... as a hyper-plane in multidimensional space, based upon the limit state value and its gradients in all directions. FORM works fine provided that the LSF is linear or near-linear in the region of interest. When the LSF is not linear enough, the higher order terms need to be included in the Taylor expansion...

... into the 2nd order GBT system, two 3rd order terms ijrk υ σ and ijrk υ τ were obtained. The complete expansions of the GBT 2nd and 3rd order terms, in the form of a series of large discretized iterated functions, were obtained by the author and used in the Newton step method as a set of tangent...

... generalized beam theory section property deflection theory equation order term university thin-walled structure ij 1 gbt membrane stress virtual work deformation thin-walled member membrane shear strain transverse davy calculation Third Order GBT Terms And Its Expression...

... according to their orders in 113 (0) (1) (1) 2 (2) (2) (2) (2) (2) 3 ( ) ( ) 0( ) = + + + + + + + + D S D S I II W F F F F F F F F F (21) The zero order term is just the buoyant force (0) (0,0, ) = mS F g z ds g Vn (22) The first order terms can be further divided into (1) (1) = m D t S F...

... order term linear incoming wave amplitude experiment wave period prediction experimental result numerical result order amplitude wave amplitude amplitude wave elevation laboratory wave tlp center probe diffraction effect tlp frequency Proceedings of the Eleventh (2001...

... height order term particle speed kurtosis airy wave wave elevation wavenumber wave kinematic listing elevation irregular wave potential function frequency third-order model amplitude Proceedings of the Third (1993) International Offshore and Polar Engineering Conference Singapore, 6-11...