MECH3300 Finite element methods. Lecture 10 Issues in modelling Solving the equations. Use of symmetry.
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Lecture 10 Issues in modelling
Solving the equations
Symmetric case Antisymmetric case
Plane of symmetry
Nodes cluster to attempt to match 2 very short side-lengths present in the geometry - these “slivers” need removing.
Some simplification of the real geometry is often needed to get an appropriate mesh.
A solid model subject to a point load will have very high stress at the load. This makes it impossible to see the stress elsewhere on a contour plot, and is unrealistic.
Hence loads must be distributed realistically. This can take some thought - eg loading due to a pin in a hole.
Quadratic by Hertz theory.
Restraints also need realistic distribution. For the pin in a hole case, polar coordinates at the centre of the hole are needed so as to fix radial displacements around the hole, but not tangential ones. Over what angle of arc?
One approach to highly nonlinear problems is to integrate in time using Newton’s law ie
FEXT+ FINT = Ma
FEXT = external forces (applied loads) at some time.
FINT= internal forces (due to elastic or plastic deformation etc.)
M = mass matrix
a = accelerations - solve for these. If M is diagonal, then these are found “explicitly” from the forces.
The new accelerations give new velocities and displacements (central difference method). These are used to find new internal forces, and to again to find new accelerations, and so on. Timestep size must be very small (eg microseconds).
(eg tension in a particular bar)
True load-deflection graph
First load increment