The torsion of a hollow square
SEAC % is used to give an approximate solution to the torsion problem for a hollow square, with accurate determination of lower and upper bounds for torsional rigidity. 1. The torsion problem for a multiply connected cross section. To solve the torsion problem for a beam of multiply connected cross section, we seek a function \f/{x, y) which is harmonic in the domain A occupied by the material, and such that 4> = §r2 on the outer boundary B0, (1.1) ^ = %r2 + C\ on the inner boundaries Bx, the constants Cx being chosen so that for each inner boundary we have