Influence of porosity and orthotropic foundation on the stability of orthotropic laminated doubly curved shallow shells

Porous materials are increasingly used in laminated composite shallow shells to reduce weight while maintaining structural performance, making it essential to understand how porosity affects buckling behavior. Simultaneously, the presence of an orthotropic Winkler–Pasternak foundation provides lateral and shear restraint that can significantly influence stability, particularly for shells with complex geometries or non-uniform stiffness distributions. Unlike previous studies that focused solely on the buckling of porous shells under non-uniform loads, this work integrates the stabilizing effects of an orthotropic Winkler-Pasternak foundation. New equilibrium equations are derived to capture the complex interaction between the shell’s porosity, the non-uniform stress field, and the foundation’s shear/normal restraints. This study investigates the buckling of porous laminated doubly curved shallow shells (PO-LDSs) resting on an orthotropic Winkler-Pasternak foundation using a higher-order shear deformation theory. The shallow shell’s layers are composed of porous material with four porosity distributions (UDP, NUDP1–3), and the shell is subjected to five compressive loading patterns (U-CL, TR-CL, TG-CL, P-CL, S-CL). The pre-buckling analysis of non-uniform loading patterns is conducted using the stress function and by minimizing the membrane strain energy. The governing PDEs are transformed into a linear system of equations using Galerkin’s method. A parametric study is conducted to investigate the impact of porosity, geometry, fiber orientation, orthotropic foundation, non-uniform edge compressions, and foundation orthotropy angles on the buckling of porous orthotropic laminated shallow shells. The results reveal that the critical buckling load increases monotonically with foundation stiffness, enhancing the buckling capacity by up to 36% for spherical shells (SS) and 51% for hyperbolic paraboloidal shells (HPS). Fiber orientation, orthotropy angles of the foundation, and porosity distribution are found to significantly modulate the critical buckling load; notably, strong foundation orthotropy can alter the buckling resistance by up to 20%. Furthermore, the foundation mitigates sensitivity to extreme fiber angles and asymmetric porosity distributions, reducing the porosity-induced stiffness penalty by approximately 12% to 14%. Additionally, as flatter shells exhibit reduced geometric stiffness, the relative contribution of the foundation support increases by up to 37%. These quantitative findings provide robust design insights for optimizing porous laminated shells under various loading and foundation conditions.