Accuracy and Convergence of the Separation of Rigid Body Displacements for Plane Curved Frames

Abstract

The method with the separation of rigid body displacements is a powerful tool for the finite displacement analysis of structures particularly with curved members, with variable cross sections, and/or with inelastic behaviors. Nevertheless, its theoretical equivalence to the solutions of the direct Lagrangian equations has not been examined so far. This paper presents the theoretical convergence and accuracy of the method, where an original curved element of variable cress section is considered as well as an approximate straight element of constant cross section.

Accuracy and Convergence of the Separation of Rigid Body Displacements for Space Frames

“…In order to be compared with the SRBD method discussed later, however, the derivatives determined from the first order differential equations of Table 3 have to be transformed into those of Rq. (12) As for the geometrical quantities, the first order differential equations for displacements are obtained by differentiating Eq. (7. a) with respect to z helped by Eqs.…”

“…In other words, an appropriate simplification of the local differential equations is none the less important to produce accurate solutions, however adequately rigid body rotations are evaluated. In the present procedures for the SRBD method for space frames, a simplified linear or nonlinear governnig equation is introduced only from physical considerations without mathematical proof and its validity as well as accuracy has not been examined theoretically so far except that for plane frames11), 12) This paper examines theoretically the convergence and accuracy of the SRBD method for the finite displacement analysis of space frames, in comparison with the solutions of the highly nonlinear differential equations in direct Lagrangian expressions.…”