Pushover analysis of an existing reinforced concrete bridge:Jamboree Road Overcrossing in Irvine, California

The work for the present thesis started in California, during my semester as an exchange student overseas. California is known worldwide for its seismicity and its effort in the earthquake engineering research field. For this reason, I immediately found interesting the Structural Dynamics Professor, Maria Q. Feng's proposal, to work on a pushover analysis of the existing Jamboree Road Overcrossing bridge. Concrete is a popular building material in California, and for the most part, it serves its functions well. However, concrete is inherently brittle and performs poorly during earthquakes if not reinforced properly. The San Fernando Earthquake of 1971 dramatically demonstrated this characteristic. Shortly thereafter, code writers revised the design provisions for new concrete buildings so to provide adequate ductility to resist strong ground shaking. There remain, nonetheless, millions of square feet of non-ductile concrete buildings in California. The purpose of this work is to perform a Pushover Analysis and compare the results with those of a Nonlinear Time-History Analysis of an existing bridge, located in Southern California. The analyses have been executed through the software OpenSees, the Open System for Earthquake Engineering Simulation. The bridge Jamboree Road Overcrossing is classified as a Standard Ordinary Bridge. In fact, the JRO is a typical three-span continuous cast-in-place prestressed post-tension box-girder. The total length of the bridge is 366 ft., and the height of the two bents are respectively 26,41 ft. and 28,41 ft.. Both the Pushover Analysis and the Nonlinear Time-History Analysis require the use of a model that takes into account for the nonlinearities of the system. In fact, in order to execute nonlinear analyses of highway bridges it is essential to incorporate an accurate model of the material behavior. It has been observed that, after the occurrence of destructive earthquakes, one of the most damaged elements on highway bridges is a column. To evaluate the performance of bridge columns during seismic events an adequate model of the column must be incorporated. Part of the work of the present thesis is, in fact, dedicated to the modeling of bents. Different types of nonlinear element have been studied and modeled, with emphasis on the plasticity zone length determination and location. Furthermore, different models for concrete and steel materials have been considered, and the selection of the parameters that define the constitutive laws of the different materials have been accurate. The work is structured into four chapters, to follow a brief overview of the content. The first chapter introduces the concepts related to capacity design, as the actual philosophy of seismic design. Furthermore, nonlinear analyses both static, pushover, and dynamic, time-history, are presented. The final paragraph concludes with a short description on how to determine the seismic demand at a specific site, according to the latest design criteria in California. The second chapter deals with the formulation of force-based finite elements and the issues regarding the objectivity of the response in nonlinear field. Both concentrated and distributed plasticity elements are discussed into detail. The third chapter presents the existing structure, the software used OpenSees, and the modeling assumptions and issues. The creation of the nonlinear model represents a central part in this work. Nonlinear material constitutive laws, for concrete and reinforcing steel, are discussed into detail; as well as the different scenarios employed in the columns modeling. Finally, the results of the pushover analysis are presented in chapter four. Capacity curves are examined for the different model scenarios used, and failure modes of concrete and steel are discussed. Capacity curve is converted into capacity spectrum and intersected with the design spectrum. In the last paragraph, the results of nonlinear time-history analyses are compared to those of pushover analysis.

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

A mixture theory based method for three-dimensional modeling of reinforce concrete members with embedded crack finite elements

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 31) composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

Ensemble wind forecasting based on the HARMONIE model and adaptive finite elements in complex orography

[EN]Ensemble forecasting is a methodology to deal with uncertainties in the numerical wind prediction. In this work we propose to apply ensemble methods to the adaptive wind forecasting model presented in. The wind field forecasting is based on a mass-consistent model and a log-linear wind profile using as input data the resulting forecast wind from Harmonie, a Non-Hydrostatic Dynamic model used experimentally at AEMET with promising results. The mass-consistent model parameters are estimated by using genetic algorithms. The mesh is generated using the meccano method and adapted to the geometry…

Efficient Modeling of Thin Wires in a Lossy Medium by Finite Elements Applied to Grounding Systems

A procedure is proposed to accurately model thin wires in lossy media by finite element analysis. It is based on the determination of a suitable element width in the vicinity of the wire, which strongly depends on the wire radius to yield accurate results. The approach is well adapted to the analysis of grounding systems. The numerical results of the application of finite element analysis with the suitably chosen element width are compared with both analytical results and those computed by a commercial package for the analysis of grounding systems, showing very good agreement.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

A general technique to embed non-uniform discontinuities into standard solid finite elements

A general technique to embed non-uniform displacement discontinuities into standard solid finite elements is presented. The technique is based on the decomposition of the kinematic fields into a component related to the deformation of the solid portion of the element and one related to the rigid-body motion due to a displacement discontinuity. This decomposition simplifies the incorporation of discontinuity interfaces and provides a suitable framework to account for non-uniform discontinuity modes. The present publication addresses two families of finite element formulations: displacement-based and stress hybrid finite element. © 2005 Elsevier Ltd. All rights reserved.

Three-dimensional analysis of reinforced concrete members via embedded discontinuity finite elements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.