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See detailA Meshless Method for the Reissner-Mindlin Plate Equations based on a Stabilized Mixed Weak Form
Hale, Jack UL; Baiz, P. M.

Scientific Conference (2013, September)

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See detailMeshless methods for shear-deformable beams and plates based on mixed weak forms
Hale, Jack UL

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 ▲]

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See detailTowards Effective Shell Modelling with the FEniCS Project
Hale, Jack UL; Baiz, P. M.

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 ▲]

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See detailA locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation
Hale, Jack UL; Baiz, P. M.

in Computer Methods in Applied Mechanics and 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 ▲]

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See detailMaximum-Entropy Meshfree Method for the Reissner-Mindlin Plate Problem based on a Stabilised Mixed Weak Form
Hale, Jack UL; Baiz, P. M.

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 ▲]

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See detailSimulation of Shear Deformable Plates using Meshless Maximum Entropy Basis Functions
Hale, Jack UL; Baiz, P. M.

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 ▲]

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See detailThe fluid mechanics of membrane filtration
Hale, Jack UL; Harris, A.; Li, Q. 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 ▲]

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See detailMathematical Modelling of Flux Decline due to Concentration Polarisation and Cake Layer Formation in Crossflow Filtration Systems
Hale, Jack UL; Li, Qilin; Harris, Alison et al

Scientific Conference (2007, May)

Crossflow membrane filtration is an effective way of removing both colloidal and dissolved organic matter from contaminated water supplies. Two phenomena domimate solute flux in crossflow systems ... [more ▼]

Crossflow membrane filtration is an effective way of removing both colloidal and dissolved organic matter from contaminated water supplies. Two phenomena domimate solute flux in crossflow systems; concentration polarization and cake layer formation. Many innovative mathematical models for predicting both flux decline and quasi-steady state flux have been produced in the literature. However, limited regime applicability and conflicting physical predictions have made choosing optimal performance parameters in design a challenging process. An overview of the current field of models was undertaken, including an assessment of mathematical assumptions, numerical computation workload and number and complexity of system constants. A new model incorporating viscosity dependence on concentration is developed for the concentration polarization regime. Preliminary results will also be presented from a Monte Carlo based molecular dynamics simulation of volume packing fraction in the cake layer regime. The novel aspects of these models will be compared with existing models and the experimental results of our collaborators. Laboratory ultrafiltration tests were undertaken using varying concentrations of Dextran. An outline of future model directions and refinements will be presented. [less ▲]

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See detailBayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

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See detailSolving the stochastic Burgers equation with a sensitivity derivative-driven Monte Carlo method
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Software (n.d.)

Please see the links below for complete information.

Detailed reference viewed: 177 (14 UL)