Periodically perforated sheets(PS) are ubiquitous in nature as well as in engineered artifacts developed for aerospace, automotive, marine, nuclear and structural applications. PS are indispensable for saving weight and cost for aircraft; for enhancing safety and integrity of heat exchangers used in nuclear and thermal power stations. Ancient PS grills and lattice frames dating back to 1000 BC continue to inspire contemporary art and architecture, buildings and furniture. PS design and analysis, however, is a complex affair stemming from the inherent configurational anisotropy induced by periodicity. In addition, complex boundary conditions complicate the analysis. Unlike atoms in crystalline media, both shape and periodicity of perforations control this anisotropic nature. This thesis explores theoretical and numerical strategies for evaluating the effective anisotropic elastic moduli of PS. Following an experimental prelude for visualizing the PS stress field in a photoelastic sheet and a brief review of PS theory, this thesis proposes a novel theoretical numerical hybrid method for determining the Airy stress function constants. The proposed hybrid method can be exploited experimentally using automated vision based imaging technologies to measure the boundary displacements noninvasively. For determining the Airy constants periodic boundary conditions to the unit cell are applied, the displacement components around the PS hole boundary are obtained using FEM. Using these constants the PS stress field is reconstructed to assess the efficacy of the proposed hybrid method. It is observed that in general while the actual and the reconstructed stress fields agree reasonably well, more refined boundary data obtained either numerically or experimentally can enhance the accuracy further. The thesis then makes an extensive presentation of anisotropic moduli in a variety of PS designs configured on rectangular or square layouts. Conventional as well as some exotic patterns with cusps and satellite holes are examined, and the results are presented graphically to aid the designer. Finally, some special topics pertaining PS design and analysis are discussed to help overcome the inherent limitations of solutions based on applying periodic boundary conditions. In this vein, strategies for achieving a functionally graded PS are presented by altering the pitch and hole size. These strategies assume importance near boundaries as well as near concentrated forces inducing stress gradients. Other special topics include the applicability of tensor transformation rule to PS anisotropy. The effective bulk modulus which remains a scalar invariant is exploited to assess the validity of tensor transformation in a square PS. The rule of mixture widely used in homogenization of composite media is also discussed briefly. Thus, this thesis makes an attempt to demonstrate the power of blending micromechanics with experiments and FEM to aid in PS design and analysis.

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Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 61-63). Also available on the Internet.

Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 61-63). Also available on the Internet.

Rising global air temperatures are causing increased melting across the surfaces of large ice masses such as the Greenland Ice Sheet and the ice caps of Arctic Canada. The fraction of this melt that refreezes within the snow and firn has a large spatial variability across the surfaces of these ice masses. This spatial variability is an important control on the surface mass balance, and has important implications for the interpretation of satellite radar altimetry data sets. The sensitivity of large ice masses to climate change depends on changes in the melt-runoff relationship, and changes in the spatial extents of surface snow zones within the accumulation zone. Therefore, this thesis develops a model used to calculate melt, near-surface refreezing and surface runoff across the surface of a large ice mass. The model is used to predict both stratigraphic changes and bulk snow and firn properties over a melt season across a transect of points. A high-resolution snow and firn data set from Devon Ice Cap is used to calibrate and validate the model. It is then run across a transect covering the entire altitude range of the ice cap for the summers of 2004 and 2006. The model matches measured trends in bulk snowpack variables across the transect in both years. Calculated fraction of melt running off is similar in both years at ~44%, though is sensitive to change in air temperature. Surface mass balance (including internal accumulation), found to be +0.26 Gt in 2004 and +0.18 Gt in 2006, changes in a parabolic way for a linear air temperature change. The model is then applied to the Greenland Ice Sheet without altering any of the calibrated parameters. It is run for two melt seasons, 2004 and 2005, over which model output compares well with measurements of snow depth, sub-surface density and altitudes of snow surface boundaries. The wet snow line responds in a linear way to change in air temperature, and the runoff line is sensitive to the specified depth within the firn of the impermeable layer. Over the next century, the model shows that the dry snow zone will disappear completely under moderate warming scenarios, and the percolation zone will also disappear under intense warming scenarios. Including a more complicated representation of vertical meltwater percolation through the snow and firn grid substantially alters modelled autumn density profiles, and produces more accurate values of meltwater percolation depth and ice fraction within the autumn snowpack. However, bulk snowpack properties are of similar accuracy to the un-modified model. Scaling up of the model, in both spatial and temporal terms, will make it useful for assistance in the interpretation of satellite radar altimetry data sets, as well as assessing future changes in the spatial variability of refreezing and runoff, reducing the uncertainty in long term surface mass balance predictions across large ice masses.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 113-116).

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