Theoretical Basis

The STAAD plate finite element is based on hybrid finite element formulations. A complete quadratic stress distribution is assumed. For plane stress action, the assumed stress distribution is as follows.

Assumed stress distribution

Complete quadratic assumed stress distribution:

(\begin{matrix} σ_{x} \\ σ_{y} \\ τ_{x y} \end{matrix}) = [\begin{matrix} 1 & x & y & 0 & 0 & 0 & 0 & x^{2} & 2 x y & 0 \\ 0 & 0 & 0 & 1 & x & y & 0 & y^{2} & 0 & 2 x y \\ 0 & - y & 0 & 0 & 0 & - x & 1 & - 2 x y & - y^{2} & - x^{2} \end{matrix}] (\begin{matrix} a_{1} \\ a_{2} \\ a_{3} \\ ⋮ \\ a_{10} \end{matrix})

Where:

a1 through a10 = constants of stress polynomials.