Nonlinear Three-Dimensional Elasto-Plastic Analysis of Slender Steel Arches

This paper aims to develop an elasto-plastic spatially curved-beam element for the three dimensional nonlinear elasto-plastic analysis of slender steel arches. An exact rotation matrix for three dimensional deformations that satisfies the orthogonality and unimodular conditions is used in deriving the nonlinear strain-deformation relationship to account for the geometric nonlinearity and to separate the rigid-space body motions from the real deformations. For material nonlinearities and plasticity, standard elasto-plastic incremental stress-strain relationships are derived based on the von Mises yield criterion, the associated flow rule, and the isotropic hardening rule. In addition, a consistent tangent operator instead of the standard tangent operator is used in conjunction with the consistent return mapping algorithm based on the operator split methodology to avoid the loss of quadratic asymptotic convergence rate of Newton-Raphson methods. The curved-beam element also includes the effects of initial geometric imperfections, residual stresses, elastic restraints and supports, and of load and restraint positions.