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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 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 & 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 detailNatural frequencies of cracked functionally graded material plates by the extended finite element method
Natarajan, S.; Baiz, P. M.; Bordas, Stéphane UL et al

in Composite Structures (2011), 93(11), 3082-3092

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on ... [more ▼]

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied. © 2011 Elsevier Ltd. [less ▲]

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See detailLinear buckling analysis of cracked plates by SFEM and XFEM
Baiz, P. M.; Natarajan, S.; Bordas, Stéphane UL et al

in Journal of Mechanics of Material and Structures (2011), 6(9-10), 1213-1238

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point ... [more ▼]

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied. © 2011 by Mathematical Sciences Publishers. [less ▲]

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See detailLinear free flexural vibration of cracked functionally graded plates in thermal environment
Natarajan, S.; Baiz, P. M.; Ganapathi, M. et al

in Computers & Structures (2011), 89(15-16), 1535-1546

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are ... [more ▼]

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are assumed to be temperature dependent and graded in the thickness direction. The effective material properties are estimated using the Mori-Tanaka homogenization scheme. The formulation is developed based on first-order shear deformation theory. The shear correction factors are evaluated employing the energy equivalence principle. The variation of the plates natural frequency is studied considering various parameters such as the crack length, plate aspect ratio, skew angle, temperature, thickness and boundary conditions. The results obtained here reveal that the natural frequency of the plate decreases with increase in temperature gradient, crack length and gradient index. © 2011 Elsevier Ltd. All rights reserved. [less ▲]

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