Nicholas A. Alexander

Production of computational portraits of bounded invariant manifolds

Abstract To develop an effective procedure for describing manifold tangencies, an automative process for describing the invariant manifolds involved is required. This paper presents such an automative process. The accurate location of the saddle is achieved by a modified Powell Hybrid procedure which finds the local solution to a non-linear system of algebraic equations. The resulting eigenvalue problem, based on the local Jacobian matrix of the Poincare map, is solved and the eigenvectors evaluated. These are then used to extrapolate the initial points on the invariant manifold. By repeated iteration of the Poincare map other points on this manifold can be located. By storing the resultant data in a singly linked list and making use of a stack reference structure and negatively signed pointers, ordering and inserting/deletion of points can be achieved while keeping a bound on computational time and space. The technique provides a basis for investigative procedures for describing global bifurcation events.

Concerning Baseline Errors in the Form of Acceleration Transients When Recovering Displacements from Strong Motion Records Using the Undecimated Wavelet Transform

Abstract This paper discusses the progression of a novel algorithm that uses a wavelet‐transform approach. The transform is a generalization of the decimated, discrete wavelet transform (DWT) that is the undecimated DWT or stationary wavelet transform (SWT) also known as the undecimated a trous algorithm. It forms the basis for recovering displacements from acceleration time histories. The approach recovers a low‐frequency fling that is usually an almost sinusoidal or cosinusoidal pulse responsible for the big ground motions in strong motion events. The algorithm implements a well known and non‐linear, denoising scheme and is applied to the low‐frequency sub‐band and, in particular, succeeds in recovering the acceleration‐fling pulse. The progression is that in order to obtain estimates of displacements, the algorithmic baseline‐correction scheme can now locate an acceleration transient (i.e., a spike), which creates the DC shift in velocity and the linear trend in displacement, and is therefore the baseline error. Once this acceleration transient is corrected for or eliminated, double‐time reintegration recovers the velocity‐fling pulse and residual displacement. The paper infers that these acceleration transients may be due to ground rotation, embedded in the translational data. The scheme provides for easier integration once the low‐ and higher‐frequency accelerations are extracted. Online Material: Additional results for the Chi‐Chi TCU068 (1999) station, the New Zealand Darfield Station (2010), and the Olfus Earthquake (2008) in Iceland.

Computational Modelling Strategies for Nonlinear Response Prediction of Corroded Circular RC Bridge Piers

A numerical model is presented that enables simulation of the nonlinear flexural response of corroded reinforced concrete (RC) components. The model employs a force-based nonlinear fibre beam-column element. A new phenomenological uniaxial material model for corroded reinforcing steel is used. This model accounts for the impact of corrosion on buckling strength, postbuckling behaviour, and low-cycle fatigue degradation of vertical reinforcement under cyclic loading. The basic material model is validated through comparison of simulated and observed responses for uncorroded RC columns. The model is used to explore the impact of corrosion on the inelastic response of corroded RC columns.

Nonlinear dynamic analysis and seismic fragility assessment of a corrosion damaged integral bridge

Purpose – The purpose of this paper is to explore the impact of corrosion of reinforcing steel in RC columns on the seismic performance of a multi-span concrete integral bridge. A new constitutive model for corroded reinforcing steel is used. This model simulates the buckling of longitudinal reinforcement under cyclic loading and the impact of corrosion on buckling strength. Cover concrete strength is adjusted to account for corrosion induced damage and core concrete strength and ductility is adjusted to account for corrosion induced damage to transverse reinforcement. This study evaluates the impact which chloride induced corrosion of the reinforced concrete columns on the seismic fragility of the bridge. Fragility curves are developed at a various time intervals over the lifetime. The results of this study show that the bridge fragility increases significantly with corrosion. Design/methodology/approach – This paper first, evaluates the impact which chloride induced corrosion of the columns has on bridg...

A multi-mechanical nonlinear fibre beam-column model for corroded columns

Purpose – A new modelling technique is developed to model the nonlinear behaviour of corrosion damaged reinforced concrete (RC) bridge piers subject to cyclic loading. The model employs a nonlinear beam-column element with multi-mechanical fibre sections using OpenSees. The nonlinear uniaxial material models used in the fibre sections account for the effect of corrosion damage on vertical reinforcing, cracked cover concrete due to corrosion of vertical bars and damaged confined concrete due to corrosion of horizontal tie reinforcement. An advance material model is used to simulate the nonlinear behaviour of the vertical reinforcing bars that accounts for combined impact of inelastic buckling and low-cycle fatigue degradation. The basic uncorroded model is verified by comparison of the computation and observed response of RC columns with uncorroded reinforcement. This model is used in an exploration study of recently tested RC components to investigate the impact of different corrosion models on the inelas...

Autotuning of Isotropic Hardening Constitutive Models on Real Steel Buckling Data with Finite Element Based Multistart Global Optimisation on Parallel Computers

An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully automatic preprocessing, including model and mesh generation, analysis, and postprocessing. The framework is applied to an isotropic power hardening plasticity using real load/displacement data from multiple steel buckling tests. M. J. D. Powellźs BOBYQA constrained optimisation package was used for local optimisation. It is shown that using the real data presents multiple problems to the optimisation process because (1) the objective function can be discontinuous, yet (2) relatively flat around multiple local minima, with (3) similar values of the objective function for different local minima. As a consequence the estimate of the global minimum is sensitive to the amount of experimental data and experimental noise. The framework includes the verification step, where the estimate of the global minimum is verified on a different geometry and loading. A tensile test was used for verification in this work. The speed of the method critically depends on the ability to effectively parallelise the finite element solver. Three levels of parallelisation were exploited in this work. The ultimate limitation was the availability of the finite element commercial solver license tokens.

Influence of non-stationary content of ground-motions on nonlinear dynamic response of RC bridge piers

Abstract This paper quantifies the impact of the non-stationary content (time-varying parameters that are not captured by power spectral content alone) of different ground-motion types (near/far field, with/without pulses time-series) on the nonlinear dynamic response of reinforced concrete bridge piers, taking into account the material cyclic degradation. Three groups of ground motions are selected to represent far-field, near-field without pulse and near-field pulse-like ground motions. Three analysis cases are considered corresponding to acceleration series matched to the mean response spectrum of: (1) far field, (2) near-field without pulse and (3) near-field pulse-like ground-motions, respectively. Using the selected ground motions, several nonlinear incremental dynamic analyses of prototype reinforced concrete bridge piers with a range of fundamental periods are conducted. Finally, a comparison between the response of the structures using the material model accounting for both buckling and low-cycle fatigue of reinforcing steel and the more conventional material model that does not account for these effects is made. The results show that the inelastic buckling and low-cycle fatigue have a significant influence on the nonlinear response of the RC bridge piers considered and that pulse effects can increase the mean acceleration response by about 50%.

Damage propagation in corroded reinforcing bars with the effect of inelastic buckling under low-cycle fatigue loading

The effect of inelastic buckling on low-cycle high amplitude fatigue life of reinforcing bars is investigated experimentally. The results show that the inelastic buckling, bar diameter and surface condition are the main parameters affecting the low-cycle fatigue life of reinforcing bars. Through nonlinear regression analyses of the experimental data a new set of empirical equations for fatigue life prediction of reinforcing bars as a function of the buckling length and yield strength are developed. Finally, these empirical models have been implemented into a new phenomenological hysteretic material model for reinforcing bars. Furthermore, the combined effect of inelastic buckling and chloride induced corrosion damage on low-cycle high amplitude fatigue life of embedded reinforcing bars is investigated experimentally. The low-cycle fatigue tests on corroded reinforcing bars varied in percentage mass loss, strain amplitudes and buckling lengths are conducted. The failure modes and crack propagation are investigated by fractography of fracture surfaces using scanning electron microscope.

Predicting collapse loads for buildings subjected to seismic shock

In this paper an analytical expression that estimates the collapse load of a generic class of multi-storey, uniform, moment-resisting steel frames is presented. This expression is validated and calibrated with nonlinear pushover analyses (NPA) and incremental dynamic analyses for a set of buildings, of differing heights, that are designed according to the Eurocodes. The efficacy of different seismically induced load profiles in NPA is discussed with a preferred profile suggested for this class of structural system. The relationship between the actual seismic force reduction factor and code specified behavior factors is underlined.