FEA_MNE772 Finite Element Application for Three-Dimensional Stress - - PowerPoint PPT Presentation

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FEA_MNE772 Finite Element Application for Three-Dimensional Stress - - PowerPoint PPT Presentation

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FEA_MNE772 Finite Element Application for Three-Dimensional Stress Analysis An Approach to Scientific Visualization Techniques of Numerical Results Ivan Assing da Silva Klaus de Geus Sergio Scheer Topics in Scientific Visualization MNE772

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FEA_MNE772

Finite Element Application for Three-Dimensional Stress Analysis

An Approach to Scientific Visualization Techniques of Numerical Results Ivan Assing da Silva Klaus de Geus Sergio Scheer

Topics in Scientific Visualization – MNE772 PPGMNE – UFPR 2017

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  • Overview
  • Workflow
  • Numerical Results
  • ViSC Techniques
  • Scalar Color Mapping
  • Scalar Isosurface
  • Scalar Cutting Plane
  • Vector Glyphs
  • Tensor Ellipsoid Glyphs
  • Tensor Superquadric Glyphs
  • Tensor Hyperstreamlines
  • Example Models and Solver Times
  • Aspects of Implementation
  • Bibliography

Summary

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Overview

model attributes visualization configurations selection of scalar execution log solver 3D views timeline controls ViSC techniques

(1) All images and graphics in this paper were produced by the author.

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INPUT MODELS

Solid3D

  • CDB Ansys Mesh File
  • FSXL XML Native File

Truss3D(1)

  • DXF Drawing Exchange Format
  • FTXL XML Native File

PRE PROCESSING

  • File Loading
  • Model Validation
  • Model Rendering

PROCESSING

  • Stiffness Matrix
  • Loading Vector
  • Boundary conditions setup
  • Solver Linear System

NUMERICAL RESULTS

  • Displacement Vector Field
  • Stress Tensor
  • von Mises Stress
  • Principal Stresses

Workflow

ViSC TECHNIQUES

POST PROCESSING

  • Scalar Color Mapping
  • Scalar Isosurface
  • Scalar Cutting Plane
  • Vector Glyphs
  • Tensor Ellipsoid Glyphs
  • Tensor Superquadric Glyphs
  • Tensor Hyperstreamlines

(1) The application solves Truss 3D models, but the visualization techniques were not implemented for this model type in this time.

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  • Displacement Field (vector)

𝒗 = (𝑣𝑦, 𝑣𝑧, 𝑣𝑨)

  • Stress Tensor (tensor)

𝝉 = σ𝑦𝑦 σ𝑦𝑧 σ𝑦𝑨 σ𝑦𝑧 σ𝑧𝑧 σ𝑧𝑨 σ𝑦𝑨 σ𝑧𝑨 σ𝑨𝑨

  • von Mises Stress (scalar)

𝜏𝑤 = (σ𝑦𝑦 − σ𝑧𝑧)2+(σ𝑧𝑧 − σ𝑨𝑨)2+(σ𝑨𝑨 − σ𝑦𝑦)2+6(σ𝑦𝑧

2 + σ𝑧𝑨 2 + σ𝑦𝑨 2 )

2

  • Absolute Displacement (scalar)

𝑣 = 𝒗

Numerical Results

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  • Principal Stress (tensor)

Eigenanalysis for stress tensor transformation (diagonalization of tensor). Eigenvalues are the values of principal stresses and the eigenvectors are vectors of the normal basis of principal stresses space.

σ𝑦𝑦 σ𝑦𝑧 σ𝑦𝑨 σ𝑦𝑧 σ𝑧𝑧 σ𝑧𝑨 σ𝑦𝑨 σ𝑧𝑨 σ𝑨𝑨 = 𝑉 σ1 σ2 σ3 𝑉𝑈

SCALARS DESCRIPTION

Numerical Results

𝑣𝑦 - displacement on x axis 𝑣𝑧 - displacement on y axis 𝑣𝑧 - displacement on z axis 𝑣 - absolute displacement 𝜏𝑦𝑦 - normal stress on x axis 𝜏𝑧𝑧 - normal stress on y axis 𝜏𝑨𝑨 - normal stress on z axis 𝜏𝑦𝑧 - shear stress on xy plane 𝜏𝑧𝑨 - shear stress on yz plane 𝜏𝑦𝑨 - shear stress on xz plane 𝜏𝑤 - von Mises stress 𝜏1 - major principal stress 𝜏2 - medium principal stress 𝜏3 - minor principal stress

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  • Scalar Color Mapping

Associates a color with the scalar value.

  • Scalar Isosurface

Shows the surfaces where the scalar has equal values. Along the surface the scalar values are constants.

  • Scalar Cutting Plane

Shows the scalars values by color mapping along the defined intersection plane.

  • Vector Glyphs

Associates a object (glyph) at every vector’s point, oriented and scaled according vector information.

  • Tensor Ellipsoid Glyphs

Associates a ellipsoid at every tensor’s point. The ellipsoid axes are oriented according the principal stress eigenvectors and scaled according the corresponding principal stress values.

  • Tensor Superquadric Glyphs

Associates a superquadric form at every tensor’s point. The superquadric glyph is oriented and scaled similarly to ellipsoid glyph, and the superquadric’s shape is define according the principal stresses isotropy.

  • Tensor Hyperstreamlines

Defines a streamline following a principal stress direction and assumes an ellipse cross section form along the streamline. The ellipse cross section is scaled according the corresponding principal stress values.

ViSC Techniques – brief description

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Scalar Color Mapping

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Scalar Isosurface

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Scalar Cutting Plane

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Vector Glyphs

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Tensor Ellipsoid Glyphs

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Tensor Superquadric Glyphs

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Tensor Hyperstreamlines

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Example Models and Solver Time(1)(2)

5 10 15 20 25 30 35 40 45 50 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 Solver Time (s) Number of Nodes Models Number of Nodes Solver Time (s)

(1) Solver time with Iterative Solver on GPU processing. (2) Reference hardware: CPU Intel Corei7 1743 MHz + GPU Nvidia GeForce 460M with 192 Cuda cores.

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Model: cube_crack.fsxl [4126; 19829; 5,641] [Number of Nodes; Number of Elements; Solver Time (s)]

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Model: beam.fsxl [1653; 4788; 4,382]

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Model: gear_v3.fsxl [5177; 18268; 12,525]

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Model: cube_v2.fsxl [6618; 34025; 12,706]

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Model: cube_v3.fsxl [1147; 5281; 0,897]

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Model: cube_v4.fsxl [4812; 24279; 8,664]

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Model: connection_v2.fsxl [1815; 6681; 2,744]

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Model: spherical tank_v2.fsxl [4141; 13002; 7,975]

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Model: plate.fsxl [5667; 26395; 11,604]

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Model: cylinder_v3.fsxl [7080; 35780; 16,109]

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Aspects of Implementation

  • Core programming language: C++
  • Compilers: GCC 6.4 on Linux and Visual Studio 2015 on MS Windows
  • Main Libraries:
  • VTK 8.0.0 [https://www.vtk.org/]
  • Qt 5.9.1 [https://www.qt.io/]
  • Atlas Blas 3.10.3 [http://math-atlas.sourceforge.net/]
  • Lapack 3.7.0 [http://www.netlib.org/lapack/]
  • Magma 2.2.0 [http://icl.cs.utk.edu/magma/]
  • Source code available at https://github.com/IvanAssing/FEA_MNE772
  • Compiled program for MS Windows available at

https://drive.google.com/open?id=1c1ZvDc2-h56PWIPmBy8pd_pomQQrthwt

  • Bug reports, comments or suggestions: please send email to ivanassing@gmail.com
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Bibliography

  • Kindlmann, G., “Superquadric Tensor Glyphs”. IEEE TCVG Symposium on Visualization,

2004.

  • Kratz, A., Meyer, B., Hotz, I., “A Visual Approach to Analysis of Stress Tensor Fields”. Zuse

Institute Berlin, 2010.

  • Lai, M., Rubin, D., Krempl, E., “Introduction to Continuum Mechanics”. 4th. ed. Elsevier Inc.

2010.

  • Laidlaw, D.H., Vilanova, A., et.al. “New Developments in the Visualization and Processing
  • f Tensor Fields”. Springer, 2012.
  • Munzner, T., “Visualization Analysis & Design”. CRC Press, 2014.
  • Schroeder, W., Martin, K. Lorensen, B., “The Visualization Toolkit: an object-oriented

approach to 3D graphics”. 4th. ed. Kitware, Inc, 2006.

  • Schroeder, W., et.al., “The VTK User’s Guide”. 11th. ed. Kitware, Inc. 2010
  • Telea, A., “Data Visualization: Principles and Practice”. 2nd. ed. CRC Press, 2015.
  • Zienkiewicz, O.C., Taylor, R.L., “The Finite Element Method, Volume 1: The Basis”, 5th. ed.,

Butterworth Heinemann, 2000.