V. Plevris and A. Ahmad, “Deriving analytical solutions using symbolic matrix structural analysis for continuous beams”, Scientific Reports, 15, Article ID 15897 (DOI: 10.1038/s41598-025-98023-x), 2025.

Abstract:
This study investigates the use of symbolic computation in Matrix Structural Analysis (MatSA) for continuous beams, using the MATLAB Symbolic Math Toolbox. By employing symbolic MatSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering deeper insights into structural behavior. This approach facilitates efficient and scalable sensitivity analysis, where partial derivatives of outputs concerning input parameters can be directly computed, enhancing design exploration. The development includes an open-source MATLAB program, hosted on GitHub, enabling symbolic analysis of continuous beams subjected to point and uniform loads. This approach is valuable for both engineering practice and pedagogy, enriching the understanding of structural mechanics and aiding in education by illustrating clear parameter relationships. The program supports deriving influence lines and identifying maximum response values.