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

Figure 2

Variations of the ceramic volume fraction 𝑉_𝐶 through the thickness for different values of the three parameters 𝑎⁽¹⁾,𝑏⁽¹⁾, and 𝑐⁽¹⁾ and the power-law index 𝑝⁽¹⁾ for a single-layered shell: (a) FGM_{1(𝑎(1)=1/𝑏}⁽¹⁾_{=0/𝑐(1)/𝑝(1))}, (b) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=0/𝑐(1)/𝑝(1))}, (c) FGM_{1(𝑎(1)=1/𝑏}⁽¹⁾_{=1/𝑐(1)=2/𝑝(1))}, (d) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=1/𝑐(1)=2/𝑝(1))}, (e) FGM_{1(𝑎=1/𝑏=0.5/𝑐=2/𝑝)}, and (f) FGM_{2(𝑎(1)=1/𝑏}⁽¹⁾_{=0.5/𝑐(1)=2/𝑝(1))}.

(a)

(b)

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(d)

(e)

(f)