Free Vibration and Buckling Behavior of Porous Orthotropic Doubly-Curved Shallow Shells Subjected to Non-Uniform Edge Compression Using Higher-Order Shear Deformation Theory

Abstract

Due to the continuous enhancement of manufacturing technology for porous materials, it is expected to be increasingly used in aerospace, aviation, and other engineering applications, where the necessity for lightweight structures is paramount. Also, the non-uniform edge loads caused by service conditions, complex adjacent structures, and external loads lead to localized stress concentrations within the shells. Localized stress concentrations result in a loss of load-carrying capacity in specific regions, causing step-by-step failure of the shell. This study investigates the buckling and free vibration behavior of porous orthotropic doubly-curved shallow shells with four different porosity distribution patterns subjected to non-uniform edge compressive loads. The equations of motion of doubly-curved shallow shells are established by using higher-order shear deformation theory and Hamilton's principle. Then, the pre-buckling in-plane stress distributions of doubly- curved shallow shells are determined and appended to the equations of motion. These fundamental partial differential equations are solved by Galerkin's method, and the critical buckling load and natural frequency formulations are achieved. By comparing with the results in published literature, the feasibility and accuracy of present formulations are validated. Finally, systematic parametric studies are carried out to discuss the effects of different non-uniform edge compression patterns, porosity distribution patterns, porosity coefficients, aspect ratios, arc length-to-thickness ratios, radius-to-arc length ratios, orthotropy ratios, and shell types on the buckling and free vibration responses of porous orthotropic doubly-curved shallow shells. Parametric studies indicate that the reduction or increment in critical buckling loads (CBLs) and fundamental natural frequencies (FNFs) of spherical shells (SSs) are more sensitive than those of hyperbolic paraboloidal shells (HPSs). The CBLs and FNFs of SSs are larger than those of HPSs. The maximum and minimum CBLs are achieved for the triangular and uniform edge compression, respectively. The porosity effect is independent of edge compression pattern types.