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Material Point Method (MPM). Variational principle Particle discretization Grid interpolation. Wednesday, 10/2/2002. Lennard-Jones Potential. Handout: Molecular dynamics of simple systems Error, page 7. force. potential. Motion equations. Tensor expression:. Engineering expression:.
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Material Point Method (MPM) Variational principle Particle discretization Grid interpolation Wednesday, 10/2/2002
Lennard-Jones Potential Handout: Molecular dynamics of simple systems Error, page 7 force potential
Motion equations Tensor expression: Engineering expression:
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.
Motion equations (Variational form) : arbitrary spatial function
Elastic Bar Dropping Acceleration due to gravity
Direct solution Solution:
Variational Form : arbitrary spatial function
Variational Equation Considering free ends at a and b
Grid Equation Since is arbitrary:
Grid Equation (F=ma) External force Internal force Mass matrix
Summary Variational principle Particle discretization Grid interpolation Next class: MPM procedure