Geometric Nonlinear Analysis For Curve Thin-walled Box Girder

Due to the excellence of torsional stiffness,economy and aestheticappearance,curved box girder bridge are widely used in urban overpass and viaductsystems.At the same time，the span of curved box girder bridge is increased constantly，the nonlinear effect of curve box girder was gradually highlighted, it is necessary tocarry out the research of geometry nonlinear of the curve thin-walled box girder.According to the mechanical characteristics of the curve box girder bridge in verticalstress mainly, based on linear elastic analysis of the curve thin-walled box girderincluded in the warp effect, only consider vertical displacement of box girder for largedisplacement, the incremental form of virtual work equation and finite element columntype about geometric nonlinear were presented,and the finite element programs ofgeometric nonlinear analysis were produced.According to those,the main contents andresults are as follows:①In this dissertation,considering the noncoincidence of torsional center andgravity center and the infiuence of initial curvature,the variable-curvature-box girderwith rectangular cross section were established.The displacement equation consideringwarping torsion of any point in curve box girder was presented,according to the theoryof three-dimensional space nonlinear finite displacement, under the premise that it isbeen assumed that only vertical displacements are large displacement,the geometricnonlinear strain-displacement relationship and the relationship of strain increment anddisplacement increment were presented were deducted.Finally, the incremental form ofgeometric nonlinear virtual work equation of curve thin-walled box girder consideringwarping-torsional effect was established.②The three-node isoparametric finite element model of curce box girder withrectangular cross section and only a vertical symmetry axis,that each node have sevendegrees of freedom,for analysis of space geometrical nonlinear was established.Introducing a shape function as a difference value function of the coordinatesa of anypoint in unit and the displacement, the array of displacement and displacementincremental array of any point in unit were presented, and the matrix ofdisplacement-strain relation and the matrix of incremental displacement-incrementalstrain relation of isoparametric curve box girder were deduced.Based on the incrementalform of virtual work equation had been deduced,the finite element virtual work incremental column type of geometric nonlinear and the equivalent load array ofconcentrated load were presented.③Based on the facts mentioned above,,the Newton iterative method was takenfor solving nonlinear equations method, the finite element programs of geometricnonlinear analysis of invariable curvature and variable cross section of curved boxgirder was produced by MATLAB.④The necessity of geometric nonlinear analysis of curve box girder with largespan was proved by numerical examples, the correctness of the research results in thispaper were tested and verified by comparing with the finite elemen method of ANSYS.