An innovative method for surmounting the constrained torsional problems of stocky beams with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties

Abstract

The constrained torsion problems of stocky beams, being still an unsurmountable challenge in solid mechanics, will be solved by the innovative method proposed, and the computational results of numerical examples signifying that the beam model proposed is reasonable and the numerical analysis methodology of nodal line method is effective. The creative cruxes are as followings:•a type of innovative beam model—stocky beam in solid mechanics analysis is defined, which uses the stress state of the beam to distinguish whether a structural member is a beam or not, and the axis of the stocky beam is the locus of the minimum torsional stiffness centre of all its cross sections;•the warpages of all cross sections of a stocky beam are depicted as a mathematical expression that signifies a family of curved surfaces evolved from Prandtl's membrane shapes;•the constrained torsion problem of a stocky beam can be transformed into the boundary value problem of a set of ordinary differential equations by using the nodal line method developed.