Variable order secant matrix technique applied to the elastic postbuckling of arches

Abstract

SUMMARYThis paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795-804) straindisplacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches.

A Full Nonlinear Curved Beam Element With Mixedformulation in State Space

“…2, has been solved previously by Jayachandran and White [7]. The beam has a rectangular cross section of B H  .…”

“…Pajunen [6] performed large deflection elasto-plastic analyses implementing Reissner's kinematically exact beam theory. Jayachanrdan and White [7] implemented these strain displacement relationships for planar beam using a variable order secant matrix.…”

“…The exact solutions for three displacement vector components at the tip are mentioned using the Castigliano's energy theorem in [11] [32] and has been analyzed by many researchers. , Jayachandran and White [7] and Wood and Zienkiewicz [33] , Ibrahimbegovic [34]). …”