A Study On Static Response Numerical Analysis Of Structures With Specially Nonlinear Material

Marine flexible pipelines and other special nonlinear material structuresabbreviated to SNMS, where Young’s modulus manifests non-identity between axialtensile stiffness and bending stiffness, have more special nonlinear materialcharacteristics as well as general material nonlinearity and geometry nonlinearity instatic response analysis. The objective of the present paper is to put forward numericalanalysis method of SNMS static response.Proceeding from generalized variational principle of nonlinear elastic body withlarge displacement, this paper eliminates constitutive law of stress-strain by higherorder Lagrange multipliers to achieve generalized variational functional with moregeneral sense. According to the generalized variational functional, a3D static finiteelement model is constructed in the CR framework by axial tension as an extra degreeof freedom on the basis of the ordinary3D beam element. A Matlab program ispresent and used for comparison between calculated values and theoretical ones of thecantilever beam. T he efficiency of the method is shown by examples.A range of cantilever beams is the research object, of which sensitivity analysis isrespectively performed on nonlinear tensile stiffness and hysteresis effect of bendingstiffness as well as a number of axial-bending Young’s modulus combination. Theresults show that:1) when the cantilever beam is subjected only to tension, the axial deformation atfree end has pretty high degree of sensitivity on the initial extension rate of nonlineartensile stiffness;2) when the cantilever beam is subjected only to bending, the displacements at freeend are sensitive to initial stiffness and curvature during loading and unloading;3) when the cantilever beam is subjected to both combined tension and bending, thedeflection at free end increases slowly with the Young’s modulus ratio of tension tobending while the x direction displacement increases much faster with the ratio.