Rigidity matrix of a bay of an anisotropic cylindrical shell with the arbitrary cross section for bending, transverse shear and torsion
Mathematics. Physics. Mechanics
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractSome bays of elastic wings of large aspect ratio and blades of helicopter rotors are made as anisotropic shells in order to couple deformation of bending, transverse shear and torsion. When changing the bending moments in this case it is possible to change correspondingly the twisting angles of the cross sections and so to control by distribution of the aerodynamic load along the span. In this work using the theory of thin-walled beams we obtained approximate analytical solution for calculation of the stress state and determined the yielding and rigidity matrixes of a bay of an anisotropic cylindrical shell with arbitrary symmetric one-closed contour or the cross section for bending, transverse shear and torsion. The results of this solution for the yielding matrix coefficients of the shell bay are compared with the numerical solution by the finite element method.
Keywords:cylindrical shell; anisotropic shell; shell with the arbitrary cross section; thin-walled beam; bay method; yielding matrix; rigidity matrix.