Strain displacement relationships used in 2D plane elastic
problem
Formulation of characteristic equation for 2D plane
stress/strain problemUsually the derivation of element equation for
stress analysis is derived by Energy method Virtual
displacementElement equation by energy method
i.e., Change in internal energy=change in external energyThis
can be written in matrix form
The external work done is created by body force (density),
surface traction (pressure)and by point load
Now , the displacement vector field can be defined in 2D elastic
problem:If triangular element is used the equation (7) can be
expanded as Similarly if rectangular element is used
Formation of characteristic equation for stress analysis
including residual stress and residual strain
Shape function of a 3 node triangular element (CST) constant
strain triangular elementkji
Writing above equations in matrix form
And in turn
Derivation of element equation of a 3 node triangular element
for plane stress/plane strain analysis
