B‐Spline Compound Strip Formulation for Braced Thin‐Walled Structures

Abstract

A B‐spline bracing element of arbitrary orientation is developed and combined with the B‐spline compound strip method (BCSM) to analyze structures having bracing members. In the BCSM, a problem is first partially discretized to an ordinary differential equation by the finite element method. Then, the equation is solved using the Ritz‐Galerkin method with unequally spaced cubic B‐spline functions. The BCSM uses a special element “strip.” The strip is described as a product of the longitudinal cubic B‐spline series and transverse finite element polynomial shape functions. The bracing element is treated as a space frame element. For including the stiffness contribution of the bracing element, transformation and interpolation matrices are derived. A direct stiffness formulation is used. This technique eliminates the repetitive solutions required for each redundant in a flexibility approach based on the traditional finite strip method (FSM). The simplicity, accuracy, and convenience of this presented method are verified by the numerical examples.