Eccentricity effects in the finite element modelling of composite beams

When modelling composite or built up beams using finite element software, analysts find it often convenient to connect two standard Euler–Bernoulli beam elements at the nodes by using a rigid bar or use master–slave type kinematic constraints to express the degrees-of-freedoms of one of the members in terms of the other. However, this type of modelling leads to eccentricity related numerical errors and special solutions that avoid eccentricity related issues may not be available for a design engineer due to the limitations of the software. In this study, a simple correction technique is introduced in the application of master–slave type constraints. It is shown that the eccentricity related numerical errors in the stiffness matrix can be completely corrected by using extra fictitious elements and springs. The correction terms are obtained by using the exact homogenous solution of the composite beam problem as the interpolation functions which impose the zero-slip constraint between the two components in the point-wise sense. The effects of the eccentricity related errors are demonstrated in numerical examples.

► A correction technique is introduced to avoid eccentricity related numerical errors in the modelling of composite beams.
► It is shown that the error can be significant in practical applications.
► Effect of loading type on the eccentricity related numerical errors is illustrated.
► Effect of relative layer stiffness on the numerical error is illustrated.