平面桁架杆件内力的虚位移原理求解

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The derivation of J-integral conservation law from the principle of virtual work

The general form of J-integral conservation law in three di-mensions has been derived from the principle of virtual work.The necessary conditions for J-integral conservation are alsogiven.     

Pacing CFD: automatic mesh adaptation as an efficient tool to improve CFD accuracy

We propose in this paper to demonstrate the impact of mesh adaptation technology on computational fluid dynamics (CFD) solution accuracy. A global methodology is presented that includes a selected number of pre-processing techniques that sensibly improve the quality of the initial meshes and accelerate the solution-adaptation process. Finally, the efficiency of the approach is demonstrated through meaningful numerical tests.     

The principle of virtual work and integral laws of motion

This paper furnishes a simple constructive proof of the equivalence of integral laws of motion for continua to the Principle of Virtual Work. The approach used is designed to avoid the artificiality of introducing the classical equations of motion in an intermediate step. The hypotheses employed are virtually the weakest possible that are consistent with the requirement that the integrals appearing in these formulations make sense as Lebesgue integrals. Particular attention is devoted to the treatment of boundary conditions, which may assume a very general form.     

The principle of virtual work in mechanical and electromechanical systems

Summary The principle of virtual work is applied to electromechanical systems as the foundation of a unifying concept for modelling mechatronical systems. After the presentation of an important result in the field of mechanics, the expansion of the principle on electrical networks and electromechanical systems is shown. The use of the principle of virtual work in the domain of electromechanics yields an analogous form to the central equation of mechanics which is valid for holonomic and nonholonomic systems. The electrotechnical part of the system is confined to networks. The derivation of the mathematical model is demonstrated on the example of a simple electromechanical oscillation circuit. In addition, the physical systems are separately treated, taking into account the explicit constraints on the basis of the Lagrangian multiplier method.     

On the asymptotic boundary conditions of an anisotropic beam via virtual work principle

In this research, an efficient and effective method is proposed to derive the boundary conditions of an anisotropic beam in the asymptotic sense. We first set up the constrained virtual work by introducing the Lagrange multiplier on the displacement prescribed boundary. The macroscopic beam and microscopic cross-section equations with the boundary conditions are simultaneously obtained by taking the asymptotic expansion on the displacement vector. In this way, the three-dimensional characteristics of the beam are asymptotically smeared into the macroscopic beam equations and the beam boundary conditions. The boundary conditions obtained are then compared to those from the decay analysis method. The beam bending slope boundary condition obtained in the frame work of variational principle is different from the well-known average condition. This new boundary condition is more accurate than the average one for a sandwich beam. This is further demonstrated and discussed via the examples of a cantilever beam loaded at the end.     

The principle of virtual work and its dual for contact problems

Summary In the first half of this paper, the variational inequalities of virtual work and its dual, the complementary virtual work are formulated for frictional contact problems with large deformations without restriction on the material properties of the bulk material. Care has been taken to formulate as many as possible terms as variations of a functional. Only the terms involving the frictional traction bound are excepted. Next the significance of the theory for the calculation of frictional contact is discussed.

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Das Prinzip der virtuellen Arbeit und sein Dual für Kontaktprobleme

Übersicht In der 1. Hälfte dieses Aufsatzes werden die Variationsgleichungen der virtuellen Arbeit und ihr Dual, die komplementäre virtuelle Arbeit, formuliert für Reibungskontaktprobleme mit großen Verschiebungen, ohne die materiellen Eigenschaften des Werkstoffes zu berücksichtigen. Möglichst viele Terme werden als Variationen eines Funktionals formuliert. Nur die Terme, welche die Reibungsgrenze enthalten, sind ausgenommen. In der 2. Hälfte wird die Bedeutung der Theorie für die Berechnung des Reibungskontakts hervorgehoben.

     

The robustness of an efficient probabilistic data-based tool for simulating the non-stationary response of non-linear systems

The stochastic response of dynamic systems has been an area of considerable interest for some time in the analysis of risk and structural reliability. The authors, in previous work, have developed a method which can analyze the response of linear multi-degree-of-freedom systems to completely general data-based non-stationary excitations in a highly efficient and analytical form. The authors extended this work to non-linear system response by using equivalent linearization techniques. This paper explores the range of application of the extension to the analysis of non-linear systems through the use of real and simulated data-sets. In particular, sensitivity issues of non-Gaussianity of the excitation data, and the degree of response non-linearity of the dynamic system, are investigated for their effect on the estimated response using this equivalent linearization-based approach.     

A dispersion force approach to modelling the effect of lift forces on fibre dispersion

Wood fibres suspended in air were studied whilst flowing through a throttle. Measurements of volume fraction and velocity were compared with results from a two-fluid model simulation. Results from earlier work have shown that the lift forces acting on the individual fibres are of importance for the dispersion of volume fraction. Since the orientation of the individual fibres cannot be determined, a dispersion force was utilised to model the dispersing effect of the lift forces. The addition of a lift dispersion model significantly improved the agreement between measurement and model data.     

The consistent Mindlin’s thermopiezoelectric equations and the principle of virtual work

The thermal field vector, an overlooked concept of importance, is introduced for the consistency in Mindlin’s thermopiezoelectric equations. The gradient of the temperature increment is defined as the thermal field vector; an analogous to the electric and magnetic field vectors (i.e., the gradients of the electric and magnetic potentials). The thermal field vector is used to state the universal gradient equations, and then, the principle of virtual work.     

The virtual work principle and linear complementary method for coupling analysis of elasto-plastic damage structure

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Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping

Summary We call piezoelectromechanical (PEM) truss beam a truss modular beam coupled with a transmission electrical line when the coupling is obtained by piezoelectric actuators which act as bars in the module and as capacitances in the electrical line. The truss module length is assumed negligible with respect to the considered wave lengths. The transmission electrical line is assumed continuously distributed along the truss beam. Applying the method of virtual power as expounded in [2] we formulate a continuum model for PEM truss beams and we prove that there exists a critical value for the transmission electrical impedance in the neighborhood of which the electromechanical modal coupling is maximum and the possible electrical dissipation of mechanical energy is relevant. Accepted for publication 1 June 1997     

The synchronous lateral excitation phenomenon: modelling framework and an application

A mathematical model conceived to simulate the mechanics of synchronous lateral excitation induced by pedestrians on footbridges is presented in this Note. The model is based on the mathematical and numerical decomposition of the coupled multiphysical non-linear system into two interacting subsystems: the Structure system, whose dynamics is described by the non-linear equation of motion, and the Crowd system, which is described by a first-order hydrodynamic model governed by the mass conservation equation. The model was applied to the simulation of a crowd event recorded on the T-bridge in Japan and results are commented on. To cite this article: F. Venuti, L. Bruno, C. R. Mecanique 335 (2007).     

The principle of virtual work and the third order wave for continua with second order constitutive equations

A generalized form of the principle of virtual work where the virtual work is a time integral of virtual power is obtained. The corresponding Euler–Lagrange equation includes the divergence of the Lie derivative of stress. The equation of motion on the stress rate field is one of the results of this paper. A generalization of the acoustic tensor is obtained for a third-order wave. The generalized acoustic tensor seems the most important result of this paper. It can also be found by investigating an acceleration wave