PRESENTATION

ACADEMIC AND PROJECT WORK

BACKGROUND

EDUCATION

• University of Wisconsin − Madison

MS/PhD Mechanical Engineering Dec 2023

• Indian Institute of Technology − Bombay

BTech/MTech Mechanical Engineering - Thermal & Fluid Engineering– 2011

Google scholar: https://scholar.google.com/citations?user=1EtqFh0AAAAJ

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RESEARCH & ACADEMIC PROJECTS

Master’s Project: “Mesh Generation for thermal diffusion using Adaptive gird refinement”

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Spatial Automation Lab

• “Systems modelling of Fabrics”
• CUDA Project: “Fabric simulation using High Performance Computing”
• “Octree simulation using MATLAB/C++”
• “Fabric Simulation models using Model based Design”

Soft Matter Lab

• ” Soft Matter and instability Simulation of Magneto Active Elastomers” − Soft Matter Lab

- 1st Author paper https://www.sciencedirect.com/science/article/pii/S002074032100583X

ADAPTIVE GRID REFINEMENT �FOR UNSTEADY DIFFUSION EQUATION �ON UNSTRUCTURED TRIANGULAR MESH

By Parag Pathak 06D10017

Discretization Methods

Spatial discretization of Equation

Finite Volume Methods

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Discretization Methods

Spatial discretization of Equation

Finite Element Methods

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Problem : Moving Gaussian

Adaptive Grid Refinement

Discretization

Temporal discretization of Equation and domain

Discretization

Discretization of Space Domain

Quadrilateral grids

Discretization

Discretization of Space Domain

Triangular Grids

Delaunay Triangulation

• Every point is outside of the circum-circle of any other triangle.
• Voronoi diagram is the dual to the Delaunay triangulation.

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Delaunay Triangulation

• The boundary points are Delaunay triangulated

Bower-Watson Point insertion

Laplace Smoothing

Mesh Quality Parameters

• Jacobian ratio>0.6
• Aspect Ratio
• Orthogonal Quality
• Skewness
• Parallel Deviation
• Warping Factor/Angle
• Maximum Corner Angle
• Taper

FABRIC MODELLING

• Simulate the draping problem.

STANDARD NURB

GENERALIZED NURB (GNURBS )

AFFINE TRANSFORMATIONS

CAT-MULL ROM SPLINES

Advantage

• It will not form loop or self-intersection within a curve segment.
• Cusp will never occur within a curve segment.
• It follows the control points more tightly.

More commonly used in the litrature

OCTREE & MARCHING CUBES

• To quickly calculate a volumetric property the volume had to be integrated using quadrature points.
• These quadrature points were fixed and belonged to a fixed grid.
• We had to perform a point membership classification query, using an octree.

FOR POINTS NEAR THE SURFACE

• Simulating an Octree surface was done using marching cubes representation.

RESULTS

Lumped parameter Modelling

SIMULINK PROJECT

Free vibrations

• The behaviour of an MAE was studied under free oscillations. The system was allowed to oscillate freely. This was compared to a simscape model system.

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Forced vibrations

• Output signal was isolated from the input signals

Conclusions

1. The MAEs could be tuned to remove noise and isolate the output from the input.
2. The equilibrium point can be adjusted by applying a magnetic field.
3. The only limitations are saturation and the stability limits for MAEs which need to be tuned for the desired output range.

References

• Pathak, P., Arora, N., & Rudykh, S. (2022). Magnetoelastic instabilities in soft laminates with ferromagnetic hyper elastic phases. International Journal of Mechanical Sciences, 213, 106862.
• Bertoldi, K., & Gei, M. (2011). Instabilities in multilayered soft dielectrics. Journal of the Mechanics and Physics of Solids, 59(1), 18-42.
• Rudykh, S., & Debotton, G. (2011). Stability of anisotropic electroactive polymers with application to layered media. Zeitschrift für angewandte Mathematik und Physik, 62(6), 1131-1142.
• Galipeau, E. (2012). Non-linear homogenization of magnetorheological elastomers at finite strain.
• Rudykh, S., & Bertoldi, K. (2013). Stability of anisotropic magnetorheological elastomers in finite deformations: a micromechanical approach. Journal of the Mechanics and Physics of Solids, 61(4), 949-967.
• Rudykh, S., Bhattacharya, K., & DeBotton, G. (2014). Multiscale instabilities in soft heterogeneous dielectric elastomers. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2162), 20130618.
• Goshkoderia, A., & Rudykh, S. (2017). Stability of magneto-active composites with periodic microstructures undergoing finite strains in the presence of a magnetic field. Composites Part B: Engineering, 128, 19-29.

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Analysis of Microscopic Instabilities for Magneto-Active Elastomers (MAEs)

Parag Pathak

What are MAEs?

• MAEs consist of magnetic particles, such as micron-size iron particles, dispersed in an elastomeric matrix. In our case, these are Fibers.
• They can undergo large deformations when excited by a magnetic field.
• Uses include tunable vibration absorbers, damping components , noise barrier system and sensors.

Transformations: Langrangian to Eulerian frame

Eulerian Formulation

Lagrangian Formulation

Stress-Energy Relation

Loading condition

Transition point

Mesh deformation modelling

• Main take way is the modelling of the displacement field and the deformation gradient.

CUDA optimization

FABRIC DRAPING

CS 750 HIGH PERFORMANCE COMPUTING – COURSE PROJECT

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Contents

• Draping Introduction
• Blossom Polynomials
• Problem definition and Inputs
• Parallelized Reduction Algorithm
• CUDA basics
• Results
• References

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Draping

• Draping of virtual characters is done using cloth simulation models.
• The Fabric needs to be rendered and simulated in a time efficient manner.
• CUDA optimization can help lower the time required to achieve this.
• For maximum performance and process control, we choose programming language C++.

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Yuksel, C., Kaldor, J. M., James, D. L., & Marschner, S. (2012). Stitch meshes for modeling knitted clothing with yarn-level detail. ACM Transactions on Graphics (TOG), 31(4), 1-12.

Rendering process

CAD model of the target

Target feature points

Grid of points for fabric

Physical simulation

Fabric geometry

Fully Rendered Fabric on Target

Our scope

• Converting a grid of control points into a fabric geometry

Scope of project

B-Spline surface

Blossoming polynomials

Bi-variate Blossom : Quadratic Bspline

Tri-variate Blossom : Cubic Bspline

B-spline Construction

B-spline Construction

Blossom Construction

Surface blossoms

Grid of Control Points + u,v grid

Inputs

u, v coordinates

CUDA Intro

CUDA virtualizes the physical hardware into threads and blocks

Threads

• Thread is a virtualized Scalar Processor

Blocks

• Thread blocks is a virtualized Streaming multiprocessor.
• Thread blocks need to be independent
• They run to completion.
• Order of blocks is undecided.

B-spline basis Construction

Thread(i,j): Across domain

Block(i_b,j_b) = 16 threads/ Per Block = 1 grid point (u,v)

Parallel Reduction: Sequential Addressing

Warps (Scheduling unit)

Each warp runs threads in a lock step fashion

Data transfer rates

Memory hierarchy

Code walk through

• __Global__ function is called from the host and runs on the device.

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• * variables are for input and output.

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• __Shared variables are shared across the threads within a block.

Thread and Block IDs obtained

• Thread ID i,j select the control points for each reduction operation.
• Block ID ib,jb select the u,v grid co-ordinate.

Barriers an Thread Synchronization

• __syncthreads ensures all threads within a block have reached here.
• Used to prevent memory conflicts and race conditions from occurring.
• Use atomic operations key words like and volatile, to prevent race conditions.

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CUDA memory management.

• Memory Allocation

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• Data transfer from host to device.

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• Data transfer from device to host.

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Nsight : Visual Studio

Profiler

NVVP

NVVP

Results

Sample duration: (without yarn info)

• Cuda time (ms)= 1.227840
• Sequential time (ms) = 4.081682

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• Speed up factor :3.33
• Tolerance<1e-4

CUDA streams for Asynchronous data transfer

References

CUDA

• NVIDIA, GPU Programming Guide, Version 8.0.
• http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html
• CS 759 Slides: High Performance Computing applications for Engineering
• Jason Sanders and Edward Kandrot: CUDA by Example: An Introduction to General-Purpose GPU Programming, Addison-Wesley Professional, 2010
• Lecture1.pdf (bu.edu)

Graphics

• ME 535 slides : CAGD
• Yuksel, C., Kaldor, J. M., James, D. L., & Marschner, S. (2012). Stitch meshes for modeling knitted clothing with yarn-level detail. ACM Transactions on Graphics (TOG), 31(4), 1-12.

Turn Profile Creation �Algorithm

Co-ordinate Transform Method

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Single sheet intersection method

• Intersect a single sheet that passes through the turn axis with the body.
• The body’s imprint on the plane is taken.
• This imprint gives the turn profile of the body.
• This method Works well for pure turn parts.

Multiple sheet Intersection method

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In this method, the body is intersected with multiple sheets in the plane of the axis and body’s imprint on the planes are extracted.

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Multiple sheet Intersection method

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The imprints are dissected and a union operation is performed on the half sheet imprints.

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Current issue with Multiple Plane Method�

Requirements of new approach

Following points need to be considered while developing the new approach.

1. Performance.
2. Mapping between turn profile/face and input body face.
3. Success rate.
4. Accuracy.
5. Simple algorithm ( easy to understand and maintain).

Co-ordinate Transform Method on Cylinder

X

Z

Y

X

R

R

X

Transformation of Points

X

R

X

Z

Y

Transformation of Edge�

X

R

1

2

0

X

Z

Y

Transformation of Face

• Each face is transformed to Cylindrical co-ordinates
• Consider the Boundary edges (BE) and the inflection edges (IE).
• Get R maximum and R minimum edges to get Turn Face.

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u

v

X

R

X

R

X

Z

Y

BE

IE

BE

IE

BE

BE

BE

IE

ISRO work

Static and dynamic analysis

Modal analysis

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Modal analysis

Failure identification

Displacement plots of component

KDTREE ALGORITHM

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KD-TREE ASSIGNMENT

KD-TREE ASSIGNMENT

INPUTS

TRAVERSAL