Advanced 3-D beam element including warping and distortional effects for the analysis of spatial framed structures. (1st June 2019) - Sapountzakis, Evangelos J.; Dikaros, Ioannis C.
Highlights: 3-D beam stiffness matrix with warping/distortion and Poisson ratio. Generation of higher-order stress resultants diagrams is possible. No thin-wall assumptions are made for the cross section. BEM is used for cross sectional and global analysis. Minimum elements are required. Warping/distortion transmission conditions in non-aligned members is alleviated. Abstract: In this paper an advanced 32 × 32 stiffness matrix and the corresponding nodal load vector of a 3-D beam element of arbitrary cross section taking into account shear deformation, generalized warping (shear lag effects) and distortional effects due to both flexure and torsion is presented. Nonuniform distortional/warping distributions are taken into account by employing 10 additional degrees of freedom per node. Local stiffness matrix and local equivalent nodal load vector of the element are computed numerically applying the Analog Equation Method (AEM), a Boundary Element Method (BEM) based technique. Warping and distortional functions as well as geometric constants of the cross section are evaluated employing a 2-D BEM approach. The developed element is incorporated into a standard Direct Stiffness Method (DSM) algorithm employed for the solution of spatial frames. The problem of handling distortional/warping transmission conditions in non-aligned members is alleviated by using an approximate technique for a proper transformation of higher-order degrees of freedom at frame joints.