3-D beam element of variable composite cross section including warping effect

Abstract

In this paper, a boundary element method is developed for the construction of a 14 × 14 stiffness matrix and a nodal load vector that take into account the additional warping degrees of freedom in a member of arbitrary variable composite cross section. The member is subjected to an arbitrarily concentrated or distributed twisting moment and consists of materials in contact each of which can surround a finite number of inclusions. The developed method takes into account the variable torsional and warping rigidities along the member length. Two boundary value problems with respect to the variable along the beam angle of twist and to the primary warping function are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The discrepancy in the elements of the resulting stiffness matrix using the developed procedure and a fine mesh of elements having “average” values for the cross section parameters necessitates the consideration of the derivatives of the variable torsional and warping rigidities along the member length. Moreover, the influence of the warping effect, especially in composite members of open form cross section of variable thickness, is analyzed in examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame.