Analysis of Curved Beams by the B-Spline Field Approximation Method

Abstract

The B-spline field approximation method is applied to the static deflection analysis of curved Euler-Bernoulli and Timoshenko beams. A formal definition of membrane locking is presented along with a simple test that allows a priori determination of a models susceptibility to membrane locking. Formulations for both types of beam models, that under certain discretizations experience membrane locking, are presented and additional formulations that can never experience membrane locking are presented for both beam models. Examples that demonstrate the efficacy of the membrane locking test and illustrate the two means of avoiding membrane locking are presented.