Predicting Tumour Location by Modelling the Deformation of the Breast using Nonlinear Elasticity
|
|
- Joella Hubbard
- 5 years ago
- Views:
Transcription
1 Predicting Tumour Location by Modelling the Deformation of the Breast using Nonlinear Elasticity November 8th, 2006
2 Outline Motivation Motivation Motivation for Modelling Breast Deformation Mesh Generation Forward, Backward and Contact Problems Results Problems with the Full Model Modelling Skin as a Membrane The Backward Problem for Skin
3 Outline Motivation Motivation Motivation for Modelling Breast Deformation Mesh Generation Forward, Backward and Contact Problems Results Problems with the Full Model Modelling Skin as a Membrane The Backward Problem for Skin
4 Motivation for a Deformable Model of the Breast Problem is to register images and match tumour location The patient is: prone during Magnetic Resonance Imaging (MRI) standing, with the breast compressed during mammography (various possible directions of compression) supine during surgery CC mammogram MLO mammogram MR image
5 Motivation for a Deformable Model of the Breast Given a point in the CC mammogram, what is the equivalent curve in the MLO mammogram? CC mammogram MLO mammogram
6 Motivation for a Deformable Model of the Breast We want to build a patient-specific, anatomically-accurate finite element model of the breast The model can be used to: Predict tumour location during surgery/biopsy Match MRI with mammograms, or CC with MLO Perform temporal matching Plan reconstructive surgery As a teaching/visualisation tool for radiologists
7 Outline Motivation Motivation Motivation for Modelling Breast Deformation Mesh Generation Forward, Backward and Contact Problems Results Problems with the Full Model Modelling Skin as a Membrane The Backward Problem for Skin
8 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
9 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
10 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
11 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
12 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
13 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
14 Mesh Generation Mesh Generation Process MR images: find boundary and segment interior Segment interior into fat, fibroglandular or tumour Fit a cubic-hermite mesh, convert into trilinear mesh Use segmentation data to assign a tissue to each element
15 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
16 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
17 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
18 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
19 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
20 Details for Breast Deformation Modelling Assumptions Assume tissues are isotropic Assume tissues are incompressible Assume hyperelasticity Boundary Conditions Assume the pectoral muscle stays fixed Simulations Normal nonlinear deformations Backward deformations... Constrained deformations...
21 Nonlinear Elasticity
22 Nonlinear Elasticity Basics Given a deformation x x(x): Define the deformation gradient F i M = xi X M Let the true stress (the Cauchy stress) be given by σ ij Cauchy s law Force balance in the deformed body gives σij + ρg i = 0 x j The corresponding weak form is σ ij (δx i) x j + ρg i δx i dv = 0 δx Ω
23 Nonlinear Elasticity Reformulation in terms of X We define the 2nd Piola-Kirchoff stress, T MN as the force acting on the undeformed body per unit undeformed area Cauchy s law can be restated as ) MN xi (T X M X N + ρg i = 0 in Ω 0 The corresponding weak form is MN xi (δx i ) T X Ω0 M X N + ρgi δx i dv 0 = 0 δx T MN and FM i related through the material law
24 The Backward Problem The Forward and Backward Problems Forward problem: given undeformed (unstressed) state, find the deformed state. Backward problem: given deformed, find undeformed. Not been carried out before with breast deformations. For forward problems start from MN xi (δx i ) T X Ω0 M X N + ρgi δx i dv 0 = 0 δx For backward problems start from σ ij (δx i) x j + ρg i δx i dv = 0 δx Ω
25 The Backward Problem Result of a forward simulation on a cube Result of subsequent backward simulation
26 The Backward Problem Speed Initially it took much longer to compute solutions to the backward problem
27 The Backward Problem and GMRES The trivial distinction between σ ij (u(x), p(x)) (δu j) Ω x i dv ± (det(f(u)) 1)δp dv Ω = 0 δu, δp makes a huge impact on GMRES convergence.
28 The Backward Problem and GMRES Consider the Stokes Problem 2 u + p = f ± u = 0 [ ] A B matrix = B T e/values real, some -ve 0 [ ] A B + matrix = B T e/values have +ve real 0 part Latter is much better for GMRES
29 The Backward Problem and GMRES Even though equations are nonlinear, the matrices have structure dominated by the linear part The choice of weak form (for both forward and backward problems) is very important For example, we must choose + in: MN xi (δx i ) T X Ω0 M X N ± (det F 1)δp dv 0 = 0 δx, δp This doesn t seem to be well-known
30 The Contact Problem Simulation of mammography - solve a deformation problem with inequality constraints Formulate equations as an energy minimisation and add a penalty function Used the Augmented Lagrangian Method: 1 ( ) 2 min : total energy + [ λ(x) + Pd(x)]+ ds0 2P skin Here P is a large penalty parameter d measures violation of the constraint λ are parameters which tend to the true Lagrange multipliers
31 Results Motivation CC compression MLO compression
32 Motivation Results simulated CC mammogram, one simulated MLO mammogram, point highlighted (red) corresponding curve in red
33 Results Motivation CC compressed state reference state MLO compressed state
34 Outline Motivation Motivation Motivation for Modelling Breast Deformation Mesh Generation Forward, Backward and Contact Problems Results Problems with the Full Model Modelling Skin as a Membrane The Backward Problem for Skin
35 Problems with the Full Model Badly-shaped skin elements Thin skin elements are badly-shaped - drastically slows Newton convergence Numerical results show little sensitivity to skin stiffness - probably due to lack of residual stress
36 Problems with the Full Model Replace thin 3D skin elements with 2D surface elements - model skin as a membrane Need to compute and include surface integral contribution thin skin membrane skin
37 Modelling Skin as a Membrane Another Reformation... Define new coordinate systems (θ α ) Define tangent vectors (A α ) and metric tensors. Let a αβ and A αβ be the metric tensors on deformed and undeformed surfaces Then strain is E αβ = 1 2 (a αβ A αβ ) Partial deriv.s covariant deriv.s Curvature becomes important
38 Modelling Skin as a Membrane Asymptotic derivation of the membrane equations Perform an asymptotic analysis in the thickness h 0 Analysis allowed us to compute the membrane strain energy, W mem (a αβ ), that is the exact equivalent to the 3D strain W(C MN ) Then considered a fluid-filled membrane model, for which the equation of state was F αβ ;β = 0 - essentially tension = constant F αβ b αβ = P - essentially tension*curvature = pressure
39 Modelling Skin as a Membrane Membrane strain energy worked... Removed the need for thin elements and fixed slow convergence Skin model Time (s) No. Newton iterations thin skin no skin 71 6 membrane thin skin no skin membrane 314 9
40 Modelling Skin as a Membrane However.. Residual stress in the skin was still an issue The fluid-filled membrane model needed residual stress to be solvable This leads to the backward problem for skin: given an unloaded but stressed state, compute the stresses..
41 Backward Problems for Skin (a) membrane with elastic interior, under gravity, in contact, (b) membrane with elastic interior, under gravity, (c) membrane with elastic interior, (d) membrane with fluid interior
42 The Backward Fluid-Filled Membrane Problem Start from: F αβ ;β = 0 F αβ b αβ = P Here: P, the pressure, is known b αβ, deformed curvature, is known F αβ F αβ (a αβ, A αβ ), where a αβ, A αβ are the known and unknown metrics Integrate for F αβ, then solve for A α,β, then integrate for X Even this simplified problem is difficult..
43 The Backward Fluid-Filled Membrane Problem Analysis into this revealed that: An undeformed shape exists (but may not be unique) Don t actually need the undeformed shape, X, just the undeformed metric, A αβ Would have to solve a mixed elliptic-hyperbolic problem One boundary condition is enough (sensible to specify it on the curve of zero Gaussian curvature) Much more research required into: Backward problem on a fluid-filled membrane Backward problem on a membrane with elastic interior
44 Outline Motivation Motivation Motivation for Modelling Breast Deformation Mesh Generation Forward, Backward and Contact Problems Results Problems with the Full Model Modelling Skin as a Membrane The Backward Problem for Skin
45 Conclusions Have shown modelling breast deformation with nonlinear elasticity is computationally tractable Discussed the three types of simulation necessary Used a patient-specific model to simulate surgical and mammographic breast shape Motivated and introduced a membrane skin model Described issues involved with membrane skin
46 Further Work Need proper validation of results, especially with patient studies Further analysis of required complexity of the model Modelling the effect of Cooper s Ligaments Analysis of the backward problem for skin
Predicting Tumour Location by Simulating Large Deformations of the Breast using a 3D Finite Element Model and Nonlinear Elasticity
Predicting Tumour Location by Simulating Large Deformations of the Breast using a 3D Finite Element Model and Nonlinear Elasticity P. Pathmanathan 1 D. Gavaghan 1 J. Whiteley 1 M. Brady 2 M. Nash 3 P.
More informationPRIMAL-DUAL INTERIOR POINT METHOD FOR LINEAR PROGRAMMING. 1. Introduction
PRIMAL-DUAL INTERIOR POINT METHOD FOR LINEAR PROGRAMMING KELLER VANDEBOGERT AND CHARLES LANNING 1. Introduction Interior point methods are, put simply, a technique of optimization where, given a problem
More informationGuidelines for proper use of Plate elements
Guidelines for proper use of Plate elements In structural analysis using finite element method, the analysis model is created by dividing the entire structure into finite elements. This procedure is known
More information2.7 Cloth Animation. Jacobs University Visualization and Computer Graphics Lab : Advanced Graphics - Chapter 2 123
2.7 Cloth Animation 320491: Advanced Graphics - Chapter 2 123 Example: Cloth draping Image Michael Kass 320491: Advanced Graphics - Chapter 2 124 Cloth using mass-spring model Network of masses and springs
More informationINTERIOR POINT METHOD BASED CONTACT ALGORITHM FOR STRUCTURAL ANALYSIS OF ELECTRONIC DEVICE MODELS
11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver
More informationProgramming, numerics and optimization
Programming, numerics and optimization Lecture C-4: Constrained optimization Łukasz Jankowski ljank@ippt.pan.pl Institute of Fundamental Technological Research Room 4.32, Phone +22.8261281 ext. 428 June
More informationLECTURE 13: SOLUTION METHODS FOR CONSTRAINED OPTIMIZATION. 1. Primal approach 2. Penalty and barrier methods 3. Dual approach 4. Primal-dual approach
LECTURE 13: SOLUTION METHODS FOR CONSTRAINED OPTIMIZATION 1. Primal approach 2. Penalty and barrier methods 3. Dual approach 4. Primal-dual approach Basic approaches I. Primal Approach - Feasible Direction
More informationA fast breast nonlinear elastography reconstruction technique using the Veronda-Westman model
A fast breast nonlinear elastography reconstruction technique using the Veronda-Westman model Mohammadhosein Amooshahi a and Abbas Samani abc a Department of Electrical & Computer Engineering, University
More informationRevised Sheet Metal Simulation, J.E. Akin, Rice University
Revised Sheet Metal Simulation, J.E. Akin, Rice University A SolidWorks simulation tutorial is just intended to illustrate where to find various icons that you would need in a real engineering analysis.
More informationExample 24 Spring-back
Example 24 Spring-back Summary The spring-back simulation of sheet metal bent into a hat-shape is studied. The problem is one of the famous tests from the Numisheet 93. As spring-back is generally a quasi-static
More informationFinite Element Simulation of Moving Targets in Radio Therapy
Finite Element Simulation of Moving Targets in Radio Therapy Pan Li, Gregor Remmert, Jürgen Biederer, Rolf Bendl Medical Physics, German Cancer Research Center, 69120 Heidelberg Email: pan.li@dkfz.de Abstract.
More informationThe 3D DSC in Fluid Simulation
The 3D DSC in Fluid Simulation Marek K. Misztal Informatics and Mathematical Modelling, Technical University of Denmark mkm@imm.dtu.dk DSC 2011 Workshop Kgs. Lyngby, 26th August 2011 Governing Equations
More informationSimulation Studies for Predicting Surgical Outcomes in Breast Reconstructive Surgery
Simulation Studies for Predicting Surgical Outcomes in Breast Reconstructive Surgery Celeste Williams 1, Ioannis A. Kakadaris 1, K. Ravi-Chandar 2, Michael J. Miller 3, and Charles W. Patrick 3 1 Visual
More informationMeshless Modeling, Animating, and Simulating Point-Based Geometry
Meshless Modeling, Animating, and Simulating Point-Based Geometry Xiaohu Guo SUNY @ Stony Brook Email: xguo@cs.sunysb.edu http://www.cs.sunysb.edu/~xguo Graphics Primitives - Points The emergence of points
More informationRevision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering. Introduction
Revision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering Introduction A SolidWorks simulation tutorial is just intended to illustrate where to
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems. Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture December, 2013
The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture 11-17 December, 2013 Institute of Structural Engineering Method of Finite Elements
More informationA MODELING METHOD OF CURING DEFORMATION FOR CFRP COMPOSITE STIFFENED PANEL WANG Yang 1, GAO Jubin 1 BO Ma 1 LIU Chuanjun 1
21 st International Conference on Composite Materials Xi an, 20-25 th August 2017 A MODELING METHOD OF CURING DEFORMATION FOR CFRP COMPOSITE STIFFENED PANEL WANG Yang 1, GAO Jubin 1 BO Ma 1 LIU Chuanjun
More informationContents. I The Basic Framework for Stationary Problems 1
page v Preface xiii I The Basic Framework for Stationary Problems 1 1 Some model PDEs 3 1.1 Laplace s equation; elliptic BVPs... 3 1.1.1 Physical experiments modeled by Laplace s equation... 5 1.2 Other
More informationParameterization. Michael S. Floater. November 10, 2011
Parameterization Michael S. Floater November 10, 2011 Triangular meshes are often used to represent surfaces, at least initially, one reason being that meshes are relatively easy to generate from point
More informationA step-by-step review on patient-specific biomechanical finite element models for breast MRI to x-ray mammography registration
A step-by-step review on patient-specific biomechanical finite element models for breast MRI to x-ray mammography registration Eloy Garcıa a) Institute of Computer Vision and Robotics, University of Girona
More informationParameterization II Some slides from the Mesh Parameterization Course from Siggraph Asia
Parameterization II Some slides from the Mesh Parameterization Course from Siggraph Asia 2008 1 Non-Convex Non Convex Boundary Convex boundary creates significant distortion Free boundary is better 2 Fixed
More informationDEFORMATION MODELING OF BREAST BASED ON MRI AND FEM.
Sandomierz, 5 th 9 th September 2016 DEFORMATION MODELING OF BREAST BASED ON MRI AND FEM. Marta Danch-Wierzchowska 1,, Damian Borys 1, Andrzej Swierniak 1 1 Institute of Automatic Control, Silesian University
More informationTOPOLOGY OPTIMIZATION OF ELASTOMER DAMPING DEVICES FOR STRUCTURAL VIBRATION REDUCTION
6th European Conference on Computational Mechanics (ECCM 6) 7th European Conference on Computational Fluid Dynamics (ECFD 7) 1115 June 2018, Glasgow, UK TOPOLOGY OPTIMIZATION OF ELASTOMER DAMPING DEVICES
More informationPATCH TEST OF HEXAHEDRAL ELEMENT
Annual Report of ADVENTURE Project ADV-99- (999) PATCH TEST OF HEXAHEDRAL ELEMENT Yoshikazu ISHIHARA * and Hirohisa NOGUCHI * * Mitsubishi Research Institute, Inc. e-mail: y-ishi@mri.co.jp * Department
More informationGEOMETRICAL CONSTRAINTS IN THE LEVEL SET METHOD FOR SHAPE AND TOPOLOGY OPTIMIZATION
1 GEOMETRICAL CONSTRAINTS IN THE LEVEL SET METHOD FOR SHAPE AND TOPOLOGY OPTIMIZATION Grégoire ALLAIRE CMAP, Ecole Polytechnique Results obtained in collaboration with F. Jouve (LJLL, Paris 7), G. Michailidis
More informationElement Order: Element order refers to the interpolation of an element s nodal results to the interior of the element. This determines how results can
TIPS www.ansys.belcan.com 鲁班人 (http://www.lubanren.com/weblog/) Picking an Element Type For Structural Analysis: by Paul Dufour Picking an element type from the large library of elements in ANSYS can be
More informationAMS527: Numerical Analysis II
AMS527: Numerical Analysis II A Brief Overview of Finite Element Methods Xiangmin Jiao SUNY Stony Brook Xiangmin Jiao SUNY Stony Brook AMS527: Numerical Analysis II 1 / 25 Overview Basic concepts Mathematical
More informationDynamic Points: When Geometry Meets Physics. Xiaohu Guo Stony Brook
Dynamic Points: When Geometry Meets Physics Xiaohu Guo SUNY @ Stony Brook Email: xguo@cs.sunysb.edu http://www.cs.sunysb.edu/~xguo Point Based Graphics Pipeline Acquisition Modeling Rendering laser scanning
More informationUnstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications
Unstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications Per-Olof Persson (persson@mit.edu) Department of Mathematics Massachusetts Institute of Technology http://www.mit.edu/
More informationADJOINT OPTIMIZATION OF 2D-AIRFOILS IN INCOMPRESSIBLE FLOWS
11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver
More informationNon-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, Politecnico di Milano, February 3, 2017, Lesson 1
Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, attilio.frangi@polimi.it Politecnico di Milano, February 3, 2017, Lesson 1 1 Politecnico di Milano, February 3, 2017, Lesson 1 2 Outline
More informationA Numerical Form Finding Method for Minimal Surface of Membrane Structure
10 th World Congress on Structural and Multidisciplinary Optimization May 19-24, 2013, Orlando, Florida, US Numerical Form Finding Method for Minimal Surface of Membrane Structure Koichi Yamane 1, Masatoshi
More informationModule 1 Lecture Notes 2. Optimization Problem and Model Formulation
Optimization Methods: Introduction and Basic concepts 1 Module 1 Lecture Notes 2 Optimization Problem and Model Formulation Introduction In the previous lecture we studied the evolution of optimization
More informationThe Immersed Interface Method
The Immersed Interface Method Numerical Solutions of PDEs Involving Interfaces and Irregular Domains Zhiiin Li Kazufumi Ito North Carolina State University Raleigh, North Carolina Society for Industrial
More informationSolid and shell elements
Solid and shell elements Theodore Sussman, Ph.D. ADINA R&D, Inc, 2016 1 Overview 2D and 3D solid elements Types of elements Effects of element distortions Incompatible modes elements u/p elements for incompressible
More informationGeometrical Modeling of the Heart
Geometrical Modeling of the Heart Olivier Rousseau University of Ottawa The Project Goal: Creation of a precise geometrical model of the heart Applications: Numerical calculations Dynamic of the blood
More informationMaterial Properties Estimation of Layered Soft Tissue Based on MR Observation and Iterative FE Simulation
Material Properties Estimation of Layered Soft Tissue Based on MR Observation and Iterative FE Simulation Mitsunori Tada 1,2, Noritaka Nagai 3, and Takashi Maeno 3 1 Digital Human Research Center, National
More informationNonrigid Registration using Free-Form Deformations
Nonrigid Registration using Free-Form Deformations Hongchang Peng April 20th Paper Presented: Rueckert et al., TMI 1999: Nonrigid registration using freeform deformations: Application to breast MR images
More informationTheoretical Background for OpenLSTO v0.1: Open Source Level Set Topology Optimization. M2DO Lab 1,2. 1 Cardiff University
Theoretical Background for OpenLSTO v0.1: Open Source Level Set Topology Optimization M2DO Lab 1,2 1 Cardiff University 2 University of California, San Diego November 2017 A brief description of theory
More informationThree dimensional finite element model for lesion correspondence in breast imaging
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 2003 Three dimensional finite element model for lesion correspondence in breast imaging Yan, Qiu University
More informationApplication of Finite Volume Method for Structural Analysis
Application of Finite Volume Method for Structural Analysis Saeed-Reza Sabbagh-Yazdi and Milad Bayatlou Associate Professor, Civil Engineering Department of KNToosi University of Technology, PostGraduate
More informationChallenges in Design Optimization of Textile Reinforced Composites
Challenges in Design Optimization of Textile Reinforced Composites Colby C. Swan, Assoc. Professor HyungJoo Kim, Research Asst. Young Kyo Seo, Research Assoc. Center for Computer Aided Design The University
More informationEngineering Effects of Boundary Conditions (Fixtures and Temperatures) J.E. Akin, Rice University, Mechanical Engineering
Engineering Effects of Boundary Conditions (Fixtures and Temperatures) J.E. Akin, Rice University, Mechanical Engineering Here SolidWorks stress simulation tutorials will be re-visited to show how they
More informationRealistic Animation of Fluids
Realistic Animation of Fluids p. 1/2 Realistic Animation of Fluids Nick Foster and Dimitri Metaxas Realistic Animation of Fluids p. 2/2 Overview Problem Statement Previous Work Navier-Stokes Equations
More informationIntroduction to geodynamic modelling Introduction to DOUAR
Introduction to geodynamic modelling Introduction to DOUAR David Whipp and Lars Kaislaniemi Department of Geosciences and Geography, Univ. Helsinki 1 Goals of this lecture Introduce DOUAR, a 3D thermomechanical
More informationContents. I Basics 1. Copyright by SIAM. Unauthorized reproduction of this article is prohibited.
page v Preface xiii I Basics 1 1 Optimization Models 3 1.1 Introduction... 3 1.2 Optimization: An Informal Introduction... 4 1.3 Linear Equations... 7 1.4 Linear Optimization... 10 Exercises... 12 1.5
More informationImaging of flow in porous media - from optimal transport to prediction
Imaging of flow in porous media - from optimal transport to prediction Eldad Haber Dept of EOS and Mathematics, UBC October 15, 2013 With Rowan Lars Jenn Cocket Ruthotto Fohring Outline Prediction is very
More informationLevel-set and ALE Based Topology Optimization Using Nonlinear Programming
10 th World Congress on Structural and Multidisciplinary Optimization May 19-24, 2013, Orlando, Florida, USA Level-set and ALE Based Topology Optimization Using Nonlinear Programming Shintaro Yamasaki
More informationCHAPTER 3. Elementary Fluid Dynamics
CHAPTER 3. Elementary Fluid Dynamics - Understanding the physics of fluid in motion - Derivation of the Bernoulli equation from Newton s second law Basic Assumptions of fluid stream, unless a specific
More informationSurgery Simulation and Planning
Surgery Simulation and Planning S. H. Martin Roth Dr. Rolf M. Koch Daniel Bielser Prof. Dr. Markus Gross Facial surgery project in collaboration with Prof. Dr. Dr. H. Sailer, University Hospital Zurich,
More informationLocking-Free Smoothed Finite Element Method with Tetrahedral/Triangular Mesh Rezoning in Severely Large Deformation Problems
Locking-Free Smoothed Finite Element Method with Tetrahedral/Triangular Mesh Rezoning in Severely Large Deformation Problems Yuki ONISHI, Kenji AMAYA Tokyo Institute of Technology (Japan) P. 1 P. 1 Motivation
More informationEUROPEAN COMSOL CONFERENCE 2010
Presented at the COMSOL Conference 2010 Paris EUROPEAN COMSOL CONFERENCE 2010 Paris November 17-19, 2010 FROM CT SCAN TO PLANTAR PRESSURE MAP DISTRIBUTION OF A 3D ANATOMIC HUMAN FOOT Pasquale Franciosa
More informationAXIAL OF OF THE. M. W. Hyer. To mitigate the. Virginia. SUMMARY. the buckling. circumference, Because of their. could.
IMPROVEMENT OF THE AXIAL BUCKLING CAPACITY OF COMPOSITE ELLIPTICAL CYLINDRICAL SHELLS M. W. Hyer Department of Engineering Science and Mechanics (0219) Virginia Polytechnic Institute and State University
More informationPolygonal Finite Elements for Finite Elasticity
Polygonal Finite Elements for Finite Elasticity Heng Chi a, Cameron Talischi b, Oscar Lopez-Pamies b, Glaucio H. Paulino a a: Georgia Institute of Technology b: University of Illinois at Urbana-Champaign
More informationSimulation of metal forming processes :
Simulation of metal forming processes : umerical aspects of contact and friction People Contact algorithms LTAS-MCT in a few words Laboratoire des Techniques Aéronautiques et Spatiales (Aerospace Laboratory)
More informationChapter 5: Introduction to Differential Analysis of Fluid Motion
Chapter 5: Introduction to Differential 5-1 Conservation of Mass 5-2 Stream Function for Two-Dimensional 5-3 Incompressible Flow 5-4 Motion of a Fluid Particle (Kinematics) 5-5 Momentum Equation 5-6 Computational
More informationStudy of Convergence of Results in Finite Element Analysis of a Plane Stress Bracket
RESEARCH ARTICLE OPEN ACCESS Study of Convergence of Results in Finite Element Analysis of a Plane Stress Bracket Gowtham K L*, Shivashankar R. Srivatsa** *(Department of Mechanical Engineering, B. M.
More information1. Carlos A. Felippa, Introduction to Finite Element Methods,
Chapter Finite Element Methods In this chapter we will consider how one can model the deformation of solid objects under the influence of external (and possibly internal) forces. As we shall see, the coupled
More informationOutline. Level Set Methods. For Inverse Obstacle Problems 4. Introduction. Introduction. Martin Burger
For Inverse Obstacle Problems Martin Burger Outline Introduction Optimal Geometries Inverse Obstacle Problems & Shape Optimization Sensitivity Analysis based on Gradient Flows Numerical Methods University
More informationParallelizing a Real-Time 3D Finite Element Algorithm using CUDA: Limitations, Challenges and Opportunities.
Parallelizing a Real-Time 3D Finite Element Algorithm using CUDA: Limitations, Challenges and Opportunities. Vukasin Strbac Biomechanics section KU Leuven 2/21 The Finite Element Method and the GPU Basically
More informationIsogeometric Analysis of Fluid-Structure Interaction
Isogeometric Analysis of Fluid-Structure Interaction Y. Bazilevs, V.M. Calo, T.J.R. Hughes Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA e-mail: {bazily,victor,hughes}@ices.utexas.edu
More informationNote Set 4: Finite Mixture Models and the EM Algorithm
Note Set 4: Finite Mixture Models and the EM Algorithm Padhraic Smyth, Department of Computer Science University of California, Irvine Finite Mixture Models A finite mixture model with K components, for
More informationCurved Mesh Generation and Mesh Refinement using Lagrangian Solid Mechanics
Curved Mesh Generation and Mesh Refinement using Lagrangian Solid Mechanics Per-Olof Persson University of California, Berkeley, Berkeley, CA 9472-384, U.S.A. Jaime Peraire Massachusetts Institute of Technology,
More informationEXACT BUCKLING SOLUTION OF COMPOSITE WEB/FLANGE ASSEMBLY
EXACT BUCKLING SOLUTION OF COMPOSITE WEB/FLANGE ASSEMBLY J. Sauvé 1*, M. Dubé 1, F. Dervault 2, G. Corriveau 2 1 Ecole de technologie superieure, Montreal, Canada 2 Airframe stress, Advanced Structures,
More informationTowards Meshless Methods for Surgical Simulation
Ashley Horton, Adam Wittek, Karol Miller Intelligent Systems for Medicine Laboratory School of Mechanical Engineering, The University of Western Australia 35 Stirling Highway, Crawley, Perth WA 6009 Australia
More informationsmooth coefficients H. Köstler, U. Rüde
A robust multigrid solver for the optical flow problem with non- smooth coefficients H. Köstler, U. Rüde Overview Optical Flow Problem Data term and various regularizers A Robust Multigrid Solver Galerkin
More informationIsotropic Porous Media Tutorial
STAR-CCM+ User Guide 3927 Isotropic Porous Media Tutorial This tutorial models flow through the catalyst geometry described in the introductory section. In the porous region, the theoretical pressure drop
More informationParameterization of triangular meshes
Parameterization of triangular meshes Michael S. Floater November 10, 2009 Triangular meshes are often used to represent surfaces, at least initially, one reason being that meshes are relatively easy to
More informationMetafor FE Software. 2. Operator split. 4. Rezoning methods 5. Contact with friction
ALE simulations ua sus using Metafor eao 1. Introduction 2. Operator split 3. Convection schemes 4. Rezoning methods 5. Contact with friction 1 Introduction EULERIAN FORMALISM Undistorted mesh Ideal for
More informationTopology Optimization and JuMP
Immense Potential and Challenges School of Engineering and Information Technology UNSW Canberra June 28, 2018 Introduction About Me First year PhD student at UNSW Canberra Multidisciplinary design optimization
More informationViscoelastic Registration of Medical Images
Viscoelastic Registration of Medical Images Zhao Yi Justin Wan Abstract Since the physical behavior of many tissues is shown to be viscoelastic, we propose a novel registration technique for medical images
More informationShape Modeling and Geometry Processing
252-0538-00L, Spring 2018 Shape Modeling and Geometry Processing Discrete Differential Geometry Differential Geometry Motivation Formalize geometric properties of shapes Roi Poranne # 2 Differential Geometry
More informationModule 1: Introduction to Finite Element Analysis. Lecture 4: Steps in Finite Element Analysis
25 Module 1: Introduction to Finite Element Analysis Lecture 4: Steps in Finite Element Analysis 1.4.1 Loading Conditions There are multiple loading conditions which may be applied to a system. The load
More informationDynamic Computational Modeling of the Glass Container Forming Process
Dynamic Computational Modeling of the Glass Container Forming Process Matthew Hyre 1, Ryan Taylor, and Morgan Harris Virginia Military Institute, Lexington, Virginia, USA Abstract Recent advances in numerical
More informationIntroduction to Computer Graphics. Animation (2) May 26, 2016 Kenshi Takayama
Introduction to Computer Graphics Animation (2) May 26, 2016 Kenshi Takayama Physically-based deformations 2 Simple example: single mass & spring in 1D Mass m, position x, spring coefficient k, rest length
More informationParticle-based Fluid Simulation
Simulation in Computer Graphics Particle-based Fluid Simulation Matthias Teschner Computer Science Department University of Freiburg Application (with Pixar) 10 million fluid + 4 million rigid particles,
More informationEmbedded Reinforcements
Embedded Reinforcements Gerd-Jan Schreppers, January 2015 Abstract: This paper explains the concept and application of embedded reinforcements in DIANA. Basic assumptions and definitions, the pre-processing
More informationIntroduction to Optimization
Introduction to Optimization Constrained Optimization Marc Toussaint U Stuttgart Constrained Optimization General constrained optimization problem: Let R n, f : R n R, g : R n R m, h : R n R l find min
More informationarxiv: v2 [math.oc] 12 Feb 2019
A CENTRAL PATH FOLLOWING METHOD USING THE NORMALIZED GRADIENTS Long Chen 1, Wenyi Chen 2, and Kai-Uwe Bletzinger 1 arxiv:1902.04040v2 [math.oc] 12 Feb 2019 1 Chair of Structural Analysis, Technical University
More informationMathematics for chemical engineers
Mathematics for chemical engineers Drahoslava Janovská Department of mathematics Winter semester 2013-2014 Numerical solution of ordinary differential equations Initial value problem Outline 1 Introduction
More informationA primal-dual framework for mixtures of regularizers
A primal-dual framework for mixtures of regularizers Baran Gözcü baran.goezcue@epfl.ch Laboratory for Information and Inference Systems (LIONS) École Polytechnique Fédérale de Lausanne (EPFL) Switzerland
More informationCollocation and optimization initialization
Boundary Elements and Other Mesh Reduction Methods XXXVII 55 Collocation and optimization initialization E. J. Kansa 1 & L. Ling 2 1 Convergent Solutions, USA 2 Hong Kong Baptist University, Hong Kong
More informationApproximation Methods in Optimization
Approximation Methods in Optimization The basic idea is that if you have a function that is noisy and possibly expensive to evaluate, then that function can be sampled at a few points and a fit of it created.
More informationThe numerical simulation of complex PDE problems. A numerical simulation project The finite element method for solving a boundary-value problem in R 2
Universidad de Chile The numerical simulation of complex PDE problems Facultad de Ciencias Físicas y Matemáticas P. Frey, M. De Buhan Year 2008 MA691 & CC60X A numerical simulation project The finite element
More informationIntroduction to Optimization Problems and Methods
Introduction to Optimization Problems and Methods wjch@umich.edu December 10, 2009 Outline 1 Linear Optimization Problem Simplex Method 2 3 Cutting Plane Method 4 Discrete Dynamic Programming Problem Simplex
More informationNon-linear Finite Element Analysis of CRTS Reflectors
Non-linear Finite Element Analysis of CRTS Reflectors C.Y. Lai and S. Pellegrino CUED/D-STRUCT/TR9 European Space Agency Contractor Report The work presented in this report was carried out under an ESA
More informationA High-Order Accurate Unstructured GMRES Solver for Poisson s Equation
A High-Order Accurate Unstructured GMRES Solver for Poisson s Equation Amir Nejat * and Carl Ollivier-Gooch Department of Mechanical Engineering, The University of British Columbia, BC V6T 1Z4, Canada
More informationIntroduction to Optimization
Introduction to Optimization Second Order Optimization Methods Marc Toussaint U Stuttgart Planned Outline Gradient-based optimization (1st order methods) plain grad., steepest descent, conjugate grad.,
More informationSTATISTICAL ATLAS-BASED SUB-VOXEL SEGMENTATION OF 3D BRAIN MRI
STATISTICA ATAS-BASED SUB-VOXE SEGMENTATION OF 3D BRAIN MRI Marcel Bosc 1,2, Fabrice Heitz 1, Jean-Paul Armspach 2 (1) SIIT UMR-7005 CNRS / Strasbourg I University, 67400 Illkirch, France (2) IPB UMR-7004
More informationME Optimization of a Frame
ME 475 - Optimization of a Frame Analysis Problem Statement: The following problem will be analyzed using Abaqus. 4 7 7 5,000 N 5,000 N 0,000 N 6 6 4 3 5 5 4 4 3 3 Figure. Full frame geometry and loading
More informationSome Aspects for the Simulation of a Non-Linear Problem with Plasticity and Contact
Some Aspects for the Simulation of a Non-Linear Problem with Plasticity and Contact Eduardo Luís Gaertner Marcos Giovani Dropa de Bortoli EMBRACO S.A. Abstract A linear elastic model is often not appropriate
More informationAn optimization method for generating self-equilibrium shape of curved surface from developable surface
25-28th September, 2017, Hamburg, Germany Annette Bögle, Manfred Grohmann (eds.) An optimization method for generating self-equilibrium shape of curved surface from developable surface Jinglan CI *, Maoto
More informationDevelopment of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics
Development of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics I. Pantle Fachgebiet Strömungsmaschinen Karlsruher Institut für Technologie KIT Motivation
More informationComputational Methods. Constrained Optimization
Computational Methods Constrained Optimization Manfred Huber 2010 1 Constrained Optimization Unconstrained Optimization finds a minimum of a function under the assumption that the parameters can take on
More informationComputational Fluid Dynamics - Incompressible Flows
Computational Fluid Dynamics - Incompressible Flows March 25, 2008 Incompressible Flows Basis Functions Discrete Equations CFD - Incompressible Flows CFD is a Huge field Numerical Techniques for solving
More informationChapter 3 Numerical Methods
Chapter 3 Numerical Methods Part 1 3.1 Linearization and Optimization of Functions of Vectors 1 Problem Notation 2 Outline 3.1.1 Linearization 3.1.2 Optimization of Objective Functions 3.1.3 Constrained
More informationIsogeometric Analysis Application to Car Crash Simulation
Isogeometric Analysis Application to Car Crash Simulation S. Bouabdallah 2, C. Adam 2,3, M. Zarroug 2, H. Maitournam 3 De Vinci Engineering Lab, École Supérieure d Ingénieurs Léonard de Vinci 2 Direction
More informationGeneralized framework for solving 2D FE problems
ENGN 2340 Computational Methods in Structural Mechanics Generalized framework for solving 2D FE problems Karthik Thalappully Overview The goal of the project was development of a FEA framework in C++ to
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 36
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 36 In last class, we have derived element equations for two d elasticity problems
More informationMesh Processing Pipeline
Mesh Smoothing 1 Mesh Processing Pipeline... Scan Reconstruct Clean Remesh 2 Mesh Quality Visual inspection of sensitive attributes Specular shading Flat Shading Gouraud Shading Phong Shading 3 Mesh Quality
More information