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26 pages, 6493 KiB

Open AccessArticle

Innovative Insights on the Thin Square Plate Large Deflection Problem

by Gilad Hakim and Haim Abramovich

Materials 2023, 16(21), 6967; https://doi.org/10.3390/ma16216967 - 30 Oct 2023

Viewed by 601

Abstract

Thin plates subjected to transverse load and undergoing large deflections have been widely studied and published in the literature. However, there is still a lack of information and understanding about the membrane stresses created under large deflections and their associated Airy stress function, as displayed in the well-known von Kármán equations set. The present study aims at providing explicit expressions for the membrane stresses, the deflections, and the Airy stress function for a general square plate area vertically uniformly loaded to reach large deflection state. This was obtained by using the results of a high-fidelity finite element analysis applied on a lateral loaded simply supported thin square plate, which are then casted to yield approximate Fourier series expressions for the membrane stresses, deflections, and the Airy stress function. The stress map figures provide a good understanding of the critical points on the plate, while the explicit mathematical expressions enabled the calculation of deflections and stresses for the entire plate area. Among other interesting findings, the presence of relatively high tensile and compressive membrane stresses existing near the plate edges was revealed, which might lead to potential failure hazards. The derivatives of the deflections and the Airy stress function enabled the validation of the large deflections von Kármán equations set for the investigated case, and it turned out that the generated expressions for the stresses and the lateral deflection based on a high-fidelity finite element model satisfy the second equation with a good accuracy, while the first one remains to further be investigated. Moreover, using the generated explicit equations, the load influence on the deflections and stresses was also analyzed to yield general novel expressions for the medium and very large deflections states. To generalize the investigated case, the stresses and the deflections were non-dimensionalized so they can be used for any material and plate dimensions. Full article

(This article belongs to the Special Issue Large Deflections of Thin-Walled Structures)

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20 pages, 4533 KiB

Open AccessArticle

Behavior of Inflatable Drop-Stitch Fabric Panels Subjected to Bending and Compression

by William G. Davids

Materials 2023, 16(21), 6919; https://doi.org/10.3390/ma16216919 - 28 Oct 2023

Viewed by 876

Abstract

In this paper, the mechanics of inflatable drop-stitch panels are investigated, including the impact of large shear deformations, nonlinearity due to wrinkling of the panel skin that occurs under net compressive strain, work done by the confined internal air, and the effect of the drop-stitch yarns on the panel skin stresses. A large deflection finite element (FE) analysis framework is presented that allows for a panel’s stability and post-buckling response to be quantified. The FE code is verified through comparison with available analytical solutions, and the impact of critical response drivers is examined. The FE models are then used to explore the capacity of panel walls when used as part of a shelter subject to realistic wind and snow loads and to assess the dependence of the capacity on the important design parameters of inflation pressure and panel depth. The analyses indicate that while the drop-stitch panel capacity is sensitive to the panel depth and inflation pressure, panels with reasonable cross-sectional dimensions are viable for use in structural applications where they must support significant compression and bending. Future work should focus on increasing the structural efficiency and capacity by increasing the panel shear stiffness and operational inflation pressure. Full article

(This article belongs to the Special Issue Large Deflections of Thin-Walled Structures)

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27 pages, 4353 KiB

Open AccessArticle

Multiwall Rectangular Plates under Transverse Pressure—A Non-Linear Experimental and Numerical Study

by Gilad Hakim and Haim Abramovich

Materials 2023, 16(5), 2041; https://doi.org/10.3390/ma16052041 - 01 Mar 2023

Cited by 1 | Viewed by 1205

Abstract

Large deflection of rectangular plates under transverse pressure is described by Föppl–von Kármán equations, which have only approximated solutions. One of these methods is the separation into a small deflection plate and a thin membrane described by a simple third order polynomial expression. The present study presents an analysis to obtain analytical expressions for its coefficients by using the plate’s elastic properties and dimensions. To validate the non-linear relationship between the pressure and the lateral displacement of the multiwall plate, a vacuum chamber loading test is used to measure the plate’s response, with a large number of plates and length–width combinations. In addition, to further validate the analytical expressions, several finite element analyses (FEA) were performed. It has been found that the polynomial expression fairly describes the measured and calculated deflections. This method allows the prediction of plate deflections under pressure as soon as the elastic properties and the dimensions are known. Full article

(This article belongs to the Special Issue Large Deflections of Thin-Walled Structures)

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