The least-squares finite element method in elasticity - Part I: Plane stress or strain with drilling degrees of freedom

A new least-squares +nite element method (LSFEM) for plane elasticity problems is developed based on the +rst-order displacement–stress–rotation formulation which includes two new +rst-order compatibility constraints among the stresses and the drilling rotation. This LSFEM can accommodate all kinds of equal-order interpolations. Numerical experiments on various examples including incompressible materials show that the method achieves an optimal rate of convergence for all variables