Reminders!
Newton's Laws:
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force
is applied to it.
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration
and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the
direction of the force vector is the same as the direction of the acceleration vector.
III. For every action there is an equal and opposite reaction.
Engineering versus True Stress Strain:
Engineering stress assumes that the area a force is acting upon remains constant, true stress takes into account the variation in the cross sectional area as a result of the stress induced deformation (strain) of a material.
Jacobian:
The Jacobian determinant (often simply called the Jacobian) is the determinant of the Jacobian matrix It has a function use in giving insight as to the quality of an FEA element mesh.
| Hooke's Law for Plane Stress: |
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For the simplification of plane stress, where the stresses in the z direction are considered to be negligible,  , the stress-strain compliance relationship for an isotropic material becomes, The three zero'd stress entries in the stress vector indicate that we can ignore their associated columns in the compliance matrix (i.e. columns 3, 4, and 5). If we also ignore the rows associated with the strain components with z-subscripts, the compliance matrix reduces to a simple 3x3 matrix, The stiffness matrix for plane stress is found by inverting the plane stress compliance matrix, and is given by, Note that the stiffness matrix for plane stress is NOT found by removing columns and rows from the general isotropic stiffness matrix. |
Mechanics: 
- or
and in tensor form, 
or inversely, 
Thermodynamics
Electromagnetism
or 