Material%20Point%20Method%20(MPM)

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Material Point Method (MPM)
Variational principle Particle discretization Grid
interpolation
Wednesday, 10/2/2002
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Lennard-Jones Potential
Handout Molecular dynamics of simple
systems Error, page 7
force
potential
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Motion equations
Tensor expression
Engineering expression
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Discretization in Material Point Method (MPM)
Solid line is an outline of the body
analyzed. Black dots are the material
points. Dashed lines show a regular, background
grid for calculation.
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Motion equations (Variational form)
? arbitrary spatial function
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Elastic Bar Dropping
Acceleration due to gravity
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Particle Discretization?How to solve?
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Direct solution
Solution
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Variational Form
? arbitrary spatial function
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Particle Discretization?
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Variational Equation
Considering free ends at a and b
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Particle Discretization
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Spatial grid
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Shape function
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Grid Interpolation
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Grid Equation
Since is arbitrary
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Grid Equation (Fma)
External force
Internal force
Mass matrix
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Derivative of Shape Function
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Summary
Variational principle Particle discretization Grid
interpolation
Next class MPM procedure