Large deflections of rectangular plates

Iyengar, K. T. Sundara Raja; Naqvi, M.Matin

doi:10.1016/0020-7462(66)90024-2

Cited by 50 publications

(12 citation statements)

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“…In particular, Figure 11b reports the maximum deflection as a function of the trans-membrane pressure. The broken line is the first-order approximated analytical solution reported by Iyengar and Naqvi [58], the solid line is the present FE numerical solution. In this case, the square membrane is 2 mm wide and 0.120 mm thick and Young’s modulus is 150 MPa.…”

Section: Methodsmentioning

confidence: 94%

“…In this case, the square membrane is 2 mm wide and 0.120 mm thick and Young’s modulus is 150 MPa. The Poisson ratio is 0.316, as the analytical solution proposed in reference [58] was specifically obtained for this value. Figure 11b shows that our numerical simulations are in good agreement with the approximate theoretical solution, the discrepancy increasing with TMP and being only ~3% at 0.8 bar.…”

Section: Methodsmentioning

confidence: 97%

“…A further validation of the FE model was performed by comparing numerical predictions with an analytical solution of structural mechanics for a two-dimensional domain [58]. A square body loaded with a uniform pressure and with all the edges clamped was considered.…”

Section: Methodsmentioning

confidence: 99%

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Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

Battaglia

Gurreri

Farulla

et al. 2019

IJMS

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In the membrane processes, a trans-membrane pressure (TMP) may arise due to design features or operating conditions. In most applications, stacks for electrodialysis (ED) or reverse electrodialysis (RED) operate at low TMP (<0.1 bar); however, large stacks with non-parallel flow patterns and/or asymmetric configurations can exhibit higher TMP values, causing membrane deformations and changes in fluid dynamics and transport phenomena. In this work, integrated mechanical and fluid dynamics simulations were performed to investigate the TMP effects on deformation, flow and mass transfer for a profiled membrane-fluid channel system with geometrical and mechanical features and fluid velocities representative of ED/RED conditions. First, a conservatively high value of TMP was assumed, and mechanical simulations were conducted to identify the geometry with the largest pitch to height ratio still able to bear this load without exhibiting a contact between opposite membranes. The selected geometry was then investigated under expansion and compression conditions in a TMP range encompassing most practical applications. Finally, friction and mass transfer coefficients in the deformed channel were predicted by computational fluid dynamics. Significant effects of membrane deformation were observed: friction and mass transfer coefficients increased in the compressed channel, while they decreased (though to a lesser extent) in the expanded channel.

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Section: Methodsmentioning

confidence: 94%

Section: Methodsmentioning

confidence: 97%

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Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

Battaglia

Gurreri

Farulla

et al. 2019

IJMS

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“…In our previous work [20], FE simulations were validated by a comparison with the authors' own bulge test results, obtained for 10 × 10 cm 2 samples of real ion exchange membranes, and with analytical solutions presented by Iyengar and Naqvi [32] for the deformation of a square elastic body loaded with a uniform pressure and having all the edges clamped. A good agreement was demonstrated, with discrepancies of only a few percent in the maximum displacement.…”

Section: Fe Meshmentioning

confidence: 99%

Pressure-Induced Deformation of Pillar-Type Profiled Membranes and Its Effects on Flow and Mass Transfer

et al. 2019

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In electro-membrane processes, a pressure difference may arise between solutions flowing in alternate channels. This transmembrane pressure (TMP) causes a deformation of the membranes and of the fluid compartments. This, in turn, affects pressure losses and mass transfer rates with respect to undeformed conditions and may result in uneven flow rate and mass flux distributions. These phenomena were analyzed here for round pillar-type profiled membranes by integrated mechanical and fluid dynamics simulations. The analysis involved three steps: (1) A conservatively large value of TMP was imposed, and mechanical simulations were performed to identify the geometry with the minimum pillar density still able to withstand this TMP without collapsing (i.e., without exhibiting contacts between opposite membranes); (2) the geometry thus identified was subject to expansion and compression conditions in a TMP interval including the values expected in practical applications, and for each TMP, the corresponding deformed configuration was predicted; and (3) for each computed deformed configuration, flow and mass transfer were predicted by computational fluid dynamics. Membrane deformation was found to have important effects; friction and mass transfer coefficients generally increased in compressed channels and decreased in expanded channels, while a more complex behavior was obtained for mass transfer coefficients.

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“…Although there has been sufficient work done on the large deflection of rectangular "plates," [113][114][115][116][117] work on the large deflection of rectangular "membranes" has been done to a lesser extent. The mechanics of membranes are appreciably different from those of plates-this can be inferred from the work on the exact deflection of circular and square plates [118] which was then followed by the exact deflection of rectangular membranes and plates.…”

Section: Introductionmentioning

confidence: 99%

Maximum Stresses in Rectangular Auxetic Membranes

Lim

2020

Physica Status Solidi (b)

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Auxetic materials exhibit a negative Poisson's ratio. Herein, the performance of rectangular auxetic membranes, under uniform load, is evaluated in terms of the maximum stress encountered. To facilitate convenient calculation, empirical modeling is conducted on the exact solution to reproduce displacement coefficients that are sufficiently accurate. A dimensionless maximum stress is then introduced to allow the effect from the membrane's Poisson's ratio and aspect ratio to be directly observed. Results reveal that 1) the dimensionless maximum stress reduces monotonically and nonmonotonically for conventional and auxetic membranes, respectively, 2) for the same Poisson's ratio magnitude the stresses in auxetic membranes are lower than those from conventional ones, 3) the optimal Poisson's ratio, on the basis of dimensionless maximum stress minimization, falls within the negative range, and 4) the dimensionless maximum stress minimization is especially effective for square membranes as well as very long and narrow membranes. It is therefore recommended that material auxeticity be taken into account-alongside geometrical and other material properties-in designing membranes and highly compliant very thin plates.

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Large deflections of rectangular plates

Cited by 50 publications

References 1 publication

Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

Pressure-Induced Deformation of Pillar-Type Profiled Membranes and Its Effects on Flow and Mass Transfer

Maximum Stresses in Rectangular Auxetic Membranes

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