Elastic response of an exponentially graded beam under diverse loading scenarios

This paper investigates the plane stress behavior of a cantilever beam under variable bending loads, emphasizing a novel approach to modeling material properties. Unlike traditional methods, this study uses an exponential distribution to represent material properties that vary continuously through the thickness, leading to a more accurate depiction of inhomogeneous materials. The research encompasses three distinct loading scenarios: uniform, linear, and parabolic, all integrated within a cohesive plane elasticity framework. Each loading case is defined by specific parameters tailored to its characteristics. The findings of the study underscore the method’s consistency and reliability, yielding results that are both accurate and satisfactory. Furthermore, the paper includes a detailed numerical example that demonstrates the profound influence of material gradation on the elastic field, reinforcing the practical significance and the overall effectiveness of the proposed modeling technique.