2025-01-082024-10-011873-7285https://hdl.handle.net/10784/34861This paper presents a method to obtain the exact closed-form solution for the static analysis of Timoshenko beams and frames on elastic Winkler foundation, subjected to arbitrary external loads and bending moments. The solution is derived using the Green’s Functions Stiffness Method (GFSM), a novel mesh reduction method that combines the strengths of the Stiffness Method (SM) and Green’s Functions (GFs). By incorporating the core concepts of the SM, the GFSM exhibits similarities to the Finite Element Method (FEM), including the use of shape functions, stiffness matrices, and fixed-end forces. The application of GFs facilitates the derivation of analytical expressions for displacement and internal force fields for arbitrary external loads and bending moments. Three examples are presented: a single-span beam, a two-span beam, and a one-bay, one-story plane frame on elastic Winkler foundations; which demonstrate applicability and efficacy of the method.engCopyright © 2024 Elsevier. All rights reserved.info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessTimoshenko beamElastic Winkler foundationStatic analysisClosed-form solutionGreen’s functionsMesh reduction methodGreen’s function stiffness methodFinite element methodTranscendental Finite element methodAcceso abierto2025-01-08Posso, CristianMolina-Villegas, Juan CamiloBallesteros Ortega, Jorge Eliecer10.1016/j.euromechsol.2024.105457