Understandingandclassifyinglocal,distortionalandglobal.pptVIP

Understanding and classifying local, distortional and global buckling in open thin-walled membersby: B.W. Schafer and S. ádány;Motivation and challenges Modal definitions based on mechanics Implementation Examples ;Thin-walled members;What are the buckling modes?;Buckling solutions by the finite strip method;Lcr;Why bother? modes ? strength;What’s wrong with what we do now?;What mode is it?;Are our definitions workable?;We can’t effectively use FEM;Generalized Beam Theory (GBT);Generalized Beam Theory;GBT inspired modal definitions;Global modes are those deformation patterns that satisfy all three criteria.;#1 membrane strains: gxy?=?0, membrane shear strains are zero, ex?=?0, membrane transverse strains are zero, and v = f(x), long. displacements are linear in x within an element.;#2 warping: ey???0, longitudinal membrane strains/displacements are non-zero along the length.;#3 transverse flexure: ky?=?0, no flexure in the transverse direction. (cross-section remains rigid!);Distortional modes are those deformation patterns that satisfy criteria #1 and #2, but do not satisfy criterion #3 (i.e., transverse flexure occurs).;Local modes are those deformation patterns that satisfy criterion #1, but do not satisfy criterion #2 (i.e., no longitudinal warping occurs) while criterion #3 is irrelevant.;Other modes (membrane modes ) do not satisfy criterion #1. Note, other modes typically do not exist in GBT, but must exist in FSM or FEM due to the inclusion of DOF for the membrane.;example ofimplementation into FSM;Constrained deformation fields;general FSM;Modal decomposition;examples;lipped channel in compression ;classical finite strip solution;modal decomposition;modal identification;I-beam cross-section;classical finite strip solution;modal decomposition;modal identification;concluding thoughts;acknowledgments;;varying lip angle in a lipped channel ;classical finite strip solution;;What mode is it?;lipped channel with a web stiffener;classical finite st