Boundary-integral-based process for calculating stiffness matrices of space frame elements with axially varying cross section

Abstract

This paper presents a strategy to directly compute the stiffness matrix of 3D (space) frame elements having arbitrary cross sections and generic rigidity variation along their axes. All the necessary section properties are determined by means of formulations based purely on boundary integrals. To determine the torsional constant and the torsion center, this strategy applies the Boundary Element Method (BEM). To model thin-walled cross-sections, the strategy calls for activating integration algorithms devised specifically to deal with the nearly singular integrals involved. To express all other section properties (i.e. area, first and second moments of area, and the shear form factors) in terms of boundary integrals, the strategy employs Green's theorem. The existing boundary-element meshes, used to determine the torsion constants, are employed to evaluate the corresponding boundary integrals. In applying the proposed strategy – the pure boundary-integral-based process (PBIP) – we consider space frame elements with geometrically complex cross-sections varying along their axes.