On snap-through instability of porous BFGM shallow arches on nonlinear elastic foundation

Shallow arches lose stability under transverse loading if the load surpasses a critical threshold, leading to a sudden and significant deformation as they transition to a new stable configuration. This snap-through buckling behavior can be beneficial in certain applications, such as toggle switches or detrimental in others. Consequently, understanding the factors that influence snap-through behavior is essential for designing structures that perform reliably under such conditions. Therefore, this study aims to investigate the large amplitude response and post-buckling stability of shallow thick arches whose material properties can vary along thickness and length according to three different patterns. Further, the material can be porous through the arch thickness according to three different porosity distribution types. Based on the Reddy's higher-order shear deformation theory and the von Kármán type of geometric nonlinearity, the porous BFGM shallow arch resting on nonlinear Pasternak foundation is modeled as a set of nonlinear governing partial differential equations. By using the numerical differential quadrature method (DQM) and Newton's method, the governing equations are solved. An incremental approach is proposed to obtain the load-deflection curves. Several comparison and parametric studies are presented to validate the model and solution methodology and to demonstrate the potential of porous BFGM shallow arches in optimizing structural behavior. Results show that several factors influence and control the snap-through characteristics of porous BFGM arches including arch geometry, material composition, porosity, and elastic foundations. The initial shape and curvature of the arch play a crucial role. Arches with a higher rise-to-span ratio and thin arches are more susceptible to snap-through. This model may introduce new opportunities for managing this instability, enabling the development of structures with customized instability characteristics.