On the treatment of non-prismatic members in FEA

摘要

2D beam members with variable cross-sections and a constant Young's modulus are examined as these construction elements are usually used for girders and columns in hall constructions. The theoretical derivations count on a geometrically linear theory whereas the superposition principle is valid. Based on Bernoulli's theory, differential equations and solution approaches for the membrane and bending parts are specified that rely on cross-sections with variable height and Width, and also on 2-point cross sections with linearly variable height. A systematic FE formulation leads to a concise notation of the element stiffness matrices and element load vectors. Therefore, an improved approximation solution is developed for arbitrary cross-sections with linearly variable shapes. Solutions of alternative approximations as well as commercial engineering programs are compared.