A study on slope variation of a cantilever beam under the effect of transverse and compressive forces

• An analytical approach using the Akbari–Ganji Method (AGM) is developed to analyze slope variation in cantilever beams under combined transverse and compressive loads. • The AGM results show excellent agreement with numerical solutions, validating its accuracy and reliability. • Parametric studies reveal the influence of key physical factors on the nonlinear slope behavior of cantilever beams. This study focuses on the slope behavior of cantilever beams subjected to transverse and axial compressive forces—a classical yet complex problem in structural mechanics. Although various numerical methods have been used to investigate beam deflection, analytical approaches for slope analysis under combined loading remain limited. To address this gap, the Akbari–Ganji Method (AGM), a recently developed meshless and semi-analytical technique, is employed to solve the governing nonlinear differential equation. The accuracy of the AGM is validated through comparison with numerical results, demonstrating excellent agreement. Additionally, the effects of key physical parameters on slope variation are explored. The findings confirm that AGM provides an efficient and accurate analytical approximation for such nonlinear boundary value problems.