Strength and deformation of arbitrary beam sections using adaptive FEM

Still today, structural design is often based on simplified hand-calculation formulas for special cases, which is tedious to apply and do not cover more general situations. To improve the situation, the paper presents a FE-program for analysis of strength and deformation of arbitrary beam cross sections of steel and concrete loaded by all six force and moment components. The program is based on (1) an enhanced beam theory with three-dimensional state of stress, (2) multi-surface elasto-plasticity for modeling of the materials and (3) efficient numerical algorithms (mesh adaptive FEM, arc-length method, etc.). The paper presents the theory behind the program and some initial numerical testing to show how the program works. The initial numerical testing on steel and reinforced concrete beam sections loaded in bending, shear and torsion show promising results.

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