Nonlinear Theory for Elastic Beams and Rods and Its Finite Element Representation

摘要

Expressions for large curvatures of elastic beams and rods are given in terms of displacement components and angular coordinates. The application of these expressions to bifurcation and stability problems, based on the principle of virtual work is discussed. This approach is compared with another finite element representation, and an error in this representation is corrected. The condition of zero extension of the axis in the case of the Euler column is shown to require division into a large number of finite elements in order to ensure an accurate result for the stability coefficient. The conditions of zero extension of the axis and zero curvature about one principal axis of the cross section in the case of the lateral buckling of the end loaded cantilever have similar consequences.