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

<table>Elliptic paraboloid: Monte Carlo optimization with  <svg height="15.35" id="M520" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 48.137501 15.35" width="48.137501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>; final optimized frequency <svg height="16.6625" id="M521" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 106.1125 16.6625" width="106.1125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and final optimized displacement <svg height="16.1625" id="M522" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 134.14999 16.1625" width="134.14999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,104.013,7.688)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,110.997,7.688)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
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</svg>.</table>

Mathematical Problems in Engineering

fig20

Figure 20

Figure 20: Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method 

Figure 20 | Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method 