en Optimal design Optimal design پژوهشي Research <span style="font-size:11.5pt"><span style="text-justify:inter-ideograph"><span new="" roman="" style="font-family:" times="">This study investigates the geometrical and material design aspects of functionally graded (FG) doubly-curved shells. The FG material system comprises a combination of metal and ceramic constituents, and the effective properties across the shell thickness are estimated using Voigt&rsquo;s rule of mixtures. To analyze the structural behaviour, the finite element method is employed within the framework of third-order shear and normal deformation theories. The grey wolf optimization (GWO) algorithm is implemented to achieve design optimization. The objective function aims to minimize both the maximum displacement and the fundamental dimensionless natural frequency in each optimization process individually. The findings indicate that under highly constrained boundary conditions, the curvature parameters remain constant. Conversely, for less constrained conditions, the parameter <i>R₂</i> assumes a value approximately ten times greater than <i>R₁.</i></span></span></span><br> &nbsp; FGM, GWO algorithm, doubly-curved shell, third-order shear and normal deformation theories 543 555 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-6463-39&slc_lang=en&sid=1 R. Kamgar kamgar@sku.ac.ir 180031947532846002869 180031947532846002869 Yes Department of Civil Engineering, Shahrekord University, Shahrekord, Iran F. Rahmani 180031947532846002870 180031947532846002870 No Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, Iran