Material Point Method Grid Equations

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Material Point MethodGrid Equations
Mass matrix Lumped mass matrix
Monday, 10/7/2002
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Elastic Bar Dropping
Acceleration due to gravity
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Variational Form
? arbitrary spatial function
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Particle Discretization?
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Grid Equations of Motion
External force
Internal force
Mass matrix
Shape function between node n and particle p
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Shape Functions (1D)
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Elastic Bar Dropping (coordinates)
Particles
Nodes
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Elastic Bar Dropping (particle mass)
Mass density
Cross section area
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Elastic Bar Dropping (mass matrix)
Mass matrix
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Elastic Bar Dropping (grid mass)
Mass matrix
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Grid mass (1,1)
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Grid mass (1,2)
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Grid mass (2,1)
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Grid mass (2,2)
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Grid equations
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Mass matrix
Compact mass matrix Only matrix elements close
to diagonal are not zero.
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Lumped Mass Matrix
Lumped grid mass
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Mass matrix vs. lumped mass matrix