A Closed-Form Solution without Small-Rotation-Angle Assumption for Circular Membranes under Gas Pressure Loading

Xiao-Ting He, Xue Li, Bin-Bin Shi and Jun-Yi Sun
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Xiao-Ting He: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Xue Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Bin-Bin Shi: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Yi Sun: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2021, vol. 9, issue 18, 1-29

Abstract: The closed-form solution of circular membranes subjected to gas pressure loading plays an extremely important role in technical applications such as characterization of mechanical properties for freestanding thin films or thin-film/substrate systems based on pressured bulge or blister tests. However, the only two relevant closed-form solutions available in the literature are suitable only for the case where the rotation angle of membrane is relatively small, because they are derived with the small-rotation-angle assumption of membrane, that is, the rotation angle ? of membrane is assumed to be small so that “sin ? = 1/(1 + 1/tan 2 ? ) 1/2 ” can be approximated by “sin ? = tan ? ”. Therefore, the two closed-form solutions with small-rotation-angle assumption cannot meet the requirements of these technical applications. Such a bottleneck to these technical applications is solved in this study, and a new and more refined closed-form solution without small-rotation-angle assumption is given in power series form, which is derived with “sin ? = 1/(1 + 1/tan 2 ? ) 1/2 ”, rather than “sin ? = tan ? ”, thus being suitable for the case where the rotation angle of membrane is relatively large. This closed-form solution without small-rotation-angle assumption can naturally satisfy the remaining unused boundary condition, and numerically shows satisfactory convergence, agrees well with the closed-form solution with small-rotation-angle assumption for lightly loaded membranes with small rotation angles, and diverges distinctly for heavily loaded membranes with large rotation angles. The confirmatory experiment conducted shows that the closed-form solution without small-rotation-angle assumption is reliable and has a satisfactory calculation accuracy in comparison with the closed-form solution with small-rotation-angle assumption, particularly for heavily loaded membranes with large rotation angles.

Keywords: circular membrane; gas pressure loading; large deflection; power series method; closed-form solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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