A Closed-Form Solution without Small-Rotation-Angle Assumption for Circular Membranes under Gas Pressure Loading Article Swipe
Xiao‐Ting He
,
Xue Li
,
Binbin Shi
,
Jun‐Yi Sun
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.3390/math9182269
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.3390/math9182269
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 θ of membrane is assumed to be small so that “sinθ = 1/(1 + 1/tan2θ)1/2” can be approximated by “sinθ = tanθ”. 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 “sinθ = 1/(1 + 1/tan2θ)1/2”, rather than “sinθ = tanθ”, 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.
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math9182269
- https://www.mdpi.com/2227-7390/9/18/2269/pdf?version=1631953539
- OA Status
- gold
- Cited By
- 4
- References
- 15
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3199259934
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3199259934Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/math9182269Digital Object Identifier
- Title
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A Closed-Form Solution without Small-Rotation-Angle Assumption for Circular Membranes under Gas Pressure LoadingWork title
- Type
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articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-09-15Full publication date if available
- Authors
-
Xiao‐Ting He, Xue Li, Binbin Shi, Jun‐Yi SunList of authors in order
- Landing page
-
https://doi.org/10.3390/math9182269Publisher landing page
- PDF URL
-
https://www.mdpi.com/2227-7390/9/18/2269/pdf?version=1631953539Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://www.mdpi.com/2227-7390/9/18/2269/pdf?version=1631953539Direct OA link when available
- Concepts
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Rotation (mathematics), Membrane, Angle of rotation, Rotational speed, Mechanics, Materials science, Geometry, Mathematics, Physics, Classical mechanics, Chemistry, BiochemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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4Total citation count in OpenAlex
- Citations by year (recent)
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2024: 2, 2022: 2Per-year citation counts (last 5 years)
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15Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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