Morphing of Bistable Composite Laminates Using Distributed Piezoelectric Actuators

<table>Equilibrium configurations predicted by the finite element model (step 1). (a) Equilibrium shape I (<svg height="15.4" id="M64" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 61 15.4" width="61" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.763,15.187)"><use xlink:href="#x1D465"></use></g>
<g transform="matrix(.017,-0,0,-.017,21.762,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,36.449,11.112)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.609,11.112)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
q53 0 90 28q4 31 4 66q0 51 -9.5 95.5t-39 80.5t-75.5 36z" id="x39"></path></g><g transform="matrix(.017,-0,0,-.017,52.768,11.112)"><use xlink:href="#x31"></use></g>
</svg> mm, <svg height="18.362499" id="M65" style="vertical-align:-5.76984pt" version="1.1" viewbox="0 0 61.237499 18.362499" width="61.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43F"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.763,15.188)"><use xlink:href="#x1D466"></use></g>
<g transform="matrix(.017,-0,0,-.017,22,11.113)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,36.687,11.113)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.846,11.113)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" id="x38"></path></g><g transform="matrix(.017,-0,0,-.017,53.006,11.113)"><use xlink:href="#x39"></use></g>
</svg> mm). (b) Equilibrium shape II (<svg height="15.4" id="M66" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 61 15.4" width="61" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D43F"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.763,15.187)"><use xlink:href="#x1D465"></use></g>
<g transform="matrix(.017,-0,0,-.017,21.762,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,36.449,11.112)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.609,11.112)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,52.768,11.112)"><use xlink:href="#x39"></use></g>
</svg> mm, <svg height="18.362499" id="M67" style="vertical-align:-5.76984pt" version="1.1" viewbox="0 0 61.237499 18.362499" width="61.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43F"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.763,15.188)"><use xlink:href="#x1D466"></use></g>
<g transform="matrix(.017,-0,0,-.017,22,11.113)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,36.687,11.113)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.846,11.113)"><use xlink:href="#x39"></use></g><g transform="matrix(.017,-0,0,-.017,53.006,11.113)"><use xlink:href="#x31"></use></g>
</svg> mm).</table>

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fig3

Figure 3

Figure 3: Morphing of Bistable Composite Laminates Using Distributed Piezoelectric Actuators 