PhD thesis abstract - de Blonk, Brett
| Author: | de Blonk, Brett |
| Degree: | Doctor of Philosophy |
| SERC #: | 4-03 |
| File type: | PDF, 2900 kB |
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Optical-Level Structural Modelling of Membrane Mirrors for Spaceborne Telescopes
The astronomy and Earth observation communities desire ever-larger space telescopes, but launch costs limit mass and technology limits size. Current research in large aperture mirrors largely supports deployed rigid optics, but efforts have already begun to develop technology that offers the possibility of a mass-optimal approach: a reflecting surface tens of microns thick over tens of meters in diameter. The manufacturing of membranes has advanced such that the community is just beginning to produce membranes with su±cient quality for optics, but the analysis of membranes is conducted with various models without verification of accuracy. Accurate structural modelling tools are required to create valid operational concepts, specify manufacturing tolerances, and define structural control needs. In the current work the accuracy of different membrane modelling tools is defined and quantified over a range of representative problems. Torsion-free, axisymmetric statics models are considered as a first step toward understanding three-dimensional dynamic behavior.
An inverse solver is developed through a new approach to the geometrically-exact model, with initial and final shapes as model inputs and load distribution as output. The current approach opens the possibility of manufacturing-driven initial shapes and performance-driven final shapes. The inverse solver is used to establish a series of benchmark problems with geometries traceable to doubly-curved telescope mirrors. Finite di®erence solutions to the benchmark problems lead to relationships between geometry, load, and model error; in the correlation with model error, geometry and load limits for optical-quality predictions are established for a set of models. Model error is defined according to a metric significant to optics, the area-averaged standard deviation of the pathlength error created from the inexact shape prediction. Hookean constitutive law is exactly derived for curved membranes, and constitutive relations from the literature are demonstrated to be inconsistent and contain more error than simpler, consistently-derived relations. Numerical considerations, from level of discretization to endpoint handling, are also discussed for high-accuracy solutions. The model error limits, constitutive relation derivations, and numerical-implementation considerations are combined into a guideline for modelling the optical-level structural behavior of curved membrane mirrors.