Christopher H. Jenkins

Nonlinear Dynamic Response of Membranes: State of the Art

Membrane structures have been used since the earliest of times. Until recently, their analysis has relied chiefly on trial and error; however, modern methods of analysis are evolving. The deformations are nearly always of the large rotation and/or strain type and are thus inherently nonlinear. Static analysis can be considered as a special case of the dynamic analysis. This paper is concerned then with reviewing methods of nonlinear dynamic analysis of membrane structures. Two problems of analysis are associated with membrane structures: (i) shape (or form) finding; (ii) response (deformation and/or stress) analysis. Shape finding (ie, determination of the surface geometry given an initial prestress, generation of cutting patterns, etc) is nontrivial but well documented in the literature and is not considered in this paper. In this review attention is instead focused on formulation of field equations, wrinkling analysis, fluid/structure interactions, material nonlinearities, and computational methods.

Large deflection analysis of pneumatic envelopes using a penalty parameter modified material model

The computational challenge associated with pneumatic envelopes, such as balloons and parachutes, is due to the complication of their underconstrained and no-compression nature. Underconstrained behavior leads to large displacements without concomitant strain energy; no-compression behavior leads to a degenerate, wrinkled state. In this paper, we discuss issues surrounding modeling such structures. We provide a method to analyze pneumatic envelopes through a penalty parameter-modified constitutive relation embedded in a non-linear finite element code. Such an approach is also adaptable to the user-provided material function port available with many commercial finite element codes. Validation examples given are the inflated cantilever cylinder subjected to transverse tip load, inflated cantilever cylinder subjected to twist moment, and the inflation of a round parachute.

Recent advances in gossamer spacecraft

* Preface * Booms and Trusses * Membrane Mirrors in Space Telescopes * Membrane Wrinkling * Functional Materials for Smart Gossamer Spacecraft * Solar Sail Propulsion Technology Development * Thermal Measurement Techniques * Photogrammetric Measurement Methods * Subject Index * Author Index * Supporting Materials.

Dynamic Wrinkling of Viscoelastic Membranes

Problems associated with viscoelastic membrane structures have been documented, e.g., dynamic wrinkling and its effects on fatigue analysis and on snap loading. In the proposed analysis method, the constitutive equation is approximated by a finite difference equation and embedded within a nonlinear finite element spatial discretization. Implicit temporal integration and a modified Newton-Raphson method are used within a time increment. The stress-strain hereditary relation is formally derived from thermodynamic considerations. Use of modified strain-energy and dissipation functions facilitates the description of wrinkling during the analysis. Applications are demonstrated on an inflated cylindrical cantilever and on a submerged cylindrical membrane excited by waves.

Intelligent shape control for precision membrane antennae and reflectors in space

After a brief history of use in space about two decades ago, a resurgence of interest in membrane structures in space is developing, motivated in large part by a great potential for reduced launch mass and stowed volume. Applications for such structures range from planar configurations in solar sails, concentrators and shields, to inflatable lenticulars for radar, radio and optics. Three key factors are paramount for the success and user acceptance of this technology: deployment, longevity and performance. The performance hinges critically on the precision of the membrane surface. The amount of precision is highly mission dependent and may entail one or more of the following issues: surface smoothness, deviation from desired surface profile and slope error. Surface precision is often estimated to be between 1/50 to 1/20 of the wavelength of interest; thus values on the order of a micron (or less) to a millimeter root mean square (RMS) are often presented. It is unlikely that such surface precision can be achieved through purely passive means. This paper addresses the problem of modeling and controlling a class of nonlinear systems that can be considered as highly compliant structures. We consider specifically planar and inflatable membranes, which are represented by complex nonlinear multi-variable models. Boundary perturbations and thermal gradients are demonstrated to be potential actuation schemes for improving the reflector profile. Nonlinear controllers developed to improve performance are often dependent on state estimation and parameter identification procedures. The existence of these procedures, within the control strategy, increases the size of the algorithms, limiting the system performance in real-time. This research has as a main objective to create an intelligent controller based on feedback error learning, which is capable of extracting performance information from precision large membrane deployables and subsequently using this information to achieve maximum surface precision.

Effective Modulus of Creased Thin Membranes

In this study, the effective moduli of creased membranes were calculated by finite element analyses. Geometrically and materially nonlinear contact analyses were performed to simulate the entire process of creasing and uni-axial tensile test. First, the creased geometry of thin membranes was predicted from creasing simulation. The creased membranes were then subjected to a series of numerical uni-axial tensile tests to calculate the effective moduli. The creased and tensile geometries were also obtained by experiments and theoretical computations, respectively, and the results were compared. Numerical specimens with various crease gauges were considered to study the effect of the amount of creasing. The size effect of the specimen was also investigated.

Transverse vibration analysis for partly wrinkled membranes

The development is reported of a membrane-based wrinkle algorithm to analyze the transverse vibration behavior of partly wrinkled, annular, and three-sided membranes. This membrane-based wrinkle algorithm was implemented in the nonlinear finite element code ABAQUS, providing implementation of a true membrane constitutive model. First, the models were validated either with analytical solutions or experimental results. Then, the transverse vibration behavior of unwrinkled membrane models was studied. Finally, the presented constitutive model was incorporated in ABAQUS to inspect how wrinkling affects the vibration behavior of membranes. The frequency and mode shapes were investigated between the unwrinkled and wrinkled membranes. It was observed that even small amounts of wrinkling can significantly affect the modal frequencies of membranes. We offer physical explanation for these results.

Compliant structures in nature and engineering

Section I - Compliant Structures in Nature Chapter 1: Compliant structures and materials in animals Chapter 2: Compliance in plants Section II - Compliant Materials Chapter 3: Reinforced polyurethane flexible foams Chapter 4: Electroactive polymers as artificial muscles Section III - Compliant Mechanics Chapter 5: Mechanics of compliant structures Section IV - Compliant Structures in Engineering Chapter 6: Pressurized membranes in nature, technology and engineering Chapter 7: Rope and rope-like structures Chapter 8: Flexible-wing-based micro air vehicles Chapter 9: Compliant habitats Chapter 10: Gossamer spacecraft Section V - Compliant Structure Design Chapter 11: Design of compliant structures

State-of-the-Art Developments in the Field of Electroactive Polymers

The paper presents a brief review in the field of electroactive polymers. it outlines the main classes of electroactive polymers, their properties and applications. Current efforts to synthesize electroactive polymers with novel or improved characteristics along with the challenges, opportunities and future research directions in the subject area are discussed.

Shape Achievement of Optical Membrane Mirrors Using Coating/Substrate Intrinsic Stresses

The U.S. Air Force, as well as many other organizations, has evinced considerable interest in developing large gossamer membrane radio antennas and optical quality telescopes. A concept is discussed of global shape maintenance of a reflective polymer membrane element after curing, coating, and release from a precision casting mold of the desired parabolic shape. The idea involves manipulation of intrinsic stresses in the coating and its membrane substrate. Results from an axisymmetric, geometrically linear, shallow-shell theory are presented as closed-form solutions for the displacement fields. A unique condition emerges from these solutions, suggesting that zero deformations can occur in a 0-g environment. Results of a finite element analysis are presented, showing that if a coated membrane satisfying this condition is subjected to a 1-g loading, rms errors of 9.3 µm and 2.8 mm can be expected fo r1 -and 20-m-diam mirrors, respectively. However, in the case of a 1-g load, another condition follows from the theory, which, if met, predicts zero deformation in the 1-g environment. Additional results of the finite element analysis are presented that lend support to these conclusions.