this will help with principles of elasticity in finite element analysis

1. PRINCIPLES OF ELASTICITY
BY
G.MURALI MOHAN

2. Equations of equilibrium

3. Strain displacement relationship

4. Constitutive relationship

5. Plain stress problems
The thin plates subject to forces in their plane only, fall under this category of the
problems. Fig. shows a
typical plane stress problem. In this, there is no force in the z-direction and no
variation of any forces in z-direction

6. Plain strain
A long body subject to significant lateral forces but very little longitudinal forces falls under
this category of problems. Examples of such problems are pipes, long strip footings,
retaining walls, gravity dams, tunnels, etc. (refer Fig. 2.7). In these problems, except for a
small distance at the ends, state of stress is represented byany small longitudinal strip. The
displacement in longitudinal direction (z-direction) is zero in typical strip.

7. Axi-symmetric
Axi-symmetric structures are those which can be generated by rotating a line or curve
about an axis. Cylinders (refer Fig. 2.8) are the common examples of axisymmetric
structures. If such structures are subjected to axisymmetric loadings like uniform internal or
external pressures, uniform self weight or live load uniform over the surface,
there exist symmetry about any axis. The advantage of symmetry may be made use to
simplify the analysis. In these problems cylindrical coordinates can be used advantageously.
Because of symmetry, the stress components
are independent of the angular (θ ) coordinate. Hence all derivatives with respect to θ
vanish i.e. in these
cases.