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Matrix Formulation (matrix + formulation)
Selected AbstractsTransient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2009A. Mesgouez Abstract The authors propose a semi-analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical derivation of contact mechanics interface laws using a finite element approach for large 3D deformationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Alex Alves Bandeira Abstract In this work a homogenization method is presented to obtain by numerical simulation interface laws for normal contact pressure based on statistical surface models. For this purpose and assuming elastic behaviour of the asperities, the interface law of Kragelsky et al. (Friction and Wear,Calculation Methods, Pergamon, 1982) is chosen for comparison. The non-penetration condition and interface models for contact that take into account the surface micro-structure are investigated in detail. A theoretical basis for the three-dimensional contact problem with finite deformations is shortly presented. The augmented Lagrangian method is then used to solve the contact problem with friction. The algorithms for frictional contact are derived based on a slip rule using backward Euler integration like in plasticity. Special attention was dedicated to the consistent derivation of the contact equations between finite element surfaces. A matrix formulation for a node-to-surface contact element is derived consisting of a master surface segment with four nodes and a contacting slave node. It was also necessary to consider the special cases of node-to-edge contact and node-to-node contact in order to achieve the desired asymptotic quadratic convergence in the Newton method. A numerical example is selected to show the ability of the contact formulation and the algorithm to represent interface law for rough surfaces. Copyright © 2003 John Wiley & Sons, Ltd. [source] Adjoint network method applied to the performance sensitivities of microwave amplifiersINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 5 2006F. Güne Abstract This work focuses on the performance sensitivities of microwave amplifiers using the "adjoint network and adjoint variable" method, via "wave" approaches, which includes sensitivities of the transducer power gain, noise figure, and magnitudes and phases of the input and output reflection coefficients. The method can be extended to sensitivities of the other performance measure functions. The adjoint-variable methods for design-sensitivity analysis offer computational speed and accuracy. They can be used for efficiency-based gradient optimization, in tolerance and yield analyses. In this work, an arbitrarily configured microwave amplifier is considered: firstly, each element in the network is modeled by the scattering matrix formulation, then the topology of the network is taken into account using the connection scattering-matrix formulation. The wave approach is utilized in the evaluation of all the performance-measurement functions, then sensitivity invariants are formulated using Tellegen's theorem. Performance sensitivities of the T- and ,-types of distributed-parameter amplifiers are considered as a worked example. The numerical results of T- and ,-type amplifiers for the design targets of noise figure Freq = 0.46 dB , 1,12 and Vireq = 1, GTreq = 12 dB , 15.86 in the frequency range 2,11 GHz are given in comparison to each other. Furthermore, analytical methods of the "gain factorisation" and "chain sensitivity parameter" are applied to the gain and noise sensitivities as well. In addition, "numerical perturbation" is applied to calculation of all the sensitivities. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006. [source] An analysis of uncertainty in non-equilibrium and equilibrium geothermobarometryJOURNAL OF METAMORPHIC GEOLOGY, Issue 9 2004J. R. ASHWORTH Abstract In statistically optimised P,T estimation, the contributions to overall uncertainty from different sources are represented by ellipses. One source, for a diffusion-controlled reaction at non-equilibrium, is diffusion modelling of the reaction texture. This modelling is used to estimate ratios, Q, between free-energy differences, ,G, of reactions among mineral end-members, to replace the equilibrium condition ,G = 0. The associated uncertainty is compared with those already inherent in the equilibrium case (from end-member data, activity models and mineral compositions). A compact matrix formulation is introduced for activity coefficients, and their partial derivatives governing error propagation. The non-equilibrium example studied is a corona reaction with the assemblage Grt,Opx,Cpx,Pl,Qtz. Two garnet compositions are used, from opposite sides of the corona. In one of them, affected by post-reaction Fe, Mg exchange with pyroxene, the problem of reconstructing the original composition is overcome by direct use of ratios between chemical-potential differences, given by the diffusion modelling. The number of geothermobarometers in the optimisation is limited by near-degeneracies. Their weightings are affected by strong correlations among Q ratios. Uncertainty from diffusion modelling is not large in comparison with other sources. Overall precision is limited mainly by uncertainties in activity models. Hypothetical equilibrium P,T are also estimated for both garnet compositions. By this approach, departure from equilibrium can be measured, with statistical uncertainties. For the example, the result for difference from equilibrium pressure is 1.2 ± 0.7 kbar. [source] | ||||||||||