Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements

Modeling complex conditions involving extensive engineering structures with large numbers of beams and columns often requires a mixture of analytical modeling based on beam theory and numerical simulations involving finite element models composed of solid or shell elements. However, high levels of deformation in the planar configuration of cross-sections arising under extreme external loads, such as intensive earthquakes, explosions, and hurricanes, greatly complicates the task of fitting the numerical simulation results to the planar cross-sections required by beam theory. The present work addresses this issue by proposing a fitting method based on a least squares approximation method. The fitting problem is first transformed into a process of solving a cubic equation whose coefficients are integrals over the simulated cross-section. The solution of the cubic equation is defined using explicit formulae developed for calculating the integrals over the surfaces of single solid or shell elements lying within the cross-section by combining the shape functions and degree of freedom results of the elements. The proposed fitting method is then applied for analyzing the blast resistance of steel structures. The potential application of the proposed method is demonstrated by evaluating the rotations, shear deformations, and moment–curvature relationships of the fitted cross-sections.