THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD

First-order Generalised Beam Theory (GBT) analysis can be used to describe the behaviour of prismatic structures by using deformation functions for bending, torsion and distortion in ordinary uncoupled differential equations. In second-order GBT, the differential equations then are involved with the effect of deviating forces. By derived the virtual works of two membrane stress terms into the GBT system, we can obtain the complete expansions of the third order GBT equation in the form of a series of large discretized iterated functions, which can be converted to sets of tangent stiffness matrices for further numerical analyses. By introducing the membrane stresses as the third order terms ^ijrkv_σ and ^ijrkv_τ and using advanced numerical techniques to find a complete solution, the third-order Generalised Beam Theory becomes a rigorous and efficient numerical tool to investigate large deflection behaviours in post-buckling of thin-walled structures.