Closed-form solution of Timoshenko frames on elastic Winkler foundation using the Green’s function stiffness method
Fecha
2024-10-01
Autores
Posso, Cristian
Molina-Villegas, Juan Camilo
Ballesteros Ortega, Jorge Eliecer
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Editor
Elsevier
Resumen
This 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.