Analytic solutions for Euler–Bernoulli beams with axial compression resting on a nonlinear elastic foundation using MADM

This article investigates the deflection behavior of Euler–Bernoulli beams subjected to axial compression and resting on a nonlinear elastic foundation. The Modified Adomian Decomposition Method (MADM) is employed to predict the beam deflection under various loading and foundation conditions. By adopting an initial polynomial ansatz, MADM effectively optimizes the construction of Adomian polynomials, resulting in rapid convergence and an accurate series solution. The accuracy and reliability of the proposed method are examined through two illustrative cases. In the first case, the formulation is verified against an analytically tractable benchmark problem, while in the second case, the MADM results are compared with previously published solutions. The comparative analysis demonstrates excellent agreement with existing studies, confirming the validity of the proposed approach. Overall, the results indicate that MADM provides a stable and efficient analytical framework for modeling the coupled effects of axial compression and nonlinear elastic foundations in Euler–Bernoulli beams.