Elastic-Plastic Analysis of Curved Structures Subjected to Static and Dynamic Loads

A method is presented for the finite-element analysis of curved planar structures consisting of a combination of thin straight and curved beam elements. In the analysis both static and dynamic loads, elastic-plastic deformations, strain-hardening and hysteresis effects are taken into consideration. The properties of the curved beam element are derived based on the exact solutions of previously developed Euler differential equations for a circular ring accounting for the effect of extensional deformations. The elements of the stiffness and consistent mass matrices of the planar curved beam element are derived in closed-form, thus eliminating the loss of computer time and round-off errors associated with extensive matrix operations in the computational algorithm. The effect of rotary inertia is also considered in the derivation of the consistent mass matrix. The applicability of the analytical method presented herein is demonstrated by the solution of some typical structures subjected to static and dynamic loads, in particular, pipe whip restraints.