A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Constitutive laws for strong geometric non-linearity

This paper is divided into two different parts. The first one provides a brief introduction to the fractal geometry with some simple illustrations in fluid mechanics. We thought it would be helpful to introduce the reader into this relatively new approach to mechanics that has not been sufficiently explored by engineers yet. Although in fluid mechanics, mainly in problems of percolation and binary flows, the use of fractals has gained some attention, the same is not true for solid mechanics, from the best of our knowledge. The second part deals with the mechanical behavior of thin wires subjected to very large deformations. It is shown that starting to a plausible conjecture it is possible to find global constitutive equations correlating geometrical end energy variables with the fractal dimension of the solid subjected to large deformations. It is pointed out the need to complement the present proposal with experimental work.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

On SETAR non-linearity and forecasting

We compare linear autoregressive (AR) models and self-exciting threshold autoregressive (SETAR) models in terms of their point forecast performance, and their ability to characterize the uncertainty surrounding those forecasts, i.e. interval or density forecasts. A two-regime SETAR process is used as the data-generating process in an extensive set of Monte Carlo simulations, and we consider the discriminatory power of recently developed methods of forecast evaluation for different degrees of non-linearity. We find that the interval and density evaluation methods are unlikely to show the linear model to be deficient on samples of the size typical for macroeconomic data

Bicorrelations and cross-bicorrelations as non-linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross-bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non-linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high-frequency exchange rate returns, and their out-of-sample forecasting performance is compared to that of other time series models

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Testing for non-linearity in daily sterling exchange rates

A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire post Bretton-Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH effects clearly demonstrated in a large number of papers, but with the tests for non-linearity which are currently available being unable to classify any additional non-linear structure.

Heat transfer in fixed bed: a model non-linearity approach

Studies have been carried out on the heat transfer in a packed bed of glass beads percolated by air at moderate flow rates. Rigorous statistic analysis of the experimental data was carried out and the traditional two parameter model was used to represent them. The parameters estimated were the effective radial thermal conductivity, k, and the wall coefficient, h, through the least squares method. The results were evaluated as to the boundary bed inlet temperature, T-o, number of terms of the solution series and number of experimental points used in the estimate. Results indicated that a small difference in T-o was sufficient to promote great modifications in the estimated parameters and in the statistical properties of the model. The use of replicas at points of high parametric information of the model improved the results, although analysis of the residuals has resulted in the rejection of this alternative. In order to evaluate cion-linearity of the model, Bates and Watts (1988) curvature measurements and the Box (1971) biases of the coefficients were calculated. The intrinsic curvatures of the model (IN) tend to be concentrated at low bed heights and those due to parameter effects (PE) are spread all over the bed. The Box biases indicated both parameters as responsible for the curvatures PE, h being somewhat more problematic. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Complexity and non-linearity in earth surface processes - concepts, methods and applications

Complexity has long been recognized and is increasingly becoming mainstream in geomorphology. However, the relative novelty of various concepts and techniques associated to it means that ambiguity continues to surround complexity. In this commentary, we present and discuss a variety of recent contributions that have the potential to help clarify issues and advance the use of complexity in geomorphology.

Motion sharpening and contrast:Gain control precedes compressive non-linearity?

Blurred edges appear sharper in motion than when they are stationary. We (Vision Research 38 (1998) 2108) have previously shown how such distortions in perceived edge blur may be accounted for by a model which assumes that luminance contrast is encoded by a local contrast transducer whose response becomes progressively more compressive as speed increases. If the form of the transducer is fixed (independent of contrast) for a given speed, then a strong prediction of the model is that motion sharpening should increase with increasing contrast. We measured the sharpening of periodic patterns over a large range of contrasts, blur widths and speeds. The results indicate that whilst sharpening increases with speed it is practically invariant with contrast. The contrast invariance of motion sharpening is not explained by an early, static compressive non-linearity alone. However, several alternative explanations are also inconsistent with these results. We show that if a dynamic contrast gain control precedes the static non-linear transducer then motion sharpening, its speed dependence, and its invariance with contrast, can be predicted with reasonable accuracy. © 2003 Elsevier Science Ltd. All rights reserved.

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Contribución del tablero y de la subestructura frente al pandeo global de pilas esbeltas de hormigón armado : determinación simplificada de una "coacción equivalente"

Las pilas de los puentes son elementos habitualmente verticales que, generalmente, se encuentran sometidos a un estado de flexión compuesta. Su altura significativa en muchas ocasiones y la gran resistencia de los materiales constituyentes de estos elementos – hormigón y acero – hace que se encuentren pilas de cierta esbeltez en la que los problemas de inestabilidad asociados al cálculo en segundo orden debido a la no linealidad geométrica deben ser considerados. Además, la mayoría de las pilas de nuestros puentes y viaductos están hechas de hormigón armado por lo que se debe considerar la fisuración del hormigón en las zonas en que esté traccionado. Es decir, el estudio del pandeo de pilas esbeltas de puentes requiere también la consideración de un cálculo en segundo orden mecánico, y no solo geométrico. Por otra parte, una pila de un viaducto no es un elemento que pueda considerarse como aislado; al contrario, su conexión con el tablero hace que aparezca una interacción entre la propia pila y aquél que, en cierta medida, supone una cierta coacción al movimiento de la propia cabeza de pila. Esto hace que el estudio de la inestabilidad de una pila esbelta de un puente no puede ser resuelto con la “teoría del pandeo de la pieza aislada”. Se plantea, entonces, la cuestión de intentar definir un procedimiento que permita abordar el problema complicado del pandeo de pilas esbeltas de puentes pero empleando herramientas de cálculo no tan complejas como las que resuelven “el pandeo global de una estructura multibarra, teniendo en cuenta todas las no linealidades, incluidas las de las coacciones”. Es decir, se trata de encontrar un procedimiento, que resulta ser iterativo, que resuelva el problema planteado de forma aproximada, pero suficientemente ajustada al resultado real, pero empleando programas “convencionales” de cálculo que sean capaces de : - por una parte, en la estructura completa: o calcular en régimen elástico lineal una estructura plana o espacial multibarra compleja; - por otra, en un modelo de una sola barra aislada: o considerar las no linealidades geométricas y mecánicas a nivel tensodeformacional, o considerar la no linealidad producida por la fisuración del hormigón, o considerar una coacción “elástica” en el extremo de la pieza. El objeto de este trabajo es precisamente la definición de ese procedimiento iterativo aproximado, la justificación de su validez, mediante su aplicación a diversos casos paramétricos, y la presentación de sus condicionantes y limitaciones. Además, para conseguir estos objetivos se han elaborado unos ábacos de nueva creación que permiten estimar la reducción de rigidez que supone la fisuración del hormigón en secciones huecas monocajón de hormigón armado. También se han creado unos novedosos diagramas de interacción axil-flector válidos para este tipo de secciones en flexión biaxial. Por último, hay que reseñar que otro de los objetivos de este trabajo – que, además, le da título - era cuantificar el valor de la coacción que existe en la cabeza de una pila debido a que el tablero transmite las cargas de una pila al resto de los integrantes de la subestructura y ésta, por tanto, colabora a reducir los movimientos de la cabeza de pila en cuestión. Es decir, la cabeza de una pila no está exenta lo cual mejora su comportamiento frente al pandeo. El régimen de trabajo de esta coacción es claramente no lineal, ya que la rigidez de las pilas depende de su grado de fisuración. Además, también influye cómo las afecta la no linealidad geométrica que, para la misma carga, aumenta la flexión de segundo orden de cada pila. En este documento se define cuánto vale esta coacción, cómo hay que calcularla y se comprueba su ajuste a los resultados obtenidos en el l modelo no lineal completo. The piers of the bridges are vertical elements where axial loads and bending moments are to be considered. They are often high and also the strength of the materials they are made of (concrete and steel) is also high. This means that slender piers are very common and, so, the instabilities produced by the second order effects due to the geometrical non linear effects are to be considered. In addition to this, the piers are usually made of reinforced concrete and, so, the effects of the cracking of the concrete should also be evaluated. That is, the analysis of the instabilities of te piers of a bridge should consider both the mechanical and the geometrical non linearities. Additionally, the pier of a bridge is not a single element, but just the opposite; the connection of the pier to the deck of the bridge means that the movements of the top of the pier are reduced compared to the situation of having a free end at the top of the pier. The connection between the pier and the deck is the reason why the instability of the pier cannot be analysed using “the buckling of a compressed single element method”. So, the question of defining an approximate method for analysing the buckling of the slender piers of a bridge but using a software less complex than what it is needed for analysing the “ global buckling of a multibeam structure considering all t”, is arisen. Then, the goal should be trying to find a procedure for analysing the said complex problem of the buckling of the slender piers of a bridge using a simplified method. This method could be an iterative (step by step) procedure, being accurate enough, using “normal” software having the following capabilities: - Related to the calculation of the global structure o Ability for calculating a multibesam strucutre using elastic analysis. - Related to the calculation of a single beam strcuture:: o Ability for taking into account the geometrical and mechanical () non linearities o Ability for taking into account the cracking of the concrete. o Ability for using partial stiff constraints (elastic springs) at the end of the elements One of the objectives of this document is just defining this simplified methodology, justifying the accuracy of the proposed procedure by using it on some different bridges and presenting the exclusions and limitations of the propose method. In addition to this, some new charts have been created for calculating the reduction of the stiffness of hollow cross sections made of reinforced concrete. Also, new charts for calculating the reinforcing of hollow cross sections under biaxial bending moments are also included in the document. Finally, it is to be said that another aim of the document – as it is stated on the title on the document – is defining the value of the constraint on the top of the pier because of the connection of the pier to the deck .. and to the other piers. That is, the top of the pier is not a free end of a beam and so the buckling resistance of the pier is significantly improved. This constraint is a non-elastic constraint because the stiffness of each pier depends on the level of cracking. Additionally, the geometrical non linearity is to be considered as there is an amplification of the bending moments due to the increasing of the movements of the top of the pier. This document is defining how this constraints is to be calculated; also the accuracy of the calculations is evaluated comparing the final results with the results of the complete non linear calculations

The impact of geometric non-linearities on the fatigue analysis of trailing edge bond lines in wind turbine rotor blades

The accurate prediction of stress histories for the fatigue analysis is of utmost importance for the design process of wind turbine rotor blades. As detailed, transient, and geometrically non-linear three-dimensional finite element analyses are computationally weigh too expensive, it is commonly regarded sufficient to calculate the stresses with a geometrically linear analysis and superimpose different stress states in order to obtain the complete stress histories. In order to quantify the error from geometrically linear simulations for the calculation of stress histories and to verify the practical applicability of the superposition principal in fatigue analyses, this paper studies the influence of geometric non-linearity in the example of a trailing edge bond line, as this subcomponent suffers from high strains in span-wise direction. The blade under consideration is that of the IWES IWT-7.5-164 reference wind turbine. From turbine simulations the highest edgewise loading scenario from the fatigue load cases is used as the reference. A 3D finite element model of the blade is created and the bond line fatigue assessment is performed according to the GL certification guidelines in its 2010 edition, and in comparison to the latest DNV GL standard from end of 2015. The results show a significant difference between the geometrically linear and non-linear stress analyses when the bending moments are approximated via a corresponding external loading, especially in case of the 2010 GL certification guidelines. This finding emphasizes the demand to reconsider the application of the superposition principal in fatigue analyses of modern flexible rotor blades, where geometrical nonlinearities become significant. In addition, a new load application methodology is introduced that reduces the geometrically non-linear behaviour of the blade in the finite element analysis.