Analytical Method for Calculating the Extreme Value of Static Bending Deflection of Two-Curvature Microshells

This study, utilizing analytical methods, presents for the first time the static bending response of a two-curvature micro shell composed of three material layers: two outer layers made of ceramic and micro-porous metal, and a middle layer featuring an auxetic structure. The stiffness of the shell can achieve its maximum when optimal geometric parameters of the auxetic core are identified. Calculation formulas are derived from classical shell theory and coupled stress theory to ascertain the impact of size effect on the static bending response of micro shells. The length scale parameter determined in this study varies with thickness. Furthermore, this research presents an explicit expression for the displacement of the micro shell under bending and demonstrates the reliability of the analytical formula by comparing it with previously published results. This study demonstrates the dependence of micro shell displacement on various geometrical and material parameters of the shell and each individual material layer. This is a compilation of reference data for designers to select suitable parameters to maximize the bending load capacity of the micro shell, hence minimizing the bending displacement of the micro shell.