AN ANALYSIS ON COMPLETENESS OF TOTAL POTENTIAL ENERGY OF THIN-WALLED MEMBERS WITH FLEXURAL-TORSIONAL BUCKLING

The omissions or multiplicities of energy items are hazardous to the completeness of the total potential energy of thin-walled members, which will cause the energy theory loosely or the incorrect values of critical load or critical moment. In order to propose complete total potential energy, the Vlasov's assumption of zero shear strain in middle surface is revised as zero linear shear strain in middle surface. The expression of the revised assumption is proposed and the linear shear strain of an arbitrary point in cross-section is deduced. The Vlasov's assumption can not be extended to non-linear shear strain and total strain range. The strain energy and the load potential energy are derived by the strain energy formula of elasticity theory, and the complete total potential energy is established. The results shown that:both the clear concept procedure and total potential energy are complete due to the linear shear strain energy; the load potential energy is derived strictly; the nonlinear shear strain energy is included accurately; and the nonlinear transverse strain energy is excluded.