Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Direct second-order elastic analysis for steel frame design

The traditional structural design procedure, especially for the large-scale and complex structures, is time consuming and inefficient. This is due primarily to the fact that the traditional design takes the second-order effects indirectly by virtue of design specifications for every member instead of system analysis for a whole structure. Consequently, the complicated and tedious design procedures are inevitably necessary to consider the second-order effects for the member level in design specification. They are twofold in general: 1) Flexural buckling due to P-d effect, i.e. effective length. 2) Sway effect due to P-D effect, i.e. magnification factor. In this study, a new system design concept based on the second-order elastic analysis is presented, in which the second-order effects are taken into account directly in the system analysis, and also to avoid the tedious member-by-member stability check. The plastic design on the basis of this integrated method of direct approach is ignored in this paper for simplicity and clarity, as the only emphasis is placed on the difference between the second-order elastic limit-state design and present system design approach. A practical design example, a 57m-span dome steel skylight structure, is used to demonstrate the efficiency and effectiveness of the proposed approach. This skylight structure is also designed by the traditional design approach BS5950-2000 for comparison on which the emphasis of aforementioned P-d and P-D effects is placed.

Material yielding by both axial and bending spring stiffness at elevated temperature

Material yielding is typically modeled either by plastic zone or plastic hinge methods under the context of geometric and material nonlinear finite element methods. In fire analysis of steel structures, the plastic zone method is widely used, but it requires extensively more computational efforts. The objective of this paper is to develop the nonlinear material model allowing for interaction of both axial force and bending moment, which relies on the plastic hinge method to achieve numerical efficiency and reduce computational effort. The biggest advantage of the plastic-hinge approach is its computational efficiency and easy verification by the design code formulae of the axial force–moment interaction yield criterion for beam–column members. Further, the method is reliable and robust when used in analysis of practical and large structures. In order to allow for the effect of catenary action, axial thermal expansion is considered in the axial restraint equations. The yield function for material yielding incorporated in the stiffness formulation, which allows for both axial force and bending moment effects, is more accurate and rational to predict the behaviour of the frames under fire. In the present fire analysis, the mechanical properties at elevated temperatures follow mainly the Eurocode 3 [Design of steel structures, Part 1.2: Structural fire design. European Committee for Standisation; 2003]. Example of a tension member at a steady state heating condition is modeled to verify the proposed spring formulation and to compare with results by others. The behaviour of a heated member in a highly redundant structure is also studied by the present approach.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

Analysis of terrain geometry representations for traversability of a Mars rover

For a planetary rover to successfully traverse across unstructured terrain autonomously, one of the major challenges is to assess its local traversability such that it can plan a trajectory to achieve its mission goals efficiently while minimising risk to the vehicle itself. This paper aims to provide a comparative study on different approaches for representing the geometry of Martian terrain for the purpose of evaluating terrain traversability. An accurate representation of the geometric properties of the terrain is essential as it can directly affect the determination of traversability for a ground vehicle. We explore current state-of-the-art techniques for terrain estimation, in particular Gaussian Processes (GP) in various forms, and discuss the suitability of each technique in the context of an unstructured Martian terrain. Furthermore, we present the limitations of regression techniques in terms of spatial correlation and continuity assumptions, and the impact on traversability analysis of a planetary rover across unstructured terrain. The analysis was performed on datasets of the Mars Yard at the Powerhouse Museum in Sydney, obtained using the onboard RGB-D camera.

Augmenting traversability maps with ultra-wideband radar to enhance obstacle detection in vegetated environments

Operating in vegetated environments is a major challenge for autonomous robots. Obstacle detection based only on geometric features causes the robot to consider foliage, for example, small grass tussocks that could be easily driven through, as obstacles. Classifying vegetation does not solve this problem since there might be an obstacle hidden behind the vegetation. In addition, dense vegetation typically needs to be considered as an obstacle. This paper addresses this problem by augmenting probabilistic traversability map constructed from laser data with ultra-wideband radar measurements. An adaptive detection threshold and a probabilistic sensor model are developed to convert the radar data to occupancy probabilities. The resulting map captures the fine resolution of the laser map but clears areas from the traversability map that are induced by obstacle-free foliage. Experimental results validate that this method is able to improve the accuracy of traversability maps in vegetated environments.

Error modeling and calibration of exteroceptive sensors for accurate mapping applications

Reliable robotic perception and planning are critical to performing autonomous actions in uncertain, unstructured environments. In field robotic systems, automation is achieved by interpreting exteroceptive sensor information to infer something about the world. This is then mapped to provide a consistent spatial context, so that actions can be planned around the predicted future interaction of the robot and the world. The whole system is as reliable as the weakest link in this chain. In this paper, the term mapping is used broadly to describe the transformation of range-based exteroceptive sensor data (such as LIDAR or stereo vision) to a fixed navigation frame, so that it can be used to form an internal representation of the environment. The coordinate transformation from the sensor frame to the navigation frame is analyzed to produce a spatial error model that captures the dominant geometric and temporal sources of mapping error. This allows the mapping accuracy to be calculated at run time. A generic extrinsic calibration method for exteroceptive range-based sensors is then presented to determine the sensor location and orientation. This allows systematic errors in individual sensors to be minimized, and when multiple sensors are used, it minimizes the systematic contradiction between them to enable reliable multisensor data fusion. The mathematical derivations at the core of this model are not particularly novel or complicated, but the rigorous analysis and application to field robotics seems to be largely absent from the literature to date. The techniques in this paper are simple to implement, and they offer a significant improvement to the accuracy, precision, and integrity of mapped information. Consequently, they should be employed whenever maps are formed from range-based exteroceptive sensor data. © 2009 Wiley Periodicals, Inc.

Frequency dielectric influence of imaginary admittance on oil-paper insulation system-a case study

Frequency Domain Spectroscopy (FDS) is used to assess the insulation condition of oil-paper power transformers. Dissipation factor is one of the conventional indicators to analyze insulation ageing status. In this paper, the imaginary admittance of the transformers insulation, after removal of the geometric capacitance, is proposed as an alternative indicator to assist in the interpretation of ageing status. Ageing effects on the imaginary admittance are investigated both through simulation results and experimental results.

Predicting the likelihood of QA failure using treatment plan accuracy metrics

This study used automated data processing techniques to calculate a set of novel treatment plan accuracy metrics, and investigate their usefulness as predictors of quality assurance (QA) success and failure. 151 beams from 23 prostate and cranial IMRT treatment plans were used in this study. These plans had been evaluated before treatment using measurements with a diode array system. The TADA software suite was adapted to allow automatic batch calculation of several proposed plan accuracy metrics, including mean field area, small-aperture, off-axis and closed-leaf factors. All of these results were compared the gamma pass rates from the QA measurements and correlations were investigated. The mean field area factor provided a threshold field size (5 cm2, equivalent to a 2.2 x 2.2 cm2 square field), below which all beams failed the QA tests. The small aperture score provided a useful predictor of plan failure, when averaged over all beams, despite being weakly correlated with gamma pass rates for individual beams. By contrast, the closed leaf and off-axis factors provided information about the geometric arrangement of the beam segments but were not useful for distinguishing between plans that passed and failed QA. This study has provided some simple tests for plan accuracy, which may help minimise time spent on QA assessments of treatments that are unlikely to pass.

An analogy between the double slit experiment and document ranking

In the last years several works have investigated a formal model for Information Retrieval (IR) based on the mathematical formalism underlying quantum theory. These works have mainly exploited geometric and logical–algebraic features of the quantum formalism, for example entanglement, superposition of states, collapse into basis states, lattice relationships. In this poster I present an analogy between a typical IR scenario and the double slit experiment. This experiment exhibits the presence of interference phenomena between events in a quantum system, causing the Kolmogorovian law of total probability to fail. The analogy allows to put forward the routes for the application of quantum probability theory in IR. However, several questions need still to be addressed; they will be the subject of my PhD research

Short term variability in urinary bisphenol A in Australian children

Used frequently in food contact materials, bisphenol A (BPA) has been studied extensively in recent years, and ubiquitous exposure in the general population has been demonstrated worldwide. Characterising within- and between-individual variability of BPA concentrations is important for characterising exposure in biomonitoring studies, and this has been investigated previously in adults, but not in children. The aim of this study was to characterise the short-term variability of BPA in spot urine samples in young children. Children aged ≥2-<4 years (n = 25) were recruited from an existing cohort in Queensland Australia, and donated four spot urine samples each over a two day period. Samples were analysed for total BPA using isotope dilution online solid phase extraction-liquid chromatography-tandem mass spectrometry, and concentrations ranged from 0.53–74.5 ng/ml, with geometric mean and standard deviation of 2.70 ng/ml and 2.94 ng/ml, respectively. Sex and time of sample collection were not significant predictors of BPA concentration. The between-individual variability was approximately equal to the within-individual variability (ICC = 0.51), and this ICC is somewhat higher than previously reported literature values. This may be the result of physiological or behavioural differences between children and adults or of the relatively short exposure window assessed. Using a bootstrapping methodology, a single sample resulted in correct tertile classification approximately 70% of the time. This study suggests that single spot samples obtained from young children provide a reliable characterization of absolute and relative exposure over the short time window studied, but this may not hold true over longer timeframes.

Development of optical ray tracing model of a standard parabolic trough collector

Parabolic trough concentrator collector is the most matured, proven and widespread technology for the exploitation of the solar energy on a large scale for middle temperature applications. The assessment of the opportunities and the possibilities of the collector system are relied on its optical performance. A reliable Monte Carlo ray tracing model of a parabolic trough collector is developed by using Zemax software. The optical performance of an ideal collector depends on the solar spectral distribution and the sunshape, and the spectral selectivity of the associated components. Therefore, each step of the model, including the spectral distribution of the solar energy, trough reflectance, glazing anti-reflection coating and the absorber selective coating is explained and verified. Radiation flux distribution around the receiver, and the optical efficiency are two basic aspects of optical simulation are calculated using the model, and verified with widely accepted analytical profile and measured values respectively. Reasonably very good agreement is obtained. Further investigations are carried out to analyse the characteristics of radiation distribution around the receiver tube at different insolation, envelop conditions, and selective coating on the receiver; and the impact of scattered light from the receiver surface on the efficiency. However, the model has the capability to analyse the optical performance at variable sunshape, tracking error, collector imperfections including absorber misalignment with focal line and de-focal effect of the absorber, different rim angles, and geometric concentrations. The current optical model can play a significant role in understanding the optical aspects of a trough collector, and can be employed to extract useful information on the optical performance. In the long run, this optical model will pave the way for the construction of low cost standalone photovoltaic and thermal hybrid collector in Australia for small scale domestic hot water and electricity production.

Entropic bounds for multi-scale and multi-physics coupling in earth sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.