unstable modes for the entire brake system which is a large structure. From an experimental point of view, the modal parameters have been measured for the brake system. We will present also the measures done at the train station giving the close-field acoustic. A comparison between these data and the numerical calculation help us to understand what happen during squeal. [ABSTRACT FROM AUTHOR]

In this paper we discuss the stability of quasi-static paths of a single degree of freedom linearly elastic system with Coulomb friction and known normal force. A common and useful approximation for the equations that govern the slow evolution of many mechanical systems is to neglect inertia effects in the dynamic balance equations, and replace them by static equilibrium equations. Slow evolutions calculated with this approximation are called quasi-static evolutions. The relationship of this issue with the theory of singular perturbations has been established in [1], where the existence of fast (dynamic) and slow (quasi-static) time scales was recognized: a change of variables is performed that replaces the (fast) physical time t by a (slow) loading parameter λ, whose rate of change with respect to time, ε = dλ/dt, is decreased to zero. This change of variables leads to a system of dynamic differential equations or inclusions that defines a singular perturbation problem: the small parameter ε multiplies some of the highest order derivatives in the system. The concept of stability of quasi-static paths used here is essentially a continuity property relatively to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, ε (as in singular perturbation problems). This study applies for the first time to a nonsmooth context, the definition of stability of quasi-static paths, recently proposed by Martins et al. ([2], [3]). [ABSTRACT FROM AUTHOR]

A numerical model based on the solution of the normal contact between elastic half-spaces and subsequent post-processing according to the Mindlin and Deresiewicz solution for cyclic tangential loading is presented. Thanks to a recent extension of the Cattaneo-Mindlin analogy to the solution of tangential contact between non-convex domains, the proposed approach enables the study of cyclic micro-slip and energy dissipation between elastic bodies with general shapes in contact. In order to make the procedure straightforward and as general as possible, a non-dimensional formulation, based only on the normal contact load displacement curve, is proposed. The cyclic behaviour of the tangential contact of self-affine fractal surfaces, like those generated by fracture of concrete or rock, is described with several examples. [ABSTRACT FROM AUTHOR]

The stability of the equilibrium states of a simple mechanical system with unilateral contact and Coulomb friction is explored. When the external force is constant, the equilibrium states are completely determined by the mechanical properties of the system and the stability or instability of each of these states is proved. When the external force varies in time two stability results are given. [ABSTRACT FROM AUTHOR]

Boundary layers are studied which are induced by micro-periodic boundary conditions as, for instance, in the case of contact of rough bodies. The adopted micromechanical framework is outlined briefly and two applications are provided. The finite element method is applied to study the normal contact compliance in the elasto-plastic regime, and the effect of macroscopic in-plane strain on contact response is analyzed. Secondly, a simple model for prediction of the effective heat transfer coefficient in steady-state conditions is presented. [ABSTRACT FROM AUTHOR]

In this work a homogenization method presented by Bandeira et al [2,3,4] is enhanced in order to obtain by numerical simulation the interface law for the normal contact pressure based on statistical surface models. For this purpose elasticplastic behavior of the asperities is considered. Statistical evaluations of numerical simulations lead to a constitutive law for the contact pressure. The resulting law compared with other laws stemming from analytical investigations, like those presented by Greenwood Williamson [11] and Yovanovich [19, 32]. The non-penetration condition and the interface model for contact that takes into account the surface microstructure are investigated in detail. [ABSTRACT FROM AUTHOR]

The elasto-plastic normal contact of fractal surfaces is numerically investigated using a halfspace model. Artificial surface data are generated using the structure function, to study the influence of different surface parameters with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range. [ABSTRACT FROM AUTHOR]

A unified interface constitutive law for the description of contact and decohesion at bi-material interfaces is proposed. To this aim, a synthesis of the nonlinear models pertaining to Fracture and Contact Mechanics is presented. The issues pertinent to the implementation within the FE discretization framework are also discussed in detail. Finally, a numerical example of fatigue modeling at the mesoscopical level in a fiber-reinforced composite is provided. [ABSTRACT FROM AUTHOR]

In Civil Engineering soils may be reinforced by different structures. Wires will interest us. Mixed sand and wire, known as TexSol, may be modelled as a continuous medium with classical behaviour laws [6] or with more sophisticated ones taking into account remote interactions [1]. [ABSTRACT FROM AUTHOR]

In this paper an approach for friction coefficient prognosis for the Groschwheel is presented. Since the solid rubber wheel (80 mm diameter) represents a simpli fied tyre model this contribution helps to investigate the rolling friction process and especially the feasibility and limitations of the automotive friction prognosis. The grip information is derived from influence parameters like road state, velocity, temperature etc. The methodical innovation of the approach proposed consists in the use of an artificial neural network as data based model that performs multi dimensional interpolation in the learning stage. The operating stage consists of common mathematical operations with low computational effort. [ABSTRACT FROM AUTHOR]

Friction of tyres is a major contributor to automotive safety. Usually friction if most demanded on wet roads. Several theories have been proposed about the physical origins of dry and wet friction. They tend to evaluate the respective contributions of adhesion forces and dissipative mechanisms at the relevant scales. We discuss their achievements and limitations. The relevance of taking into account these physical mechanisms to improve the simulation of tire friction problems is addressed. [ABSTRACT FROM AUTHOR]

The modeling of rubber frictional properties on rough surfaces is of considerable importance for the prediction of tire traction properties. The presented work consists in a physically based model describing the dynamic contact and the sliding friction of elastomers on rough surfaces. The self-affine character of rough substrates is analytically treated with correlation functions which depend on three surface descriptors. This allows a generalization of the concepts introduced by Greenwood and Williamson and a quantitative estimation of the velocity dependent real area of contact. The hysteresis friction can be modelled in the frame of this theory, originating from the energy losses due to the local deformation of the rubber from the surface asperities during dynamic contact. The experimental results show that the frictional behaviour under wet conditions is fairly described by the hysteresis friction. The transition from wet to dry friction is explained via an adhesion component assumed to be related with the real area of contact. This approach is also confirmed by the experiment and gives a deeper insight in the relationship between the material viscoelastic properties, the surface roughness and the frictional behavior. [ABSTRACT FROM AUTHOR]