AEROSPACE ENGINEERS DEVELOP SOLAR CONCENTRATORS FOR BOOSTING SATELLITES TO HIGHER ORBIT WITH NONLINEAR FINITE ELEMENT ANALYSIS SOFTWARE

An artist's conception of a solar thermal propulsion vehicle shows the two inflatable, polyimide solar concentrators developed by SRS Technologies. The concentrators collect the Sun's energy and use it to transfer satellites to a higher energy, geosynchronous orbit required by communications and surveillance satellites. SRS Technologies was able to use the nonlinear static stress analysis capabilities of ALGOR, Inc. to predict the shape and stresses of the solar concentrators and optimize their geometry to form the best optical shape in orbit for collecting solar energy.

September 6, 1999, Pittsburgh, Pennsylvania -- Each year more satellites are boosted into orbit, providing communications links, military surveillance, data about the Earth's climate, even digital television signals. The United States Air Force Research Laboratory's Propulsion Directorate at Edwards Air Force Base, California, is developing a low-cost method for transferring satellites from lower-Earth orbits to a higher energy, geosynchronous orbit required by the surveillance satellites that help the military to safeguard our nation's security and the communications satellites on which we all depend. The new concept is called "solar thermal propulsion" and it involves highly accurate inflatable solar concentrators developed by SRS Technologies (SRS), Huntsville, Alabama. The concentrators drastically reduce cost-to-orbit because they are lightweight, easily stowed on a launch vehicle and use concentrated solar energy to heat the propellant, providing the thrust needed to achieve a higher orbit.

When designing the solar concentrators, which are made of castable, clear polyimide film, SRS engineers realized the concentrators may experience excess deflection when inflated in orbit. Excess deflection caused by inflation loading would prevent the pre-molded concentrators from forming the ideal surface shape needed to collect the maximum amount of solar energy for propulsion. SRS was able to use the nonlinear static stress analysis software capabilities of Pittsburgh-based ALGOR, Inc. to predict the shape and stresses of the concentrators during inflation loading. The company then optimized the concentrator's geometry with ALGOR's software to form the best optical shape in orbit for collecting solar energy. The company also saved thousands of dollars by avoiding the manufacture and testing of prototypes.

Solar Concentrators Must Meet Optical Requirements When Inflated in Orbit

When deployed around 2002, each solar thermal propulsion vehicle will have two pre-molded, inflatable solar concentrators made almost entirely of a new polyimide material developed by the NASA Langley Research Center, Hampton, Virginia. The LaRC-CP1^TM polyimide is a clear, lightweight material with a large thermal operating range. It is ideal for this aerospace application because it effectively forms compound curved shapes, it is resistant to UV radiation, stable in a space vacuum and lightweight compared to glass or metal optics.

The solar concentrators must be designed so that their 9 x 13-foot reflectors achieve a precise surface slope when inflated in orbit. A precise shape is needed to focus an optimal amount of the Sun's energy on a heat exchanger engine that heats hydrogen gas. The expanding gas provides enough thrust to transfer the satellite to the higher orbit.

SRS Technologies' solar concentrators are made almost entirely of castable, clear polyimide film, a lightweight material compared to glass or metal optics. Jim Moore, program manager at SRS' Aerospace Directorate, modeled one-half of the concentrator's reflector and the Kevlar threads that attach it to an inflatable support ring using Superdraw III, ALGOR's single user interface and precision finite element model-building tool. He then used ALGOR's Accupak/VE nonlinear stress analysis capabilities to optimize the reflector's geometry to form the best optical shape in orbit for collecting solar energy.

To avoid the expense and time involved in creating and testing prototype solar concentrators to ensure they form the necessary surface shape, SRS used ALGOR's Accupak/VE nonlinear static loading analysis capabilities to test the solar concentrators on a computer. (This analysis could also have been performed with ALGOR's Accupak/NLM software, which offers the static nonlinear loading capabilities and nonlinear material models included as part of Accupak/VE.)

Physical Test Proves ALGOR Can be Used for Optimization

Prior to optimizing the solar concentrator's design, SRS first performed a physical test to verify the accuracy of ALGOR software. They created a solar concentrator prototype based on specifications provided by SRS optical engineers that dictated the shape required to collect the optimal amount of solar energy for propulsion. Engineers applied various internal pressures to the physical prototype and measured the variances in deflection. These measurements were compared to ALGOR's software analysis results for the same applied internal pressures on a 3-D ALGOR model. The results correlated 94 percent, confirming that ALGOR could be used to optimize the solar concentrator design.

"We learned the value of verifying the software's accuracy first with a physical test," said Jim Moore, program manager at SRS' Aerospace Directorate. "It gave us the confidence that ALGOR's software analysis results were indicative of real-world results. It also enabled us to save thousands of dollars on tooling for solar concentrator prototypes that would have been necessary to optimize the design and many months building and testing those prototypes."

Modeling the Ideal Solar Concentrator

Once Moore was confident that the pressure loadings would yield real-world results, he began working on the ALGOR model he wished to optimize. A solar concentrator consists of two polyimide reflectors. Each reflector has two symmetrical .001-inch-thick layers that are bound together at their edges. One contains a reflective coating for focusing solar energy. Hydrogen gas is released between the two layers in orbit to inflate them to the required optical slope.

Moore modeled one-half of a reflector using Superdraw III, ALGOR's single user interface and precision finite element model-building tool. He modeled the polyimide layer without the reflective coating for simplification because SRS engineers had calculated that the coating is too thin to have a significant effect on the reflector's displacement. He used 3-D plate elements for the reflector and beam elements to represent a catenary suspension system made of Kevlar threads that attach the reflector to an inflatable polyimide support ring. He then applied fixed boundary conditions at the catenaries' ends to represent their attachment to the support ring. The support ring maintains the optical shape of the reflector, but was not modeled with ALGOR because the support ring is relatively insensitive to small deflections.

Moore used Supergen, Algor's automatic 2-D surface mesh engine, to create an FEA surface mesh and performed manual mesh refinement to enhance the surface mesh before generating a solid FEA mesh. He specified the material properties for LaRC-CP1 polyimide film manufactured in SRS' Polymer Manufacturing Laboratory. The catenaries' material properties were based on published data for the space-rated material. He specified an elastic material model to best represent the polyimide's stress-strain curve.

Based on previous analyses with ALGOR, SRS determined that a pressure of 9.032 x 10^-4 PSI applied to each element's surface was necessary to create stress of approximately 200 PSI in the reflector's film. This pressure represented the required hydrogen gas pressure needed to inflate the film enough to remove wrinkles upon inflation, but avoid tearing. The pressure level would also create tension in the supporting catenaries that would best contribute to the ideal surface shape for collecting solar energy.

Moore subjected the solar concentrator model to increased pressure loading slowly over time. He found that applying the load incrementally resulted in a reduced analysis run time and improved convergence.

Nonlinear Static Stress Analysis Predicts Deflections and Stress Caused by Inflation

After performing the nonlinear analysis with ALGOR, Moore used the displacement results to determine the inflated concentrator's deviation from the ideal slope. Then he adjusted the original geometry where necessary to account for the displacements. For example, the geometry of a node that experienced deflection measuring one inch in the Z-direction was altered to negative one inch in the Z-direction. He also noted from ALGOR's analysis results that stress was near 200 PSI in the reflector's film. This is the optimal amount of stress needed to inflate the film to remove wrinkles, but not tear.

When re-analyzed with ALGOR, the revised concentrator model's shape achieved the required optical slope. SRS will create a prototype concentrator based on ALGOR's analysis results later this year. The introduction of these highly accurate solar concentrators to the aerospace industry will reduce the cost of transferring satellites to a geosynchronous orbit while using a clean, abundant and safe power source - the Sun.

SRS Technologies used the displacement results from ALGOR's nonlinear static stress analysis to determine the inflated polyimide deflector's deviation from the ideal slope. The company then adjusted the original geometry where necessary to account for the displacements so that it would form the best optical shape in orbit. Engineers also noted ALGOR's stress results, which verified that stress was near 200 PSI in the reflector's film, the optimal amount of stress needed to inflate the film to remove wrinkles, but not tear.