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Tangential Direction (tangential + direction)
Selected AbstractsA numerical method for the study of shear band propagation in soft rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2009Marta Castelli Abstract This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre-existing natural defect. This is done through the application of the principles of fracture mechanics, a slip-weakening model (SWM) being used to simulate the non-linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non-linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non-linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non-linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd. [source] Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicatorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002K. H. Muci-Küchler Abstract In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd. [source] Compliant grasping with passive forcesJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 5 2005Cai-Hua Xiong Because friction is central to robotic grasp, developing an accurate and tractable model of contact compliance, particularly in the tangential direction, and predicting the passive force closure are crucial to robotic grasping and contact analysis. This paper analyzes the existence of the uncontrollable grasping forces (i.e., passive contact forces) in enveloping grasp or fixturing, and formulates a physical model of compliant enveloping grasp. First, we develop a locally elastic contact model to describe the nonlinear coupling between the contact force with friction and elastic deformation at the individual contact. Further, a set of "compatibility" equations is given so that the elastic deformations among all contacts in the grasping system result in a consistent set of displacements of the object. Then, combining the force equilibrium, the locally elastic contact model, and the "compatibility" conditions, we formulate the natural compliant model of the enveloping grasp system where the passive compliance in joints of fingers is considered, and investigate the stability of the compliant grasp system. The crux of judging passive force closure is to predict the passive contact forces in the grasping system, which is formulated into a nonlinear least square in this paper. Using the globally convergent Levenberg-Marquardt method, we predict contact forces and estimate the passive force closure in the enveloping grasps. Finally, a numerical example is given to verify the proposed compliant enveloping grasp model and the prediction method of passive force closure. © 2005 Wiley Periodicals, Inc. [source] Mathematical analysis of vortex sheetsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2006Sijue Wu We consider the motion of the interface separating two domains of the same fluid that moves with different velocities along the tangential direction of the interface. The evolution of the interface (the vortex sheet) is governed by the Birkhoff-Rott (BR) equations. We consider the question of the weakest possible assumptions such that the Birkhoff-Rott equation makes sense. This leads us to introduce chord-arc curves to this problem. We present three results. The first can be stated as the following: Assume that the Birkhoff-Rott equation has a solution in a weak sense and that the vortex strength is bounded away from 0 and ,. Moreover, assume that the solution gives rise to a vortex sheet curve that is chord-arc. Then the curve is automatically smooth, in fact analytic, for fixed time. The second and third results demonstrate that the Birkhoff-Rott equation can be solved if and only if only half the initial data is given. © 2005 Wiley Periodicals, Inc. [source] Service conditions and their influence on oxide scale formation on metallic high temperature alloys for application in innovative combustion processesMATERIALS AND CORROSION/WERKSTOFFE UND KORROSION, Issue 2 2006G. Teneva-Kosseva Abstract The present paper focuses on two aspects: the service conditions of a flame tube in a low-NOx recirculation burner (maximum temperature experienced by the material: 1000 °C) and the interrelationship between service conditions and both the structure and growth of the oxide scale. The flame tube is exposed to extreme thermal and atmospheric conditions during service. Due to the short burner operation time followed by a pause, rapid changes of the temperature and gaseous environment occur. Three Ni-based alloys (alloy 602 CA, alloy 603 XL and alloy 693) were investigated in cyclic oxidation tests under typical conditions for the combustion of fuel oil. Flame tube temperature measurements in both the axial and the tangential directions are presented together with results concerning the influence of the fuel quality, duration of the air ventilation after burner shut down and temperature on the thickness and composition of the oxide scale. [source] Null-field approach for Laplace problems with circular boundaries using degenerate kernelsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Jeng-Tzong Chen Abstract In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] | |||||||||||||