Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

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.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element

Based on the refined non-conforming element method for geometric nonlinear analysis, a refined nonlinear non-conforming triangular plate element is constructed using the Total Lagrangian (T.L.) and the Updated Lagrangian (U.L.) approach. The refined nonlinear non-conforming triangular plate element is based on the Allman's triangular plane element with drilling degrees of freedom [1] and the refined non-conforming triangular plate element RT9 [2]. The element is used to analyze the geometric nonlinear behavior of plates and the numerical examples show that the refined non-conforming triangular plate element by the T.L. and U.L. approach can give satisfactory results. The computed results obtained from the T.L. and U.L. approach for the same numerical examples are somewhat different and the reasons for the difference of the computed results are given in detail in this paper. © 2003 Elsevier Science Ltd. All rights reserved.

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

Numerical modelling of braided fibres for reinforced concrete

Fire has been always a major concern for designers of steel and concrete structures. Designing fire-resistant structural elements is not an easy task due to several limitations such as the lack of fire-resistant construction materials. Concrete reinforcement cover and external insulation are the most commonly adopted systems to protect concrete and steel from overheating, while spalling of concrete is minimised by using HPFRC instead of standard concrete. Although these methodologies work very well for low rise concrete structures, this is not the case for high-rise and inaccessible buildings where fire loading is much longer. Fire can permanently damage structures that cost a lot of money. This is unsafe and can lead to loss of life. In this research, the author proposes a new type of main reinforcement for concrete structures which can provide better fire-resistance than steel or FRP re-bars. This consists of continuous braided fibre rope, generally made from fire-resistant materials such as carbon or glass fibre. These fibres have excellent tensile strengths, sometimes in excess of ten times greater than steel. In addition to fire-resistance, these ropes can produce lighter and corrosive resistant structures. Avoiding the use of expensive resin binders, fibres are easily bound together using braiding techniques, ensuring that tensile stress is evenly distributed throughout the reinforcement. In order to consider braided ropes as a form of reinforcement it is first necessary to establish the mechanical performance at room temperature and investigate the pull-out resistance for both unribbed and ribbed ropes. Ribbing of ropes was achieved by braiding the rope over a series of glass beads. Adhesion between the rope and concrete was drastically improved due to ribbing, and further improved by pre-stressing ropes and reducing the slacked fibres. Two types of material have been considered for the ropes: carbon and aramid. An implicit finite element approach is proposed to model braided fibres using Total Lagrangian formulation, based on the theory of small strains and large rotations. Modelling tows and strands as elastic transversely isotropic materials was a good assumption when stiff and brittle fibres such as carbon and glass fibres are considered. The rope-to-concrete and strand-to-strand bond interaction/adhesion was numerically simulated using newly proposed hierarchical higher order interface elements. Elastic and linear damage cohesive models were used effectively to simulate non-penetrative 'free' sliding interaction between strands, and the adhesion between ropes and concrete respectively. Numerical simulation showed similar de-bonding features when compared with experimental pull-out results of braided ribbed rope reinforced concrete.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

Long-Range Pollution Transport: Trans-Atlantic Mechanisms and Lagrangian Modeling Methods

Over the past several decades, it has become apparent that anthropogenic activities have resulted in the large-scale enhancement of the levels of many trace gases throughout the troposphere. More recently, attention has been given to the transport pathway taken by these emissions as they are dispersed throughout the atmosphere. The transport pathway determines the physical characteristics of emissions plumes and therefore plays an important role in the chemical transformations that can occur downwind of source regions. For example, the production of ozone (O3) is strongly dependent upon the transport its precursors undergo. O3 can initially be formed within air masses while still over polluted source regions. These polluted air masses can experience continued O3 production or O3 destruction downwind, depending on the air mass's chemical and transport characteristics. At present, however, there are a number of uncertainties in the relationships between transport and O3 production in the North Atlantic lower free troposphere. The first phase of the study presented here used measurements made at the Pico Mountain observatory and model simulations to determine transport pathways for US emissions to the observatory. The Pico Mountain observatory was established in the summer of 2001 in order to address the need to understand the relationships between transport and O3 production. Measurements from the observatory were analyzed in conjunction with model simulations from the Lagrangian particle dispersion model (LPDM), FLEX-PART, in order to determine the transport pathway for events observed at the Pico Mountain observatory during July 2003. A total of 16 events were observed, 4 of which were analyzed in detail. The transport time for these 16 events varied from 4.5 to 7 days, while the transport altitudes over the ocean ranged from 2-8 km, but were typically less than 3 km. In three of the case studies, eastward advection and transport in a weak warm conveyor belt (WCB) airflow was responsible for the export of North American emissions into the FT, while transport in the FT was governed by easterly winds driven by the Azores/Bermuda High (ABH) and transient northerly lows. In the fourth case study, North American emissions were lofted to 6-8 km in a WCB before being entrained in the same cyclone's dry airstream and transported down to the observatory. The results of this study show that the lower marine FT may provide an important transport environment where O3 production may continue, in contrast to transport in the marine boundary layer, where O3 destruction is believed to dominate. The second phase of the study presented here focused on improving the analysis methods that are available with LPDMs. While LPDMs are popular and useful for the analysis of atmospheric trace gas measurements, identifying the transport pathway of emissions from their source to a receptor (the Pico Mountain observatory in our case) using the standard gridded model output, particularly during complex meteorological scenarios can be difficult can be difficult or impossible. The transport study in phase 1 was limited to only 1 month out of more than 3 years of available data and included only 4 case studies out of the 16 events specifically due to this confounding factor. The second phase of this study addressed this difficulty by presenting a method to clearly and easily identify the pathway taken by only those emissions that arrive at a receptor at a particular time, by combining the standard gridded output from forward (i.e., concentrations) and backward (i.e., residence time) LPDM simulations, greatly simplifying similar analyses. The ability of the method to successfully determine the source-to-receptor pathway, restoring this Lagrangian information that is lost when the data are gridded, is proven by comparing the pathway determined from this method with the particle trajectories from both the forward and backward models. A sample analysis is also presented, demonstrating that this method is more accurate and easier to use than existing methods using standard LPDM products. Finally, we discuss potential future work that would be possible by combining the backward LPDM simulation with gridded data from other sources (e.g., chemical transport models) to obtain a Lagrangian sampling of the air that will eventually arrive at a receptor.

Lagrangian back-tracing results for Kohnen station; output of time dependent numerical experiment with a 3D nested Antarctic ice sheet model

A nested ice flow model was developed for eastern Dronning Maud Land to assist with the dating and interpretation of the EDML deep ice core. The model consists of a high-resolution higher-order ice dynamic flow model that was nested into a comprehensive 3-D thermomechanical model of the whole Antarctic ice sheet. As the drill site is on a flank position the calculations specifically take into account the effects of horizontal advection as deeper ice in the core originated from higher inland. First the regional velocity field and ice sheet geometry is obtained from a forward experiment over the last 8 glacial cycles. The result is subsequently employed in a Lagrangian backtracing algorithm to provide particle paths back to their time and place of deposition. The procedure directly yields the depth-age distribution, surface conditions at particle origin, and a suite of relevant parameters such as initial annual layer thickness. This paper discusses the method and the main results of the experiment, including the ice core chronology, the non-climatic corrections needed to extract the climatic part of the signal, and the thinning function. The focus is on the upper 89% of the ice core (appr. 170 kyears) as the dating below that is increasingly less robust owing to the unknown value of the geothermal heat flux. It is found that the temperature biases resulting from variations of surface elevation are up to half of the magnitude of the climatic changes themselves.

Petroleomics By Electrospray Ionization Ft-icr Mass Spectrometry Coupled To Partial Least Squares With Variable Selection Methods: Prediction Of The Total Acid Number Of Crude Oils.

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

Evaluation Of Characteristic-to-total Spectrum Ratio: Comparison Between Experimental And A Semi-empirical Model.

Primary X-ray spectra were measured in the range of 80-150kV in order to validate a computer program based on a semiempirical model. The ratio between the characteristic and total air Kerma was considered to compare computed results and experimental data. Results show that the experimental spectra have higher first HVL and mean energy than the calculated ones. The ratios between the characteristic and total air Kerma for calculated spectra are in good agreement with experimental results for all filtrations used.

The Total Synthesis Of (-)-cryptocaryol A.

A stereoselective total synthesis of (-)-cryptocaryol A () is described. Key features of the 17-step route include the use of three boron-mediated aldol reaction-reduction sequences to control all stereocenters and an Ando modification of the Horner-Wadsworth-Emmons olefination that permitted the installation of the Z double bond of the α-pyrone ring.

Determinação de açúcar total em café cru por espectroscopia no infravermelho próximo e regressão por mínimos quadrados parciais

In this work a fast method for the determination of the total sugar levels in samples of raw coffee was developed using the near infrared spectroscopy technique and multivariate regression. The sugar levels were initially obtained using gravimety as the reference method. Later on, the regression models were built from the near infrared spectra of the coffee samples. The original spectra were pre-treated according to the Kubelka-Munk transformation and multiplicative signal correction. The proposed analytical method made possible the direct determination of the total sugar levels in the samples with an error lower by 8% with respect to the conventional methodology.