A novel mesh-reduction technique for deriving closed-form solutions of framed structures using a single finite element per structural member

This paper presents a novel mesh reduction technique designed to enhance the accuracy of Finite Element Method (FEM) results for the analysis of framed structures idealized using rod and beam theories. The proposed method facilitates the derivation of closed-form solutions, including exact nodal displacements, reaction forces, displacement and internal forces response fields within structural elements, while employing a single finite element per structural member. Inspired by the Green’s Functions Stiffness Method, this approach is based on the decomposition of the element’s response into homogeneous and particular or fixed components, both calculated exclusively using analytical shape functions and the stiffness matrix coefficients, which are key inputs in standard FEM formulations for framed elements. This technique can be seamlessly integrated into the post-processing stage of traditional FEM implementations, offering improved computational efficiency and precision of results.