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

Figure 3

Variations of the ceramic volume fraction 𝑉_𝐶 through the thickness for two-layered and three-layered laminated shells for different values of the power-law index 𝑝=𝑝⁽¹⁾=𝑝⁽²⁾ and 𝑝=𝑝⁽¹⁾=𝑝⁽³⁾: (a) FGM_{1(𝑎(1)=1/𝑏}⁽¹⁾_{=0/𝑐(1)/𝑝(1))}/FGM_{2(𝑎(2)=1/𝑏}⁽²⁾_{=0/𝑐(2)/𝑝(2))}, (b) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=0/𝑐(1)/𝑝(1))}/FGM_{1(𝑎(2)=1/𝑏}⁽²⁾_{=0/𝑐(2)/𝑝(2))}, (c) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=0/𝑐(1)/𝑝(1))}/FGM_𝐶/FGM_{1(𝑎(3)=1/𝑏}⁽³⁾_{=0/𝑐(3)/𝑝(3))}, and (d) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=0.5/𝑐(1)=2/𝑝(1))}/FGM_𝐶/FGM_{1(𝑎(3)=1/𝑏}⁽³⁾_{=0.5/𝑐(3)=2/𝑝(3))}.

(a)

(b)

(c)

(d)