A highly redundant coordinate formulation for constrained rigid bodies

The paper presents a formulation for the dynamic analysis of rigid multibodies. An introductory part carries out the kinematic analysis and the definition of the highly redundant differential framework along with the choice of unknowns and equations. From the differential formulation the variational principles, either in Lagrangian or Hamiltonian form, are developed. The Hamiltonian formulation is then used to develop the numerical approximation by applying the finite element method in time. The application of the method in its multifield form is discussed and a solution algorithm is proposed. Some examples are finally presented in order to verify the effectiveness of the formulation.

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Sommario Il lavoro presenta una formulazione per lo studio della dinamica dei sistemi multicorpo rigidi. Nella parte introduttiva viene svolta l'analisi cinematica e si definisce il quadro differenziale con la scelta delle incognite e delle equazioni. Dalla formulazione differenziale vengono poi sviluppati dei principi variazionali nella forma Lagrangiana ed Hamiltoniana. La formulazione Hamiltoniana é quindi utilizzata per sviluppare l'approssimazione numerica col metodo degli elementi finiti di tempo. Viene discussa l'applicazione del metodo nella forma multi-campo e viene proposto un algoritmo di soluzione. Da ultimo, vengono discussi alcuni esempi per verificare la correttezza della formulazione.

     

Compatibility conditions for the Cauchy-Green strain fields: Solutions for the plane case

This paper considers the issues related to uniqueness and existence of a finite deformation generated by prescribed right or left Cauchy-Green strain tensor field in the plane. First, the questions of uniqueness and existence to a pre-assigned right strain field C are discussed. It is shown that the existence condition, in the context of continuum mechanics, are naturally posed using the field corresponding to the square root of C instead of C, the latter a classical approach. Then, the corresponding questions for the left strain field are considered, which is more involved. The analysis of uniqueness gives rise to an appropriate classification of the deformation fields. The question of existence is discussed and a complete solution is presented. In both the right and left cases, we stress the techniques for obtaining the corresponding deformation fields.     

Diffuser stall and rotating zones of separated boundary layer

Unsteady flows and rotating stall in vaneless diffusers were investigated by measuring both the wall fluctuating pressures and the unsteady velocity field using hot-wires and laser Doppler anemometers. Experiments were carried out with a fixed impeller and fixed diffuser inlet and outlet radii. However, the diffuser width was varied so that its effect on rotating stall could be examined. Results show that the variation of _r with b/r _i is in qualitative agreement with the prediction of Senoo et al. (1977). Therefore, the onset of stall is delayed as diffuser width is decreased. For diffusers with small width, stall emerges first with one stall cell and then develops into 2 and 4 stall cells as the mass flow rate is decreased. On the other hand, for the diffuser with the largest width tested, stall emerges with one stall cell and quickly develops into 3 stall cells. The ratio of the speed of rotation of the stall cell to impeller speed is independent of diffuser width, but decreases slightly as the number of stall cells increases. Finally, rotating stall is associated with reversed flow originating from the hub side rather than from the shroud side.     

A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void

In this paper, we carry out an explicit analysis of a bifurcation problem for a solid circular cylinder composed of a particularcompressible nonlinearly elastic material. This problem is concerned with the bifurcation of a solid body into a configuration involving an internal cavity. A discussion of its physical interpretation is then carried out. In particular, it is shown that this model may be used to describe the nucleation of a void from apre-existing micro-void.     

The elastic modulus of particulate composites using the concept of a mesophase

A theoretical model for the evaluation of the elastic modulus in particulate composites has been developed. The method takes into account the existence of a mesophase between main phases, which constitutes an important parameter influencing the behaviour of a composite material. This layer between the matrix and filler develops different physico-chemical properties from those of the constituent phases and variable ones along its thickness. The effect of the progressive variation of the elastic modulus of the mesophase on the modulus of the composite was estimated by applying various simple laws of variation. Convenient laws of variation were introduced, varying from a simple one, assuming a linear law, to a more refined one using a parabolic law. Experimental results with particulates, based on iron-filled epoxy composites, compared satisfactorily with other models. However, the model based on a parabolic law was superior to all others on physical grounds.List of symbols E elastic modulus - v Poisson's ratio - volume fraction - r radius - V volume - K bulk modulus - r thickness of mesophase - parameter which depends on the sudden changes of the heat capacity for the filled and unfilled polymer C _p ^f and C _p ⁰      

Quasiconvexity and partial regularity in the calculus of variations

We prove partial regularity of minimizers of certain functionals in the calculus of variations, under the principal assumption that the integrands be uniformly strictly quasiconvex. This is of interest since quasiconvexity is known in many circumstances to be necessary and sufficient for the weak sequential lower semicontinuity of these functionals on appropriate Sobolev spaces. Examples covered by the regularity theory include functionals with integrands which are convex in the determinants of various submatrices of the gradient matrix.     

Kinking of a crack emanating from the free surface of a beam under pure bending

A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K₁₁ the crack path is obtained as well as a path stability condition. From conditions on K₁ a material parameter r^* akin to that of Ramulu and Kobayashi's r_c is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K₁₁. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.     

The interrelation between void fraction fluctuations and flow patterns in two-phase flow

A fast response, linearized X-ray void measurement system has been used to obtain statistical measurements in normally fluctuating air-water flow in a rectangular channel. It is demonstrated that the probability density function (PDF) of the fluctuations in void fraction may be used as an objective and quantitative flow pattern discriminator for the three dominant patterns of bubbly, slug, and annular flow. This concept is applied to data over the range of 0.0 to 37 m/sec mixture velocities to show that slug flow is simply a transitional, periodic time combination of bubbly and annular flows. Film thicknesses calculated from the PDF data are similar in magnitude in both slug and annular flows. Calculation of slug length and residence time ratios along with bubble lengths in slug flow are also readily obtainable from the statistical measurements. Spectral density measurements showed bubbly flow to be stochastic while slug and annular flows showed periodicities correlatable in terms of the liquid volume flux.     

Hydraulic fracturing of a saturated porous medium-II: Special cases

This investigation deals with the problem of steady state hydraulic fracture in an infinite isotropic fluid-saturated elastic porous medium induced by a uniform pressure applied to the crack surfaces. A quasi-static approach is employed in the study. A boundary value problem is formulated and then analyzed by means of the Fourier transform associated with the Wiener-Hopf technique. Stress intensity factor and potential energy release rate are found by asymptotic analysis and the superposition principle as functions of the speed of crack propagation. The material breakdown process at the crack tip is discussed based on Dugdale's model. Finally, a brief discussion of the effect of pressure drop on the hydraulic fracture process and the decrease in crack speed during crack extension is included.