Analytical integration of cross section properties for numerical analysis of reinforced concrete, steel and composite frames

Nonlinear analysis of partially connected composite beams using interface elements

“…The analytical strategy employed here considers the possibility of polygonal cross-sections of various different materials in the same beam, and relies on a piecewise polynomial description of the uniaxial stress-strain relations. By means of a contouring algorithm and using Green's theorem, the area integrals are transformed into line integrals on the cross-section boundaries, see details as presented by Sousa and coworkers [30,31]. The main advantage of this strategy is the possibility of considering generic polygonal cross-section geometries, associated to a fast and exact evaluation of the cross-section properties.…”

Displacement-based nonlinear finite element analysis of composite beam–columns with partial interaction

“…This work employs the analytical evaluation of the resultant forces and tangent stiffnesses of the cross sections, using an algorithm described by Sousa Jr. and Muniz [20]. This algorithm performs the exact evaluation of the area integrals, based on the application of Green's theorem, as long as the uniaxial stress-strain relation is given by a polynomial expression.…”

A parametric subdomain discretization for the analysis of the multiaxial response of reinforced concrete sections

“…Many other methods have been proposed utilizing from Green's theorem [19,21] to graphical pixel integration [20] and closed form solutions of curved trapezoidal subsections [9].…”