A Laplace Transform Approach for Static Analysis of Cracked Axially Functionally Graded Beams with Variable Cross Section

This study presents a comprehensive analytical investigation of the static analysis of a cracked axially functionally graded cantilever beam with exponentially varying material properties and cross-sectional geometry in the longitudinal direction. The crack is defined in the system using an equivalent rotational spring model. The main focus of this study is to solve this system, which contains complex discontinuities and variable coefficient differential equations, within a high-precision analytical framework, eliminating the computational cost imposed by numerical methods. Laplace transform method is effectively applied in solving the governing equations. The developed analytical model can express the effect of material gradient and crack stiffness parameters on beam deflection in closed form. The obtained analytical results are compared with exact integration solutions in the literature under different crack stiffness values. This study provides a faster, mathematically stable, and reliable solution method for functionally graded structures compared to traditional numerical methods, thus creating a unique and powerful analytical infrastructure for structural health monitoring and design optimization processes.

کلیدواژه ها:

Functionally Graded Materials ، Cracked Beam ، Variable Cross-Section Beam ، Static Analysis ، Laplace Transform