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Meshfree methods for shear-deformable structures based on mixed weak forms Hale, Jack Scientific Conference (2014, July 24) Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories. Many successful ... [more ▼] Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed variational form, where the shear stress is treated as an independent variational quantity in addition to the usual displacements. Because of its sound mathematical underpinnings this is the methodology I have chosen to solve the shear-locking problem when using meshfree basis functions. In this talk I will discuss the mathematical origins of the shear-locking problem and the applicability of the celebrated LBB stability condition for designing well-behaved mixed meshfree approximation schemes. I will show results from two new formulations that demonstrate the effectiveness of this approach. The first method is a meshfree formulation for the Timoshenko beam problem that converges to a classic inf-sup stable finite element method when using Maximum- Entropy basis functions. The second method is a generalised displacement meshfree method for the Reissner- Mindlin problem where the shear stress is eliminated prior to the solution of the linear system using a local patch-projection technique, resulting in a linear system expressed in terms of the original displacement unknowns only. Stability is ensured by using a stabilised weak form which is necessary due to the loss of kernel coercivity for the Reissner-Mindlin problem. [less ▲] Detailed reference viewed: 65 (7 UL)Parallel simulations of soft-tissue using an adaptive quadtree/octree implicit boundary finite element method Hale, Jack ; Bordas, Stéphane ; et al in 11th. World Congress on Computational Mechanics (2014, July 23) Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation ... [more ▼] Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms applied to medical scans [5]. In this work we consider the simulation of soft-tissue which can be modelled with a incompressible hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties in our model. Similarly to Moumnassi et al. [2] we use the implicitly defined level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary on the cartesian quadtree/octree mesh. In addition we introduce arbitrary cuts and discontinuities in the domain using ideas from the classical extended finite element method [3]. Because of its hydrated nature soft-tissue is nearly incompressible [1]. We explore the use of a classical two-field displacement-pressure (u-p) mixed approach to deal with the problem of volumetric-locking in the incompressible limit [4]. We exploit the existing parallel capabilities available in the open-souce finite element toolkit deal.ii [6], including the advanced mesh partitioning and balancing recently introduced in the p4est library [7]. The resulting method scales to run over hundreds of cores on the University of Luxembourg HPC platform. [less ▲] Detailed reference viewed: 449 (26 UL)Meshfree volume-averaged nodal projection methods for incompressible media problems ; Hale, Jack ; Scientific Conference (2014, July 21) Detailed reference viewed: 384 (5 UL)An overview of our research directions in advanced discretisation methods for PDEs Hale, Jack Presentation (2014, July 10) Detailed reference viewed: 43 (1 UL)Stress analysis, damage tolerance assessment and shape optimisation without meshing Hale, Jack ; Bordas, Stéphane ; et al Poster (2014, June 24) Detailed reference viewed: 103 (3 UL)Direct image-analysis methods for surgical simulation and mixed meshfree methods Hale, Jack ; Bordas, Stéphane ; et al Presentation (2014, May 28) Detailed reference viewed: 117 (11 UL)Reducing the Mesh-burden and Computational Expense in Multi-scale Free Boundary Engineering Problems Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, May 12) We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second ... [more ▼] We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric boundary elements and extended finite element methods for multi-crack propagation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 200 (6 UL)Model and mesh-burden reduction for multiscale fracture: applications to polycrystals, delamination and surgical simulation Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, April 23) ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a ... [more ▼] ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric extended boundary elements/finite element methods for multi-crack propagation and an asynchronous GPU/CPU method for contact and cutting of heterogeneous materials in real-time with applications to surgical simulation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 659 (17 UL)From image to analysis: an extended finite element method to simulate the mechanical response of soft-tissue Hale, Jack ; Bordas, Stéphane ; Presentation (2014, April 10) In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a ... [more ▼] In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a conforming mesh of the problem domain, we use implicitly defined domains described using the level-set method. We then include information about the implicitly defined domains by enriching the usual finite element basis functions defined on a cartesian quadtree or octree mesh with hanging nodes. This approach introduces significant complexities compared with classical finite element methods. We will discuss difficulties with the treatment of hanging nodes, numerical integration and imposing Dirichlet boundary conditions. We will discuss the possible future of extensions of this work, including cutting of soft tissue, multiscale problems with complex microstructure, and model order reduction problems. [less ▲] Detailed reference viewed: 154 (8 UL)Meshfree volume-averaged nodal pressure methods for incompressible elasticity Hale, Jack ; ; Scientific Conference (2014, April 03) We present a generalisation of the meshfree method for incompressible elasticity developed in Ortiz et al. (10.1016/j.cma.2010.02.013). We begin with the classical u-p mixed formulation of incompressible ... [more ▼] We present a generalisation of the meshfree method for incompressible elasticity developed in Ortiz et al. (10.1016/j.cma.2010.02.013). We begin with the classical u-p mixed formulation of incompressible elasticity before eliminating the pressure using a volume-averaged nodal projection technique. This results in a family of projection methods of the type Q_p/Q_p-1 where Q_p is an approximation space of polynomial order p. These methods are particularly robust on low-quality tetrahedral meshes. Our framework is generic with respects to the type meshfree basis function used and includes various types of existing finite element methods such as B-bar and nodal-pressure techniques. As a particular example, we use maximum-entropy basis functions to build a scheme Q_1+/Q_1 with the displacement field being enriched with bubble-like functions for stability. The flexibility of the nodal placement in meshfree methods allows us to demonstrate the importance of this bubble-like enrichment for stability; with no bubbles the pressure field is liable to oscillations, whilst with bubbles the oscillation is eliminated. Interestingly however with half the bubbles removed, a scheme we call Q_1*/_Q_1, certain undesirable tendencies of the full bubble scheme are also eliminated. This has important applications in non-linear hyperelasticity. We also discuss some difficulties associated with moving to second-order maximum entropy shape functions associated with numerical integration errors. [less ▲] Detailed reference viewed: 77 (8 UL)An enriched quadtree/octree implicit boundary finite element method for the simulation of incompressible hyperelastic materials Hale, Jack ; Bordas, Stéphane ; et al Scientific Conference (2014, April 03) Octree (and quadtree) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms ... [more ▼] Octree (and quadtree) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms applied to medical scans. In this work we consider the simulation of soft-tissue which can be modelled with a hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties. Similarly to Legrain et al. (10.1002/nme.3070) and Moumnassi et al. (10.1016/j.cma.2010.10.002) we use the implicitly designed level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary. Furthermore we use traditional extended finite element (XFEM) ideas to introduce arbitrary cuts and discontinuities in the domain. We explore the use of a two-field u-p mixed approach as well as a smoothed finite element method (SFEM) to deal with the problem of volumetric-locking in the incompressible limit. We will discuss the extension of our method towards both traditional parallel and GPU implementation. We aim to solve extremely large problems as well as produce snapshots to feed into model order reduction methods for real-time surgical simulations. [less ▲] Detailed reference viewed: 393 (26 UL)Meshless Methods for the Reissner-Mindlin Plate Problem based on Mixed Variational Forms Hale, Jack Presentation (2013, October 31) Meshless numerical methods such as the element free Galerkin (EFG) method and $hp$-clouds method rely on a field of particles to construct a basis for the solution of partial differential equations (PDEs ... [more ▼] Meshless numerical methods such as the element free Galerkin (EFG) method and $hp$-clouds method rely on a field of particles to construct a basis for the solution of partial differential equations (PDEs). This is in contrast with methods such as the finite element method (FEM) and finite difference method (FDM) which rely upon a mesh or grid. Because of this increased flexibility, meshfree methods have shown themselves to be effective tools for simulating difficult problems such as those with discontinuities, complex geometries and large deformations. The Reissner-Mindlin problem is widely used by engineers to describe the deformation of a plate including the effects of transverse shear. A well-known problem which must be overcome when designing an effective numerical method for the Reissner-Mindlin problem is shear-locking. Shear-locking is the inability of the constructed approximation space (meshless or otherwise) to richly represent the limiting Kirchhoff mode. This inability manifests itself as an entirely incorrect solution as the thickness of the plate approaches zero. We will demonstrate and explain the shear-locking problem and potential solutions to it using a simple one-dimensional example. The most effective, robust and general approaches to the shear-locking problem developed in the FEM literature are based on mixed variational forms, where a combination of displacements, stresses and strains are approximated directly. In our approach we start with a mixed variational form before eliminating the extra stress unknowns using the local patch projection technique of A Ortiz et. al. We will discuss the issues presented by the well-known LBB stability conditions and present a solution based upon the stabilising properties of both the augmented Lagrangian and additional `bubble' type functions. We will then show the good performance of the method and its shear-locking free properties. [less ▲] Detailed reference viewed: 67 (7 UL)A Meshless Method for the Reissner-Mindlin Plate Equations based on a Stabilized Mixed Weak Form Hale, Jack ; Scientific Conference (2013, September) Detailed reference viewed: 36 (1 UL)Meshless methods for shear-deformable beams and plates based on mixed weak forms Hale, Jack Postdoctoral thesis (2013) Thin structural theories such as the shear-deformable Timoshenko beam and Reissner-Mindlin plate theories have seen wide use throughout engineering practice to simulate the response of structures with ... [more ▼] Thin structural theories such as the shear-deformable Timoshenko beam and Reissner-Mindlin plate theories have seen wide use throughout engineering practice to simulate the response of structures with planar dimensions far larger than their thickness dimension. Meshless methods have been applied to construct numerical methods to solve the shear deformable theories. Similarly to the finite element method, meshless methods must be carefully designed to over- come the well-known shear-locking problem. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed weak form. In the mixed weak form the shear stresses are treated as an independent variational quantity in addition to the usual displacement variables. We introduce a novel hybrid meshless-finite element formulation for the Timoshenko beam problem that converges to the stable First-order/zero-order finite element method in the local limit when using maximum entropy meshless basis functions. The resulting formulation is free from the effects shear-locking. We then consider the Reissner-Mindlin plate problem. The shear stresses can be identified as a vector field belonging to the Sobelov space with square integrable rotation, suggesting the use of rotated Raviart-Thomas-Nedelec elements of lowest-order for discretising the shear stress field. This novel formulation is again free from the effects of shear-locking. Finally we consider the construction of a generalised displacement method where the shear stresses are eliminated prior to the solution of the final linear system of equations. We implement an existing technique in the literature for the Stokes problem called the nodal volume averaging technique. To ensure stability we split the shear energy between a part calculated using the displacement variables and the mixed variables resulting in a stabilised weak form. The method then satisfies the stability conditions resulting in a formulation that is free from the effects of shear-locking. [less ▲] Detailed reference viewed: 433 (60 UL)Towards Effective Shell Modelling with the FEniCS Project Hale, Jack ; Scientific Conference (2013, March) Fast and efficient simulations of shell structures are required in a wide range of engineering fields such as fluid-structure interaction and structural optimisation. Because of its expressive high-level ... [more ▼] Fast and efficient simulations of shell structures are required in a wide range of engineering fields such as fluid-structure interaction and structural optimisation. Because of its expressive high-level form language UFL the FEniCS project is in an ideal position to tackle tough problems such as large deformations of non-isotropic shells. In this talk we will discuss some aspects of achieving this goal; generalised mixed formulations, reduction and projection operators for eliminating shear and membrane locking, the general shell model vs classical models and the recent work by Rognes et al. on manifolds. [less ▲] Detailed reference viewed: 97 (5 UL)Rapid Testing of Stabilised Finite Element Formulations for the Reissner-Mindlin Plate Problem using the FEniCS Project Hale, Jack ; Scientific Conference (2012, June) Detailed reference viewed: 71 (6 UL)Maximum-Entropy Meshfree Method for the Reissner-Mindlin Plate Problem based on a Stabilised Mixed Weak Form Hale, Jack ; Scientific Conference (2012) Meshless methods, such as the Element Free Galerkin (EFG) method, hold various advantages over mesh-based techniques such as robustness in large-deformation problems and high continuity. The Reissner ... [more ▼] Meshless methods, such as the Element Free Galerkin (EFG) method, hold various advantages over mesh-based techniques such as robustness in large-deformation problems and high continuity. The Reissner-Mindlin plate model is a particularly popular choice for simulating thin structures. It is well known in the Finite Element and Meshless literature that the simplest numerical treatments of the Reissner-Mindlin model lead to shear-locking which in turn produces erroneous results. This is due to the inability of the approximation functions to satisfy the Kirchoff constraint in the thin-plate limit. A recent advance in the area of meshless approximation schemes are Maximum-Entropy (MaxEnt) approximants. MaxEnt schemes provide a weak Kronecker-delta property on convex node sets which allows the direct imposition of Dirichlet (essential) boundary conditions. In this work, we derive a shear-locking free meshless method using MaxEnt approximants by consider- ing a stabilised mixed weak form. We include a scalar parameter which splits the energy from the shear bilinear form into two parts; the first is formed from the displacement fields only and the second from the independently interpolated shear strain field and the displacement fields. This splitting greatly eases the satisfaction of the LBB stability condition. We then eliminate the independently interpolated shear strain field using a localised projection operator, related to the “volume-averaged pressure” technique, which produces a final system of equations in the original displacement unknowns only. We show the good performance of the method for a variety of test problems. [less ▲] Detailed reference viewed: 54 (2 UL)A locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation Hale, Jack ; in Computer Methods in Applied Mechanics & Engineering (2012), 241-244 The problem of shear-locking in the thin-plate limit is a well known issue that must be overcome when discretising the Reissner-Mindlin plate equations. In this paper we present a shear-locking-free ... [more ▼] The problem of shear-locking in the thin-plate limit is a well known issue that must be overcome when discretising the Reissner-Mindlin plate equations. In this paper we present a shear-locking-free method utilising meshfree maximum-entropy basis functions and rotated Raviart-Thomas-Nédélec elements within a mixed variational formulation. The formulation draws upon well known techniques in the finite element literature. Due to the inherent properties of the maximum-entropy basis functions our method allows for the direct imposition of Dirichlet (essential) boundary conditions, in contrast to methods based on moving least squares basis functions. We present benchmark problems that demonstrate the accuracy and performance of the proposed method. © 2012. [less ▲] Detailed reference viewed: 156 (18 UL)Simulation of Shear Deformable Plates using Meshless Maximum Entropy Basis Functions Hale, Jack ; Scientific Conference (2011, June) First-order Shear Deformable Plate Theory (FSDT) is widely used throughout engineering practice to simulate structures with planar dimensions much larger than their thickness. Meshless methods have seen ... [more ▼] First-order Shear Deformable Plate Theory (FSDT) is widely used throughout engineering practice to simulate structures with planar dimensions much larger than their thickness. Meshless methods have seen use in the literature as a method for discretising the FSDT equations and hold numerous advantages over traditional mesh based techniques. A recent advance in the area of meshless methods are Maximum Entropy approximants (MaxEnt). MaxEnt combines many properties of various prior meshless approximants such as a weak Kronecker-delta property, seamless blending with Delaunay triangulations, high continuity, and convexity. In this work MaxEnt along with other meshless approximants have been implemented in a hybrid object-oriented Python/C++/Fortran computer simulation for the simulation of static deflection, free vibration and linear buckling of FSDT plates. The relative performance and ease of implementation of each of the methods will be discussed. The causes of shear locking along with the merits of various alleviation techniques will be covered, including matching fields method, mixed-variational formulations and construction of higher order polynomial basis via both intrinsic and extrinsic (partition of unity) methods. Convergence results show that MaxEnt provides in most cases similar and in some cases superior behaviour to MLS and RPIM approximants when used to discretise the FSDT equations. [less ▲] Detailed reference viewed: 44 (0 UL)The fluid mechanics of membrane filtration Hale, Jack ; ; et al in ASME International Mechanical Engineering Congress and Exposition, Proceedings (2008), 8 PART A Reverse osmosis and nanofiltration membranes remove colloids, macromolecules, salts, bacteria and even some viruses from water. In crossflow filtration, contaminated water is driven parallel to the ... [more ▼] Reverse osmosis and nanofiltration membranes remove colloids, macromolecules, salts, bacteria and even some viruses from water. In crossflow filtration, contaminated water is driven parallel to the membrane, and clean permeate passes through. A large pressure gradient exists across the membrane, with permeate flow rates two to three orders of magnitude smaller than that of the crossflow. Membrane filtration is hindered by two mechanisms, concentration polarization and caking. During filtration, the concentration of rejected particles increases near the membrane surface, forming a concentration polarization layer. Both diffusive and convective transport drive particles back into the bulk flow. However, the increase of the apparent viscosity in the concentration polarization layer hinders diffusion of particles back into the bulk and results in a small reduction in permeate flux. Depending on the number and type of particles present in the contaminated water, the concentration polarization will either reach a quasi-steady state or particles will begin to deposit onto the membrane. In the later case, a cake layer eventually forms on the membrane, significantly reducing the permeate flux. Contradictive theories suggest that the cake layer is either a porous solid or a very viscous (yield stress) fluid. New and refined models that shed light on these theories are presented. Copyright © 2007 by ASME. [less ▲] Detailed reference viewed: 265 (0 UL) |
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