ACME 2011 Proceedings of the 19 UK National Conference of the ...

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Slicer [3]; 3D Slicer allows the registration and fusion of CT and MRI data enabling the user to more accurately extract soft and hard tissue. The bone surface meshes were smoothed using a volume preserving Laplacian algorithm [4], before a volume mesh was created. Various different volume meshing software was explored and Ansys ICEM CFD was chosen due to its ability to produce high quality meshes of complex geometry. 3 RESULTS Figure 1: Sandwich model (a) material distribution and (b) boundary conditions Two separate numerical approaches are employed to model the hip joint: the finite element approach and the finite volume approach. Commercial software Abaqus is employed using the finite element approach, and open-source software OpenFOAM (Open Field Operation and Manipulation) using the finite volume approach. OpenFOAM is a general 3D based, open source, object-oriented C++ library and was selected due to its ease of customisability. Two different material properties were considered for the model: a homogenous model and a sandwich model. The homogenous model assumed bone be a homogenous isotropic linear-elastic material with a Young’s modulus of 500 MPa and a Poisson’s coefficient of 0.2. The sandwich model assumed bone to be composed of a flexible cancellous core sandwiched inside a stiffer cortical shell, as shown in figure 1(a). The variable cortical bone thickness was segmented directly from CT scans. The thickness of the cortical bone ranged from almost 10 mm in the femur shaft to less than 1 mm in the ilium and the femur head. Cortical bone was given a Young’s modulus of 17 GPa and a Poisson’s coefficient of 0.3 [6]. The effect of including a layer of 1 mm constant thickness cartilage on the articular surfaces was examined. The articular cartilage was assumed to have a Young’s modulus of 25 MPa and a Poisson’s coefficient of 0.45 [5]. The Abaqus homogenous model without cartilage contains 384,843 linear C3D4 solid tetrahedral elements. The cartilage volume comprises 17,036 linear C3D6 wedge elements. The Abaqus sandwich model uses the same mesh as the homogenous model with the appropriate elements assigned cortical bone properties. The OpenFOAM homogenous model contains 10,073 polyhedral cells. Initially the stance phase of gait has been simulated; a force of 1000 N (approximately 1.2 times body weight) was applied to the distal end of the femur corresponding the ground reaction force experienced by the hip during the stance phase of the gait analysis. The distal femur was fixed in the two directions orthogonal to the applied vertical force. The pelvis was fixed at the iliopubic joint and the iliosacral 22
(a) Abaqus model von Mises stress (Pa) Figure 2: Sandwich model stress results joint corresponding to physiological conditions. The model boundary conditions are shown graphically in figure 1(b). The contact was assumed to be frictionless. When the homogenous model including articular cartilage was simulated, both the Abaqus and the OpenFOAM models gave comparable results with a maximum contact pressure of 10 MPa. When the layer of articular cartilage was excluded from the model, the maximum contact pressure rose considerably to 50 MPa. This increase in contact pressure is due to the absence of articular cartilage to distribute the joint force, resulting in a much lower contact area. Examining the initial results obtained from the Abaqus sandwich model, as expected the stiff cortical bone shell supported the majority of the load. The sandwich model with cartilage gave a maximum contact pressure of 14 MPa. Von Mises stress results from the Abaqus sandwich model are shown in Figure 2(a). Figure 2(b) shows the region of maximum contact pressure and maximum contact area. When the layer of articular cartilage was excluded from the sandwich model, the contact pressure increased appreciably to over 100 MPa. This sizable and unrealistic increase in pressure is due to stiff cortical bone surfaces coming into contact producing a smaller contact area. The OpenFOAM sandwich model is currently being developed. When the Abaqus sandwich model was compared with the OpenFOAM and Abaqus homogenous models, it was observed that higher stresses are experienced by the articular cartilage in the sandwich model. The maximum von Mises stress in the homogenous model was 5 MPa, while a maximum von Mises stress of 8 MPa was found in the sandwich model. This increase in cartilage stress is due to the cartilage being constrained considerably more by the cortical bone in the sandwich model than by the less stiff cancellous bone in the homogenous model. 4 CONCLUSIONS A procedure has been developed to create a patient-specific 3D hip joint model from CT and MRI scans. Cortical bone is segmented separately from cancellous bone, preserving the interface between the two types of bone. Articular cartilage was assumed to have a constant thickness, which has been shown to be a valid assumption [7]. Numerical analysis was performed using both finite element based software Abaqus and finite volume based software OpenFOAM. The stance phase of gait has been simulated using a homogenous material model and a sandwich material model. The homogenous models predicted maximum contact pressures of 10 MPa, while the sandwich model predicted maximum contact 23
Page 1: ACME 2011 Proceedings of the 19 th
Page 4 and 5: First published 2011 by Heriot-Watt
Page 7 and 8: CONTENTS Invited Lectures CHALLENGE
Page 9 and 10: A DAMAGE-MECHANICS-BASED RATE-DEPEN
Page 11: A PROJECTED QUASI-NEWTON METHOD FOR
Page 14 and 15: minimise the strain energy density.
Page 16 and 17: through individual rock blocks and
Page 18 and 19: (a) Finite element mesh (b) Gas mes
Page 21 and 22: Proceedings of the 19 th UK Confere
Page 23 and 24: T E −1 ( ) ( ) T ∂s ∂T − du
Page 27 and 28: nondimensional tangential velocity
Page 31 and 32: Figure 2: Results for an open arter
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Page 39 and 40: Vle Vli De Di k1 (MPa) 8.34 2.11 1.
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Page 55 and 56: Figure 1: 2D slope model geometry (
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Proceedings of the 19 th UK Confere
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where ∂fin ∂UM force 2.5 2 1.5
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Practicallly, the perturbation fiel
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3 SIMULATING CONCRETE MESO-STRUCTUR
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¯K i is an approximation of the co
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h = 5.36 matrix 4.3 z P E f νf 0.9
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From the total hoop strainε θ , t
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3 EXTERIOR POINT ESHELBY BASED CRAC
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is applied uniformly on the edge to
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(a) (b) (c) (d) Figure 1: Influence
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On each subdomain, we then have to
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( i�1) ( i�1) �Un�1 � ε
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� ~ � 1 ψ ~ � � ~ (2) �
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For the case of uni-axial tension,
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3 Numerical results Preliminary num
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The coefficients An cannot be deriv
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The spatial semi-discretisation is
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3 CRITICAL TIME STEP INCREASED WITH
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v/vo 2E-05 1.5E-05 1E-05 5E-06 0 -3
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3 RESULTS AND DISCUSSION Fig. 1a sh
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Model updating from eigenvalue and
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1. If R = ω 2 n, there is no eigen
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F = ´ Ω STv CSv dΩ A = ´ Γ U
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Fig. 3 Wall normal pressure in the
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contact contact (ii). f ≈ f ( d,
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In the analysis of the incident P-w
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elow a certain threshold. In both t
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K/d 2 Effective Permeability 0.0032
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METHOD 2 (Mellor and Herring Type)
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(a) Free Surface Profile from Janos
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2 IMMERSED FLUID SOLVER Consider th
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References [1] R. Mittal and G. Iac
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a second impact on the forward fuse
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Acknowledgement L. Papagiannis is f
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acceptable probability throughout t
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algorithm was then responsible for
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strategy of saving the computationa
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(a) (b) Figure 5. Comparison of (a)
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Thermal load step i i i i Update ,
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Displacement (mm) Conclusions 45 40
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load carrying of the structure to b
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compressive stress field between co
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Unbonded flexible pipes and risers
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Figure 2: (a) Riser configuration (
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Furthermore the total strain varies
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Displacement 14 12 10 8 6 4 2 0 Mem
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As this project was in the conceptu
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kg and additional mass to represent
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1 Step make box 2 Step make cylinde
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element method. The solid model is
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just new element classes) without t
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Fig.4. Frame model and the displace
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capacities to meet with such demand
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esponses. Severe cases are to be co
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2 Numerical results In this section
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the frequency intially increases un
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and F (R) = ⎡ ⎢ ⎣ ... UαT (R
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Merit function g 10 1 10 0 10 -1 10
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2 STRUCTURAL CHARACTERISTICS OF PTM
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Fig. 5. Simplified FE model of a PT
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general the computational results o
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References [1] Ainsworth M, Oden JT
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Error Cause Interpolation Error Ele
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(a) Before Improvement (b) After Im
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een applied to FE fluid flow proble
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Acknowledgements Figure 2: Flowchar
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1 1 ′′ 1 ′′′ 3 ′′ 2
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3 COMBINING SHAPE FUNCTIONS The exp
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electron current). For the case of
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electron concentration (1/cm 3 ) x
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2 CONSERVATION LAW FOR A MOVING CV
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5 NUMERICAL RESULTS A 1-D cellular
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FEM can be found in [3]. In this pa
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h Y 1 0 −1 −2 −3 −4 −5
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applications. The partition of unit
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1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 2
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2 NURBS BASIS FUNCTIONS NURBS are a
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4 RESULTS To illustrate the isoBEM
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290
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1 1 2 { σ ( ξ, s) } = [ D] { ε (
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4.4 Example 4 - A single edge crack
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