Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

Table 3

Perceptual relative errors in first frequtency 𝑒_𝑓=((𝑓₁−𝑓_1𝑇)/𝑓_1𝑇)⋅100 and in maximum bending displacement 𝑒_𝑤=((𝑤_max−𝑤_max𝑇)/𝑤_max𝑇)⋅100 with Monte Carlo, Particle Swarm Optimization, and Genetic Algorithm methods.

Optimization method	Square plate	Cylindrical panel	Conical shell		Toroidal shell panel	Catenoidal panel	Elliptic paraboloid
	𝑒𝑓	𝑒𝑤	𝑒𝑓	𝑒𝑤	𝑒𝑤	𝑒𝑓	𝑒𝑓	𝑒𝑤
MC	−1.261	−0.431	2.884	−1.076	0.534	0.899	1.665	−0.786
GA	0.024	0.188	0.070	−0.029	−0.053	0.037	0.119	0.010
PSO	−0.016	0.059	0.118	−0.046	0.008	−0.074	0.049	−0.042