Finite Difference Accuracy in Structural Analysis

An accuracy study is made of central finite difference methods for solving boundary value problems in structural analysis which are governed by equations with variable coefficients leading to odd order derivatives. Two methods are studied through application to beam-columns with nonuniform inplane loads and nonuniform stiffness. Definitive expressions for the error in each method are obtained by using Taylor series to derive the differential equations which exactly represent the finite difference approximations. The resulting differential equations are accurately solved by a perturbation technique which yields the error directly. A half station method, which corresponds to making finite difference approximations before expanding derivatives of function production in the beam-column differential equations, is found clearly superior to a whole station method which corresponds to expanding such products first.