An anisotropic beam theory based on the extension of Boley’s method

Abstract

The objective of this contribution is the computation of the Airy stress function for anisotropic beam-type structures. In the first part an iterative procedure is applied for the determination of the stress function by means of Boley’s method. This method was successfully applied by Boley for two-dimensional (2D) isotropic plates under plane stress conditions in order to compute the displacement field and the stress distribution. In this contribution a higher order theory for anisotropic beams is derived with Boley’s iterative procedure and an analytical formula for the Airy stress function is given. In the second part of the paper a beam with rectangular cross section is considered and the derived anisotropic beam model is compared to two-dimensional (2D) finite element results performed in ABAQUS. Two examples are studied: first a cantilever with constant distributed load is investigated, then an axially end-loaded redundant beam that is clamped at the one end and simply supported at the other end is studied. In both cases the analytical results are in perfect agreement with the ABAQUS outcome. Furthermore the effects of different kinematic restrictions for realizing clamped boundary conditions are investigated and compared. For the redundant axially loaded beam it is shown that the Bernoulli-Euler beam theory yields misleading results because it does not take into account shear coupling. This phenomenon is included in our presented solution for anisotropic beams.