•Form finding and optimization method for flexible-supported cable nets is proposed.•The interactive effect is captured by solving the non-compatibility problem.•Linear form for the determination of ...free node coordinates is derived.•The method is applied to mesh reflector antennas to demonstrate the efficiency.
Cable network structures consist of the cable networks and supporting frames, and the whole structures form the equilibrium states under the interactions between them. The existing methods haven’t considered the flexibility of the supporting frames and thus fail to fully capture the interactive effect between cable networks and flexible frames in the design optimization. This leads to the deviations between the design results and the real equilibrium states. Here we propose a form finding and design optimization approach for cable network structures with flexible frames. By solving the non-compatibility problem between cable and beam elements (due to rotation DOF), the cable network and supporting frame can be coupled to accurately model the real equilibrium state in the optimization model. We also derive the linear form for the determination of the free node coordinates from systematic equilibrium equations, which greatly reduces the computing cost of the optimization design and makes the multi-variable optimization more achievable. The proposed approach is effective for the form finding and design optimization of flexible supported cable networks with high surface accuracy requirements and multiple design variables. It is applied to mesh reflector antennas, and case studies are provided to verify the effectiveness of the methodology.
The work presented in this paper provides a reliable method to model and analyze smart beams with arbitrary sectional geometries and material properties, including initially curved and twisted beams. ...It incorporates the modified constitutive equations into the intrinsic equations to formulate a generalized set of solutions applicable for both the actuator and sensor application of piezoelectric smart beams. The radial field problem, sometimes referred to as radially electroded problem, where the potential is applied on the surfaces along the length (i.e., along the reference line) of the smart beam, is considered in the present study. Three different cases of smart beam geometries are discussed to highlight the capabilities of this method. VABS 4.0, a prerelease version of the variational asymptotic cross-sectional analysis tool for composite beams, is used to obtain the intermediate results containing sectional properties, which are used as inputs into the modified intrinsic equations. The main advantage of this method is its ability to quickly and accurately analyze deformation in smart beams. The values of displacements and rotations obtained along the length can be further used to recover the unknown 3D displacements, stresses and electric potentials using recovery relations. Successful verification of results obtained from the linear equations is presented and is accomplished using a commercially available finite element code ABAQUS.
The efficiency and operating envelope of rotorcraft are constrained by the speed of the rotor. Most helicopters operate with a constant rotor speed. Varying the speed of the rotor based on the ...operating condition could significantly improve the rotor's performance. In this study, a hingeless rotor model with elastic blades is built-in DYMORE to study various aspects of variable speed rotor technology. The rotor blades are modeled as one-dimensional beams using state-of-the-art beam theory known as the geometrically exact beam theory. An unsteady aerodynamics model with dynamic stall and finite-state dynamic inflow is used to obtain the aerodynamic loads acting on the rotor. The power savings that can be achieved at various advance ratios by varying the speed of the rotor is evaluated. Maximum power savings of 41% was achieved at a nominal advance ratio of 0.2. However, changing the rotor speed leads to vibration issues when a rotor blade passes through a resonance point. A methodology to identify the important resonance points for a given flight condition and rotor speed transition is also provided. The forces acting on the rotor blade during resonance crossings at different advance ratios are evaluated. It is found that the amplitude increase during resonance crossing is strongly dependent on the amplitude of the cyclic pitch angles during resonance.
High Altitude, Long Endurance (HALE) aircraft can achieve sustained, uninterrupted flight time if they use solar power. Wing morphing of solar powered HALE aircraft can significantly increase solar ...energy absorbency. An example of the kind of morphing considered in this paper requires the wings to fold so as to orient a solar panel to be hit more directly by the sun's rays at specific times of the day. An example of the kind of morphing considered in this paper requires the wings to fold so as to orient a solar panel that increases the absorption of solar energy by decreasing the angle of incidence of the solar radiation at specific times of the day. In this paper solar powered HALE flying wing aircraft are modeled with three beams with lockable hinge connections. Such aircraft are shown to be capable of morphing passively, following the sun by means of aerodynamic forces and engine thrusts. The analysis underlying NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft), a computer program that is based on geometrically exact, fully intrinsic beam equations and a finite-state induced flow model, was extended to include the ability to simulate morphing of the aircraft into a “Z” configuration. Because of the “long endurance” feature of HALE aircraft, such morphing needs to be done without relying on actuators and at as near zero energy cost as possible. The emphasis of this study is to substantially demonstrate the processes required to passively morph a flying wing into a Z-shaped configuration and back again.
The ability of a structural assembly to carry loads and forces determines how stable it will be over time. Viewing structural assemblages as comprising columns, beams, arches, rings, and plates, this ...book will introduce the student to both a classical and advanced understanding of the mechanical behavior of such structural systems under load and how modeling the resulting strains can predict the overall future performance-the stability-of that structure. While covering traditional beam theory, the book is more focused on elastica theory in keeping with modern approaches. This text will be an expanded and updated version a similar, previously published book, but with pedagogical improvements and updated analytical methods. This engineering textbook will provide a focused treatment on the study of how structures behave and perform when under stress loading, including plastic deformation and buckling. All advanced engineering students studying engineering mechanics, structural analysis and design, fatigue and failure, and other related subjects need to have this knowledge, and this book will provide it in a thorough and coherent fashion. Written by two of the world's leading engineering professors in this subject area, the pedagogy has been classroom-tested over many years and should find a receptive readership among both students and instructors. * An understandable introduction to the theory of structural stability, useful for a wide variety of engineering disciplines, including mechanical, civil and aerospace engineering * Covers both static and dynamic loads, for both conservative and nonconservative systems * Emphasizes elastic behavior under loads, including vertical buckling, torsional buckling and nonlinear affects of structural system buckling and stability * Case examples to illustrate real-world applications of Stability Theory.
Stiffened panels buckle under compressive loads which would degrade load-bearing capabilities of the structures. Fast yet accurate estimations of buckling loads and associated mode shapes are ...critical in the early stages of design and optimization. This paper presents a method based on the mechanics of structure genome (MSG) for the global buckling analysis of stiffened composite panels. The original geometrically nonlinear problem is mathematically reduced to a geometrically linear constitutive modeling of the structure genome and a geometrically nonlinear formulation of the macroscopic plate analysis. Validation case studies show that MSG is highly accurate and efficient as compared to the detailed finite element analysis. The buckling behaviors of stiffened panels under various boundary conditions and loadings are investigated.
By using the variational-asymptotic method, a universal asymptotic model for composite sandwich plates is established to achieve a great compromise between efficiency and accuracy through the ...synthesis of two competing theories: equivalent single-layer theories and layer-wise theories. When each layer of a sandwich structure can be individually considered as an elastic plate, and all material constitutive constants of such plates can be assumed to be of the same order, an equivalent plate model can be constructed from the equivalent single-layer perspective. It has an asymptotically correct energy functional, capable of capturing the transverse deformations, but still limited to the zeroth-order approximation. Then, by taking into account mismatched constituent material properties, a universal model for predicting mechanical behavior of composite sandwich plates is then systematically derived from the layer-wise perspective. It has another asymptotically correct energy functional with respect to the core-layer’s plate variables and implements into a single unified representation for subsequent application to sandwich plate problems with any face-to-core-stiffness and length-to-thickness ratios. In particular, to resolve theoretical shortcomings found in published works, complementary theoretical procedures are incorporated and used into the present approach by considering the interlaminar transverse stress continuity conditions as essential conditions in conventional layer-wise theories and by providing three-dimensional recovery relations as necessary ingredients for theories based on various dimensional reduction processes. Finally, as a preliminary validation, several examples available in the literature are presented and investigated. Together with critical comparisons of the three-dimensional exact solutions, the close agreement demonstrates the capability and accuracy of this present approach.
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