Size-dependent buckling of multidirectional porous metal foam nanoshells resting on an orthotropic elastic foundation

This research addresses challenges in theoretical modeling of complex metal foam nanoshell structures and introduces a more accurate approach. It utilizes a nonclassical nanomechanics continuum approach to model novel tridirectionally porous metal foam nanoshell structures with varying microstructures, incorporating intrinsic characteristic lengths and spatial variations in material properties. The research endeavors to analyze the buckling response exhibited by multidirectional functionally graded (FG) porous metal foam nanoshells resting on an orthotropic elastic foundation. Employing the nonlocal higher-order strain gradient theory in conjunction with the principle of virtual work, the study establishes static stability equilibrium equations. Methodologically, the Galerkin method is applied to derive analytical solutions for critical buckling loads under diverse boundary conditions. Within the scope of investigation, two distinct types of porous shells are examined: softcore (SC) and hardcore (HC). These shells are further characterized by five distribution patterns: tridirectional (Type-A), bidirectional (Type-B and Type-C), transverse unidirectional (Type-D), and axial unidirectional (Type-E). This model demonstrates its efficacy in analyzing and designing shell element structures across a broad spectrum of industries, including motorcycle helmet manufacturing, petrochemical processing, aerospace engineering, and civil construction.