Hierarchical Bernoulli-Euler beam finite elements

Abstract

A method is described to model the dynamics of a uniform Bernoulli-Euler beam finite element in terms of static constraint modes and interface restrained assumed modes. This is in contrast with the regular finite element method where no interface restrained assumed modes are retained. Element mass and stiffness matrices are developed using two different types of interface restrained assumed modes, namely, normal modes and trigonometric functions. The proposed models are hierarchical in the sense that lower order models are embedded into higher order models. Consequently, different levels of approximation can be obtained with little additional effort and without further physical subdivision of the beam element, thereby preserving the original grid layout. Numerical examples are included to demonstrate the superior convergence characteristics of these elements compared to that developed via the standard consistent mass matrix approach.