A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

Finite element analysis of compressor disc heat transfer using the transient conduction method with sparse boundary collocation points

Surface temperature measurements from two discs of a gas turbine compressor rig are used as boundary conditions for the transient conduction solution (inverse heat transfer analysis). The disc geometry is complex, and so the finite element method is used. There are often large radial temperature gradients on the discs, and the equations are therefore solved taking into account the dependence of thermal conductivity on temperature. The solution technique also makes use of a multigrid algorithm to reduce the solution time. This is particularly important since a large amount of data must be analyzed to obtain correlations of the heat transfer. The finite element grid is also used for a network analysis to calculate the radiant heat transfer in the cavity formed between the two compressor discs. The work discussed here proved particularly challenging as the disc temperatures were only measured at four different radial locations. Four methods of surface temperature interpolation are examined, together with their effect on the local heat fluxes. It is found that the choice of interpolation method depends on the available number of data points. Bessel interpolation gives the best results for four data points, whereas cubic splines are preferred when there are considerably more data points. The results from the analysis of the compressor rig data show that the heat transfer near the disc inner radius appears to be influenced by the central throughflow. However, for larger radii, the heat transfer from the discs and peripheral shroud is found to be consistent with that of a buoyancy-induced flow.

Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials

The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.

Finite Element studies on indentation size effect using a higher order strain gradient theory

In this work, a Finite Element implementation of a higher order strain gradient theory (due to Fleck and Hutchinson, 2001) has been used within the framework of large deformation elasto-viscoplasticity to study the indentation of metals with indenters of various geometries. Of particular interest is the indentation size effect (ISE) commonly observed in experiments where the hardness of a range of materials is found to be significantly higher at small depths of indentation but reduce to a lower, constant value at larger depths. That the ISE can be explained by strain gradient plasticity is well known but this work aims to qualitatively compare a gamut of experimental observations on this effect with predictions from a higher order strain gradient theory. Results indicate that many of the experimental observations are qualitatively borne out by our simulations. However, areas exist where conflicting experimental results make assessment of numerical predictions difficult. © 2012 Elsevier Ltd. All rights reserved.

Finite element analysis of the ring rolling process with integrated closed-loop control

In FEA of ring rolling processes the tools' motions usually are defined prior to simulation. This procedure neglects the closed-loop control, which is used in industrial processes to control up to eight degrees of freedom (rotations, feed rates, guide rolls) in real time, taking into account the machine's performance limits as well as the process evolution. In order to close this gap in the new simulation approach all motions of the tools are controlled according to sensor values which are calculated within the FE simulation. This procedure leads to more realistic simulation results in comparison to the machine behaviour. © 2012 CIRP.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

Modelling of settlement induced building damage

This thesis focuses on the modelling of settlement induced damage to masonry buildings. In densely populated areas, the need for new space is nowadays producing a rapid increment of underground excavations. Due to the construction of new metro lines, tunnelling activity in urban areas is growing. One of the consequences is a greater attention to the risk of damage on existing structures. Thus, the assessment of potential damage of surface buildings has become an essential stage in the excavation projects in urban areas (Chapter 1). The current damage risk assessment procedure is based on strong simplifications, which not always lead to conservative results. Object of this thesis is the development of an improved damage classification system, which takes into account the parameters influencing the structural response to settlement, like the non-linear behaviour of masonry and the soil-structure interaction. The methodology used in this research is based on experimental and numerical modelling. The design and execution of an experimental benchmark test representative of the problem allows to identify the principal factors and mechanisms involved. The numerical simulations enable to generalize the results to a broader range of physical scenarios. The methodological choice is based on a critical review of the currently available procedures for the assessment of settlement-induced building damage (Chapter 2). A new experimental test on a 1/10th masonry façade with a rubber base interface is specifically designed to investigate the effect of soil-structure interaction on the tunnelling-induced damage (Chapter 3). The experimental results are used to validate a 2D semi-coupled finite element model for the simulation of the structural response (Chapter 4). The numerical approach, which includes a continuum cracking model for the masonry and a non-linear interface to simulate the soil-structure interaction, is then used to perform a sensitivity study on the effect of openings, material properties, initial damage, initial conditions, normal and shear behaviour of the base interface and applied settlement profile (Chapter 5). The results assess quantitatively the major role played by the normal stiffness of the soil-structure interaction and by the material parameters defining the quasi-brittle masonry behaviour. The limitation of the 2D modelling approach in simulating the progressive 3D displacement field induced by the excavation and the consequent torsional response of the building are overcome by the development of a 3D coupled model of building, foundation, soil and tunnel (Chapter 6). Following the same method applied to the 2D semi-coupled approach, the 3D model is validated through comparison with the monitoring data of a literature case study. The model is then used to carry out a series of parametric analyses on geometrical factors: the aspect ratio of horizontal building dimensions with respect to the tunnel axis direction, the presence of adjacent structures and the position and alignment of the building with respect to the excavation (Chapter 7). The results show the governing effect of the 3D building response, proving the relevance of 3D modelling. Finally, the results from the 2D and 3D parametric analyses are used to set the framework of an overall damage model which correlates the analysed structural features with the risk for the building of being damaged by a certain settlement (Chapter 8). This research therefore provides an increased experimental and numerical understanding of the building response to excavation-induced settlements, and sets the basis for an operational tool for the risk assessment of structural damage (Chapter 9).

3D numerical analysis of tunnelling induced damage: the influence of the alignment of a masonry building with the tunnel axis.

The development of infrastructure in major cities often involves tunnelling, which can cause damage to existing structures. Therefore, these projects require a careful prediction of the risk of settlement induced damage. The simplified approach of current methods cannot account for three-dimensional structural aspects of buildings, which can result in an inaccurate evaluation of damage. This paper investigates the effect of the building alignment with the tunnel axis on structural damage. A three-dimensional, phased, fully coupled finite element model with non-linear material properties is used as a tool to perform a parametric study. The model includes the simulation of the tunnel construction process, with the tunnel located adjacent to a masonry building. Three different type of settlements are included (sagging, hogging and a combination of them), with seven different increasing angles of the building with respect to the tunnel axis. The alignment parameter is assessed, based on the maximum occurring crack width, measured in the building. Results show a significant dependency of the final damage on the building and tunnel alignment.