Theoretical Research And The Applications Of The Curved Beam Element

With the rapid development of our science and technology, the curved beam structure has been widely applied in our daily life and bridge construction owing to its beautiful streamlined shape and good mechanical properties. However, the bending and torsion coupling of the curved beam resulted from its curvature makes the study of curved beams more difficult than that of straight beams. Hence, it is necessary to carry out in-depth research on curved beams.Firstly, a 3-node plane curved beam element is constructed in the present study, which takes its axial tension and bending effects into consideration, and involves three degrees of freedom per node. And meanwhile, its element stiffness matrix in local coordinates are derived. Hermite and Lagrange interpolation function are adopted to construct the displacement function of the curved beam element, and then the shape function of the element is attained. And then, taking the geometric nonlinearity into consideration, the variational principle is used to derive the expression of stiffness matrix of plane curved beam element under local coordinates.And then, on the basis of the derived stiffness matrix of the plane curved beam element, its coordinate transformation is carried out under the global coordinate system, which results in stiffness matrix that can be applied to the overall coordinates. And meanwhile, the load equivalent of curved beams under the circumstance of radial distribution loads, concentrated loads, as well as concentrated couple is also calculated. And after that, MATLAB programming is adopted in the examples to solve nonlinear equations, and then, the results are compared with the theoretical derivations, which illustrates the correctness of curved beam element.And finally, a secondary exploitation of the finite element software ANSYS is carried out on the basis of above theoretical studies. By virtue of user-defined unit, the theoretical derivation of the curved beam element is constructed in ANSYS with a new type, and applied to engineering examples analysis. What’s more, bridge dedicated software Midas Civil combined with examples is adopted to illustrate that the new beam element derived in the present study can be better applied to example analysis.