To study the influence of the time-dependent behavior of various materials being considered for use in orbiting precision segmented reflectors, simple sandwich beam models are developed. The beam models included layers representing face sheets, core and adhesive. The issue of time-dependency is essential because the expected life of a reflector is on the order of 20 years. Using the principle of stationary potential energy, the elastic response of three-layer and five-layer symmetric sandwich beams to mechanical and thermally-induced loads is studied. The sensitivity of the three-layer and five-layer sandwich beams to reductions of the material properties is studied. Using the correspondence principle of viscoelasticity, these elastic models are transformed to time-dependent models. Representative cases of time-dependent material properties are used to demonstrate the application of the correspondence principle and evaluate the time-dependent response of the reflector. To verify the viscoelastic models, and to obtain a better idea of the amount of time-dependency to expect from the materials, simple time-dependent experiments on candidate materials were performed. Candidate materials include a quartz-epoxy face sheet material and a glass-imide honeycomb core material. The percent increase in strain for a constant stress for the quartz-epoxy in tension and the honeycomb in shear were measured. For both, a four-parameter fluid model captured the essential characteristics of their behavior. These four-parameter fluid models were then used in the three-layer sandwich beam model to predict the time-dependent response of the beam to three-point bending. This predicted response was compared to experimental results of a sandwich beam subjected to three-point bending. / Master of Science

Linear elastic theory of torsion and flexure of thin-walled beams as developed by Vlasov and Timoshenko respectively are well known and commonly used in everyday engineering practice. However there are noticeable differences between calculations and experimental results. The difference is partly due to one of the basic assumption of classical theory, namely that the secondary shear strains due to warping are negligible. In the present work a new three noded, with CO continuity, isoparametric beam finite element is developed based on a torsion theory by Benscoter. In the classical theory warping is assumed to be proportional to the rate of twist, whereas in Benscoter's theory it is assumed to be proportional to an independent quantity called the "warping function". The exact form of this function can be evaluated from equilibrium equations. This assumption of Benscoter's allows the formulation of a Co element based on the assumed displacement method. The other advantage of Benscoter's theory is that it takes into account the effects of secondary shear strains. These effects are quite significant for closed sections. The element is validated for several cases of a cantilevered beam of rectangular cross section and in every case the results are in good agreement with the exact solution. It is also shown that the element gives a very good representation of curved beams, for which there is torsional-flexural coupling. A number of cases of a curved I-beam under various loading and boundary conditions are analysed, and in every case the results agree closely with the analytical solution. In order to represent the torsional response the element uses seven degrees of freedom per node. This seventh degree of freedom is the "warping function" mentioned earlier. To make the element compatible with standard finite-element programs which have six degrees of freedom per node, static condensation is used. / Master of Science