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We present an isogeometric boundary element method (IGABEM) capable of delivering accurate and efficient solutions in the heat transfer analysis of 2D coated structures such as those commonly found in turbomachinery. Although we consider very thin coatings (of thickness down to 10 −7 m), they are modelled explicitly as BEM zones, and this is made possible by the development of a new integration scheme (sinh +) aimed particularly at the challenging nearly singular integrals that arise. Sinh + is a hybrid of adaptive and sinh transformation approaches, and we make further extensions to the latter to improve its robustness. The scheme is tuned to deliver results of engineering accuracy in an optimal time. The scheme is adaptable, by changing a tolerance, to enable engineers to achieve a different balance between accuracy and computational efficiency as may be required for different applications. A set of numerical examples demonstrates the ability of the scheme to produce accurate temperature distributions efficiently in the presence of very thin coatings.

Extracting gas from shale rocks is one of the current engineering challenges but offers the prospect of cheap gas. Part of the development of an effective engineering solution for shale gas extraction in the future will be the availability of reliable and efficient methods of modelling the development of a fracture system, and the use of these models to guide operators in locating, drilling and pressurising wells. Numerous research papers have been dedicated to this problem, but the information is still incomplete, since a number of simplifications have been adopted such as the assumption of shale as an isotropic material. Recent works on shale characterisation have proved this assumption to be wrong. The anisotropy of shale depends significantly on the scale at which the problem is tackled (nano, micro or macroscale), suggesting that a multiscale model would be appropriate. Moreover, propagation of hydraulic fractures in such a complex medium can be difficult to model with current numerical discretisation methods. The crack propagation may not be unique, and crack branching can occur during the fracture extension. A number of natural fractures could exist in a shale deposit, so we are dealing with several cracks propagating at once over a considerable range of length scales. For all these reasons, the modelling of the fracking problem deserves considerable attention. The objective of this work is to present an overview of the hydraulic fracture of shale, introducing the most recent investigations concerning the anisotropy of shale rocks, then presenting some of the possible numerical methods that could be used to model the real fracking problem.

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures.', Computer methods in applied mechanics and engineering., 367 . p. 113099.

Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching and coalescence without special assumptions. Up to date, anisotropic materials were modelled in the PD framework as different isotropic materials (for instance, fibre and matrix of a composite laminate), where the stiffness of the bond depends on its orientation. A non-ordinary state-based formulation will enable the modelling of generally anisotropic materials, where the material properties are directly embedded in the formulation. Other material models include rocks, concrete and biomaterials such as bones. In this paper, we implemented this model and validated it for anisotropic composite materials. A composite damage criterion has been employed to model the crack propagation behaviour. Several numerical examples have been used to validate the approach, and compared to other benchmark solution from the finite element method (FEM) and experimental results when available.Fracture mechanics have been studied for nearly a century, from the first work of Griffith [15] for brittle materials. Over the years a number of researchers have modelled fracture mechanics analytically [28,36] for simple problems and geometries, and more commonly using numerical frameworks, such as the extended finite element method (XFEM) [4,27] and the extended boundary element method (XBEM) [16], among many others. Nevertheless, these methods suffer when crack branching or coalescence are involved.The phase-field method has been shown to model crack branching behaviour [1,18]. The method consists in describing the crack as an interface directly in the formulation and is used conjointly to the finite element method (FEM) [35]. Nevertheless, the method requires a fine mesh around the crack to model the interface correctly. Another drawback of the method is that it can provide unrealistic results. A novel numerical method entitled peridynamics (PD) [40] has been recently developed, and has shown great potential in fracture mechanics problems involving initiating, propagating, branching and coalescing cracks.The original peridynamics (PD) formulation was proposed by Silling [40], where he redefined the classical approach for continuum mechanics using an integral framework instead of partial derivatives. The main reason for using this approach is that the partial derivatives pose a challenge when dealing with fracture mechanics problems, since the governing partial differential equations in elasticity imply that singularities will appear due to the presence of discontinuities, which is not desirable. Due to the integral form of the formulation, no special assumptions are needed to deal with singularities, such as a crack in the domain.The first PD formulation described a continuum medium through discrete particles, interacting between each other through physical connections entitled bonds. Each bond has a stif...

. (2015) 'Contact stiness estimation in ANSYS using simplied models and articial neural networks.', Finite elements in analysis and design., 97 . pp. 43-53. Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Concrete is the most widely used man made material in the world. Reinforced with steel, it forms a key enabler behind our rapidly urbanising built environment. Yet despite its ubiquity, the failure behaviour of the material in shear is still not well understood. Many different shear models have been proposed over the years, often validated against sets of physical tests, but none of these has yet been shown to be sufficiently general to account for the behaviour of all possible types and geometries of reinforced concrete structures. A key barrier to a general model is that concrete must crack in tension, and in shear such cracks form rapidly to create brittle failure. Peridynamics (PD) is a non-local theory where the continuum mechanics equilibrium equation is reformulated in an integral form, thereby permitting discontinuities to arise naturally from the formulation. On the one hand, this offers the potential to provide a general concrete model. On the other hand, PD models for concrete structures have not focussed on applications with reinforcement. Moreover, a robust model validation that assesses the strengths and weakness of a given model is missing. The objectives of this paper are twofold: (1) to evaluate the benchmark tests involving shear failure for RC structures; and (2) to review the most recent PD theory and its application for reinforced concrete (RC) structures. We investigate these models in detail and propose benchmark tests that a PD model should be able to simulate accurately.

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.