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Academic literature on the topic 'Curved Beam'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Curved Beam"

1

Wang, Yuquan. "Improved Strategy of Two-Node Curved Beam Element Based on the Same Beam’s Nodes Information." Advances in Materials Science and Engineering 2021 (September 2, 2021): 1–9. http://dx.doi.org/10.1155/2021/2093096.

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The curved beam with a great initial curvature is the typical structure and applied widely in real engineering structures. The common practice in the current literature employs two-node straight beam elements as the elementary members for stress and displacement analysis, which needs a large number of divisions to fit the curved beam shape well and increases computational time greatly. In this paper, we develop an improved accurate two-node curved beam element (IC2) in 3D problems, combining the curved Timoshenko beam theory and the curvature information calculated from the same beam curve. The strategy of calculating the curvature information from the same bean curve in the IC2 beam element and then transferring the curvature information to the two-node straight beam element can greatly enhance the accuracy of the mechanical analysis with no extra calculation burden. We then introduce the finite element implementation of the IC2 beam element and verify by the complex curved beam analysis. By comparison with simulation results from the straight two-node beam element in the MIDAS (S2-MIDAS) and the three-node curved beam element adopted in the ANSYS (C3-ANSYS), the simulation results of the typical quarter arc examples under constant or variable curvature show that the IC2 beam element based on curved beam theory is a combination of efficiency and accuracy. And, it is a good choice for analysis of complex engineering rod structure with large initial curvature.

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2

Mao, Hancheng, Guangbin Yu, Wei Liu, and Tiantian Xu. "Out-of-Plane Free Vibration and Forced Harmonic Response of a Curved Beam." Shock and Vibration 2020 (December 29, 2020): 1–14. http://dx.doi.org/10.1155/2020/8891585.

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Based on the governing differential equation of out-of-plane curved beam, the wave propagation behavior, free vibration, and transmission properties are presented theoretically in this paper. Firstly, harmonic wave solutions are given to investigate the dispersion relation between frequency and wave number, cut-off frequency, displacement, amplitude ratio, and phase diagram. The frequency spectrum results are obtained to verify the work by Kang and Lee. Furthermore, natural frequencies of the single and composite curved beam are calculated through solving the characteristic equation in the case of free-free, clamped-clamped, and free-clamped boundaries. Finally, the transfer matrices of the out-of-plane curved beam are derived by combining the continuity between the different interfaces. The transmissibility curves of the single and composite curved beam are compared to find the vibration attention band. This work will be valuable to extend the study of the out-of-plane vibration of curved beams.

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Pan, Ke-Qi, and Jin-Yang Liu. "Geometric nonlinear dynamic analysis of curved beams using curved beam element." Acta Mechanica Sinica 27, no. 6 (November 18, 2011): 1023–33. http://dx.doi.org/10.1007/s10409-011-0509-x.

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4

Nadi, Azin, and Mehdi Raghebi. "Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis." FME Transactions 49, no. 3 (2021): 615–26. http://dx.doi.org/10.5937/fme2103615n.

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Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

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5

Song, Yu Min, and Ding Jun Wu. "Establishment of Vibration Differential Equation and Analysis of Dynamics Characteristics for Curved Beam." Advanced Materials Research 250-253 (May 2011): 1329–33. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1329.

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In this paper, a differential segment of curved beam in the vibration state is analyzed, and the internal force equilibrium equations are established, then the vibration differential equations of curved beam are derived by considering Timoshenko’s geometric equations and physical equations. The vibration differential equations derived are similar to the Vlasov’s static differential equation of curved beam. By analyzing the vibration differential equations, some characteristics of vibration are obtained, and ideas of solving the vibration differential equations are also proposed. The vibration differential equations of curved beam can be reduced to those of corresponding straight beams, validating the derived vibration differential equation of curved beam.

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6

Wang, Guang-Ming, Li Zhu, Xin-Lin Ji, and Wen-Yu Ji. "Finite Beam Element for Curved Steel–Concrete Composite Box Beams Considering Time-Dependent Effect." Materials 13, no. 15 (July 22, 2020): 3253. http://dx.doi.org/10.3390/ma13153253.

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Curved steel–concrete composite box beams are widely used in urban overpasses and ramp bridges. In contrast to straight composite beams, curved composite box beams exhibit complex mechanical behavior with bending–torsion coupling, including constrained torsion, distortion, and interfacial biaxial slip. The shear-lag effect and curvature variation in the radial direction should be taken into account when the beam is sufficiently wide. Additionally, long-term deflection has been observed in curved composite box beams due to the shrinkage and creep effects of the concrete slab. In this paper, an equilibrium equation for a theoretical model of curved composite box beams is proposed according to the virtual work principle. The finite element method is adopted to obtain the element stiffness matrix and nodal load matrix. The age-adjusted effective modulus method is introduced to address the concrete creep effects. This 26-DOF finite beam element model is able to simulate the constrained torsion, distortion, interfacial biaxial slip, shear lag, and time-dependent effects of curved composite box beams and account for curvature variation in the radial direction. An elaborate finite element model of a typical curved composite box beam is established. The correctness and applicability of the proposed finite beam element model is verified by comparing the results from the proposed beam element model to those from the elaborate finite element model. The proposed beam element model is used to analyze the long-term behavior of curved composite box beams. The analysis shows that significant changes in the displacement, stress and shear-lag coefficient occur in the curved composite beams within the first year of loading, after which the variation tendency becomes gradual. Moreover, increases in the central angle and shear connection stiffness both reduce the change rates of displacement and stress with respect to time.

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7

Khaleel, W. H., A. A. Talal, N. H. Baidaa, K. S. Abdul-Razzaq, and A. A. Dawood. "Previous Research Works on Reinforced Concrete Curved Beams." E3S Web of Conferences 318 (2021): 03011. http://dx.doi.org/10.1051/e3sconf/202131803011.

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The current research work summarizes some previous research works on horizontally curved beams. Because of curvature, torsional effects in the analysis and design should be included. Diameter of ring beam, number of supports, beam width, compressive strength of the concrete, and bearing plate width. Which can be summarized from previous studies is that increasing diameter of ring by about 25-75% decreases the capacity load by about 14-36%, while increasing number of supports by about 33-100%, beam width by about 25-75%, compressive strength of concrete by about 24-76%, and bearing plate width by about 25-75% increases the capacity load by about 62-189%, 25-75%, 24-76%, and 5-16%, respectively due to the beam section increase and/or its properties. Frequently, reinforced concrete deep ring beams exhibit shear failure in a manner similar to straight beams. Strut and tie model (STM) and plastic analysis are useful tools for efficiently analyzing ring or curved deep beams. In addition, the nonlinear three-dimensional finite element modeling is typical for predicting the deep curved beams strength and behavior.

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8

Li, Xiaofei, Haosen Zhai, and Dongyan Zhao. "Out-of-Plane Dynamic Response of Elliptic Curved Steel Beams Based on the Precise Integration Method." Buildings 13, no. 2 (January 28, 2023): 368. http://dx.doi.org/10.3390/buildings13020368.

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The dynamic response of curved steel beams has long been a research focus in curved bridges. The formula for the dynamic response under a moving load was derived according to the basic principles of the precise integration method. Combined with the necessary conditions of this method, the stiffness matrix of a variable-curvature beam was obtained using matrix inversion, and the mass matrix of the structure was obtained using the concentrated mass method. The dynamic response of the structure was obtained by applying moving loads and masses at different speeds to the curved beam. Finite element simulation and laboratory curved-beam models of the variable-curvature steel beam were established. By comparing the laboratory measurement results against the theoretical data obtained in this study, we propose that our theory has practical engineering significance. It can be used as a theoretical basis for the study of variable curvature steel beam structures and for guiding the construction of curved beams.

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9

Saji, Ms Ansu P., and Ms Lekshmi Priya R. "Flexural Behaviour of SFRC Curved Deep Beams." International Journal for Research in Applied Science and Engineering Technology 10, no. 7 (July 31, 2022): 574–79. http://dx.doi.org/10.22214/ijraset.2022.45372.

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Abstract: As per IS 456:2000, deep beams can be defined as the structures that having span to depth ratio less than 2 for a simply supported beam and 2.5 for a continuous beam. Also these members are loaded on one face and supported on the opposite face. Uses of curved deep beams are increasing in structures like rounded corners of buildings, circular balconies, water tanks etc. Steel Fiber Reinforced Concrete (SFRC) is a concrete with short, discrete lengths of steel fibers which are randomly dispersed. The load deformation behavior of curved deep beam of different curvatures gives an idea about the effect of curvature on the performance of curved deep beam. The structure that generates comparatively small deformation within the applied load can be considered as relatively safe. This paper illustrates the effect of curvature or central angle on the ultimate load behavior of SFRC curved deep beam and analyzing its flexural behaviour. Steel Fiber Reinforced Concrete with 1% steel fiber is used in the current study. The central subtended angles adopted for the study are 00 , 450 , 600 , 900 , 1200 , and 1800 . As the central subtended angle increases, curvature also increases. The analysis of the structure has been carried out using ANSYS Software

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10

Koziey, B. L., and F. A. Mirza. "Consistent curved beam element." Computers & Structures 51, no. 6 (January 1994): 643–54. http://dx.doi.org/10.1016/s0045-7949(05)80003-3.

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Dissertations / Theses on the topic "Curved Beam"

1

Jagirdar, Saurabh. "Kinematics of curved flexible beam." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001853.

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2

Uzhan, Tevfik. "Experimental Analysis Of Curved Laminated Beam." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612114/index.pdf.

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ABSTRACT EXPERIMENTAL ANALYSIS OF CURVED LAMINATED GLASS BEAM Uzhan, Tevfik M.S., Department of Engineering Sciences Supervisor: Prof. Dr. M. Zü
lfü
ASik May 2010, 33 Pages In this thesis, experimental studies are carried out on curved laminated glass beams to form a database for the scientists who may like to test their mathematical models. Beams which are only free to rotate and constrained in radial direction at both ends are tested to make the data available for further calculations. Test setup is prepared to minimize error that could occur due to test setup and data readings. Material testing machine and 4 channel data collecting machine are used to measure the signals at the strain gauges located over the glass beam. Within the range of force applied to the specimens, laminated curved beam shows linear behavior without any fracture. Data collected from the specimens are in conformance with each other. Results obtained from experiments are compared with the results obtained from the mathematical model developed by ASik and Dural (2006). As it is observed from the graphs presented, experimental results from the tests and numerical results from the mathematical model are in good agreement.

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3

Zhang, Cheng. "A curved beam element and its application to traffic poles." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ32291.pdf.

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4

Li, Jing. "A Geometrically nonlinear curved beam theory and its finite element formulation." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/31071.

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This thesis presents a geometrically exact curved beam theory, with the assumption that the cross-section remains rigid, and its finite element formulation/implementation. The theory provides a theoretical view and an exact and efficient means to handle a large range of nonlinear beam problems. A geometrically exact curved/twisted beam theory, which assumes that the beam cross-section remains rigid, is re-examined and extended using orthonormal reference frames starting from a 3-D beam theory. The relevant engineering strain measures at any material point on the current beam cross-section with an initial curvature correction term, which are conjugate to the first Piola-Kirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The Green strains and Eulerian strains are explicitly represented in terms of the engineering strain measures while other stresses, such as the Cauchy stresses and second Piola-Kirchhoff stresses, are explicitly represented in terms of the first Piola-Kirchhoff stresses and engineering strains. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the three-dimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also re-examined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the three-dimensional beam level. The cross-section elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. For the finite element formulation and implementation of the curved beam theory, some basic concepts associated with finite rotations and their parametrizations are first summarized. In terms of a generalized vector-like parametrization of finite rotations under spatial descriptions (i.e., in spatial forms), a unified formulation is given for the virtual work equations that leads to the load residual and tangent stiffness operators. With a proper explanation, the case of the non-vectorial parametrization can be recovered if the incremental rotation is parametrized using the incremental rotation vector. As an example for static problems, taking advantage of the simplicity in formulation and clear classical meanings of rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to conservative and non-conservative loads. Several examples are used to test the formulation and the Fortran implementation of the element.
Master of Science

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5

Bhouri, Mohamed Aziz. "Curved beam based model for piston-ring designs in internal combustion engines." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/111772.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 169-173).
Characterizing the piston ring behavior is inherently associated with the oil consumption, friction, wear and blow-by in internal combustion engines. This behavior varies along the ring's circumference and determining these variations is of utmost importance for developing ring-packs achieving desired performances in terms of sealing and conformability. This study based on straight beam model was already developed but does not consider the lubrication sub-models, the tip gap effects and the characterization of the ring free shape based on any final closed shape. In this work, three numerical curved beam based models were developed to study the performance of the piston ring-pack. The conformability model was developed to characterize the behavior of the ring within the engine. In this model, the curved beam model is adopted with considering ring-bore and ring-groove interactions. This interactions include asperity and lubrication forces. Besides, gas forces are included to the model along with the inertia and initial ring tangential load. In this model we also allow for bore, groove upper and lower flanks thermal distortion. We also take into account the thermal expansion effect of the ring and the temperature gradient from inner diameter (ID) to outer diameter (OD) effects. The piston secondary motion and the variation of oil viscosity on the liner with its temperature in addition to the existence of fuel and the different hydrodynamic cases (Partially and fully flooded cases) are considered as well. This model revealed the ring position relative to the groove depending on the friction, inertia and gas pressures. It also characterizes the effect of non-uniform oil distribution on the liner and groove flanks. Finally, the ring gap position within a distorted bore also reveals the sealing performance of the ring. Using the curved beam model we also developed a module determining the twist calculation under fix ID or OD constraint. The static twist is an experimental characterization of the ring during which the user taps on the ring till there is a minimum clearance between the ring lowest point and the lower plate all over the ring's circumference but without any force contact. Our last model includes four sub-models that relate the ring free shape, its final shape when subjected to a constant radial pressure (this final shape is called ovality) and the force distribution in circular bore. Knowing one of these distribution, this model determines the other two. This tool is useful in the sense that the characterization of the ring is carried out by measuring its ovality which is more accurate than measuring its free shape or force distribution in circular bore. Thus, having a model that takes the ovality as an input is more convenient and useful based on the experiments carried out to characterize the ring.
by Mohamed Aziz Bhouri.
S.M.

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6

Bhouri, Mohamed Aziz. "Curved beam based model for piston-ring designs in internal combustion engines." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/111772.

Full text

Abstract:

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 169-173).
Characterizing the piston ring behavior is inherently associated with the oil consumption, friction, wear and blow-by in internal combustion engines. This behavior varies along the ring's circumference and determining these variations is of utmost importance for developing ring-packs achieving desired performances in terms of sealing and conformability. This study based on straight beam model was already developed but does not consider the lubrication sub-models, the tip gap effects and the characterization of the ring free shape based on any final closed shape. In this work, three numerical curved beam based models were developed to study the performance of the piston ring-pack. The conformability model was developed to characterize the behavior of the ring within the engine. In this model, the curved beam model is adopted with considering ring-bore and ring-groove interactions. This interactions include asperity and lubrication forces. Besides, gas forces are included to the model along with the inertia and initial ring tangential load. In this model we also allow for bore, groove upper and lower flanks thermal distortion. We also take into account the thermal expansion effect of the ring and the temperature gradient from inner diameter (ID) to outer diameter (OD) effects. The piston secondary motion and the variation of oil viscosity on the liner with its temperature in addition to the existence of fuel and the different hydrodynamic cases (Partially and fully flooded cases) are considered as well. This model revealed the ring position relative to the groove depending on the friction, inertia and gas pressures. It also characterizes the effect of non-uniform oil distribution on the liner and groove flanks. Finally, the ring gap position within a distorted bore also reveals the sealing performance of the ring. Using the curved beam model we also developed a module determining the twist calculation under fix ID or OD constraint. The static twist is an experimental characterization of the ring during which the user taps on the ring till there is a minimum clearance between the ring lowest point and the lower plate all over the ring's circumference but without any force contact. Our last model includes four sub-models that relate the ring free shape, its final shape when subjected to a constant radial pressure (this final shape is called ovality) and the force distribution in circular bore. Knowing one of these distribution, this model determines the other two. This tool is useful in the sense that the characterization of the ring is carried out by measuring its ovality which is more accurate than measuring its free shape or force distribution in circular bore. Thus, having a model that takes the ovality as an input is more convenient and useful based on the experiments carried out to characterize the ring.
by Mohamed Aziz Bhouri.
S.M.

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7

Moghal, Khurram Zeshan. "Analysis of a thin-walled curved rectangular beam with five degrees of freedom." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-11112003-122013.

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8

Gupta, Sayan. "Vibration Analysis Of Structures Built Up Of Randomly Inhomogeneous Curved And Straight Beams Using Stochastic Dynamic Stiffness Matrix Method." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/224.

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Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of systems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assessment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understanding phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with difficulties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further compounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the formulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochastic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is considered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the previous chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteristics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinctive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical solutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been accepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

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9

Gupta, Sayan. "Vibration Analysis Of Structures Built Up Of Randomly Inhomogeneous Curved And Straight Beams Using Stochastic Dynamic Stiffness Matrix Method." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/224.

Full text

Abstract:

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of systems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assessment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understanding phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with difficulties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further compounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the formulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochastic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is considered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the previous chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteristics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinctive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical solutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been accepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

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Patlolla, Vamsidhar. "Improvements and effects of porosity on interlaminar tensile strength of curved beam carbon fiber composites." Thesis, Wichita State University, 2012. http://hdl.handle.net/10057/5607.

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The orthotropic nature of composites provides excellent performance in the fiber direction, but it is susceptible to failure in the orthogonal direction. Failure due to the delamination is limited to composites, and has an adverse consequence on its mechanical properties. The interlaminar tensile (ILT) strength of a composite part is compromised by delamination failure caused mainly by the applied loads and environmental factors. This phenomenon creates a challenge in design and manufacturing of composite parts for the aerospace industry. This study is focused on improving the ILT strength of a curved composite laminate by suppressing failure modes associated with free edge effects and to evaluate the ILT strength of a curved section with various porosities. Composite panels were built on an angle bend tool using the fiber reinforced carbon/epoxy tape pre-pregs. The manufactured panels were machined using a water jet to produce test coupons as required by ASTM 6415. The curved sections of the test coupons were reinforced with metal clamps manufactured from aluminum 7075-O alloy and another pre-preg material (glass fiber reinforced pre-preg). The observed ILT strength of the reinforced coupons was found to be much higher than the baseline because the reinforcement reduces the effects of the stresses induced by the free edge of the composite specimen. There was a 25% increase in the interlaminar tensile strength for the coupons reinforced by the metal clamps and a 21% increase in strength for the coupons reinforced with the glass pre-preg material. We also observed that with various percentages of porosity, the ILT strength varied significantly, which needs to be addressed in the future studies. The failure of the coupons occurred due to the delaminations caused by the interlaminar stresses under the applied loads. This study may open up new possibilities to reinforce the various fiber reinforced composites used in many manufacturing industries in the field.
Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical Engineering

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Books on the topic "Curved Beam"

1

A, Pifko, United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., and Grumman Aerospace Corporation. Research and Development Center., eds. Addendum to the DYCAST user's manual describing the curved, warp beam finite element. Washington, D.C: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1991.

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Tran, Fleischer Van, and Hugh L. Dryden Flight Research Center, eds. Extension of Ko straight-beam displacement theory to deformed shape predictions of slender curved structures. Edwards, CA: National Aeronautics and Space Administration, Dryden Flight Research Center, 2011.

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United States. National Aeronautics and Space Administration., ed. A semi-micromechanic interlaminar strain analysis on curved-beam specimens: Final report, April-December 31 1990 under grant NCC 2-673. [Washington, DC: National Aeronautics and Space Administration, 1990.

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Ranta-Maunus, Alpo. Curved and cambered glulam beams. Espoo: Technical Research Centre of Finland, 1994.

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Hong, Yoo Chai, ed. Analysis and design of curved steel bridges. New York: McGraw-Hill, 1988.

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Clean Air Technology Center (U.S.). Ultraviolet and electron beam (UV/EB) cured coatings, inks and adhesives. Research Triangle Park, N.C: U.S. Environmental Protection Agency, Office of Air Quality Planning and Standards, 2001.

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Rossikhin, Yury A., and Marina V. Shitikova. Dynamic Response of Pre-Stressed Spatially Curved Thin-Walled Beams of Open Profile. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20969-7.

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Rossikhin, Yury A. Dynamic Response of Pre-Stressed Spatially Curved Thin-Walled Beams of Open Profile. Berlin, Heidelberg: Yury A. Rossikhin, 2011.

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Lydzinski, John C. Finite element analysis of the Wolf Creek multispan curved girder bridge. Charlottesville, Va: Virginia Transportation Research Council, 2008.

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Gowda, Shankare. Duration of load effect on curved glulam beams: Part 2. Long term load tests and analysis. Espoo, Finland: VTT, Technical Research Centre of Finland, 1998.

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Book chapters on the topic "Curved Beam"

1

Barber, J. R. "Curved Beam Problems." In Solid Mechanics and Its Applications, 107–19. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2454-6_10.

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Barber, J. R. "Curved Beam Problems." In Solid Mechanics and Its Applications, 135–48. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3809-8_10.

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Barber, J. R. "Curved Beam Problems." In Solid Mechanics and Its Applications, 147–62. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-15214-6_10.

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Prathap, G. "Simple Curved Beam Elements." In The Finite Element Method in Structural Mechanics, 73–98. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-3319-9_3.

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Prathap, G. "General Curved Beam Elements." In The Finite Element Method in Structural Mechanics, 153–99. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-3319-9_6.

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Gan, Buntara S. "Circular Curved Beam Element Examples." In An Isogeometric Approach to Beam Structures, 193–203. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56493-7_7.

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Gan, Buntara S. "General Curved Beam Element Examples." In An Isogeometric Approach to Beam Structures, 205–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56493-7_8.

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Gan, Buntara S. "Free Curved Beam Element Examples." In An Isogeometric Approach to Beam Structures, 217–24. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56493-7_9.

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Xu, Zhi-wei, Li-xia Lin, Nan-hong Ding, and Lei Chen. "The External Prestress Effect of Curved Tendons on the Natural Vibration Characteristics of Steel Beams." In Advances in Frontier Research on Engineering Structures, 517–26. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8657-4_46.

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AbstractIn order to explore the external prestress effect of the curved tendons on the stiffness and natural vibration characteristics of the steel beam, this paper deduced the calculation equation of the natural frequency on the external prestressed simply supported steel beam of the curved arrangement, which was based on the Hamilton principle. The natural frequency is calculated by combining the example of I-shaped simply supported steel beam, which was analyzed and verified by establishing the finite element model. The results show that: the calculation of the equation is well demonstrated by the finite element results, and the validity of model equation was verified. When the applied prestress increases, the natural vibration frequency decreases and the change range is not large, which indicates that the magnitude of the prestress has little effect on the natural frequency of simply supported steel beams.

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Tomioka, Takahiro. "Vibration of Straight and Curved Beam Coupled Systems." In Lecture Notes in Mechanical Engineering, 929–37. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38077-9_108.

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Conference papers on the topic "Curved Beam"

1

Zhao, Yiming, and Jason D. Dykstra. "Vibrations of Curved and Twisted Beam." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9880.

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This paper studies the vibration of beams in 3D space with arbitrary shape. Based on results from differential geometry of curves, a set of beam vibration dynamics equations is developed, comprising six partial differential equations (PDE). The beam dynamics equations account for both the in-plane and out-of-plane beam vibrations simultaneously. In addition, the equations explicitly capture the coupling between different vibration mode types, which occur when the beam exhibits geometric irregularities such as bending, torsion, and twisting. The proposed beam dynamics equations are solved numerically. Comparison between experimental results and numerical results obtained by solving the PDEs proposed in this paper shows a good match for in-plane and out-of-plane curved beam vibrations.

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Tanaka, Michihiko, and Motoki Kobayashi. "Finite Element Technique for the Curved Beam Analysis: In-Plate Vibration of Curved Beam With Varying Cross Section." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0111.

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Abstract The purpose of this paper is to present details of an algorithm for performing the numerical analysis of in-plane free vibration problem of curved beam by using the finite element technique. Although the finite element techniques for the straight or flat structures such as rods, beams and plates are well established, the finite element formulation for curved beam has not yet been completely discussed because of analytical complexity of the beam. The analysis of curved beam is reduced to the coupled problems of the axial and the transverse components of forces, bending moments, displacements and slopes in the beam. Sabir and Ashwell have discussed the vibrations of a ring by using the shape functions (interpolation functions) based on simple strain functions[1]. The discrete element displacement method was applied to the vibrations of shallow curved beam by Dawe[2]. Suzuki et al have presented the power series expansions method for solving free vibration of curved beams[3]. Irie et al have used spline functions to analyse the in-plane vibration of the varying cross section beams supported at one end[4].

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Jauregui, Juan C., Diego Cardenas, Hugo Elizalde, and Oliver Probst. "Dynamic Modelling of Blades Based on a Novel Curved Thin Walled Beam Theory." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76016.

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There are several Thin-Walled Beam models for straight beams, but few TWB models consider beams with arbitrary curvatures. Although, a curved beam can be modelled using finite elements, the number of degrees of freedom is too large and a nonlinear dynamic solution is very cumbersome, if not impossible. In this work, a general description of arbitrary three-dimensional curves, based on the Frenet-Serret field frame, is applied to determine the dynamic stresses in wing turbines blades. The dynamic model is developed using the Isogeometric Analysis (IGA) and the in plane and out-of-plane curvature’s gradients are found in an Euler-type formulation, allowing the treatment of cases with highly-curved geometry. An Isogeometrical (IGA) formulation relies on a linear combination of Non-Uniform Rational B-Splines (NURBS) to represent not just the model’s geometry, a standard practice in most Computer-Aided Design (CAD) platforms, but also the unknown solution field of each sought variable. For the unified model hitherto described, these variables are represented by a NURBS curve.

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Barbaric, Dominik, and Zvonimir Sipus. "Synthesis of Curved Beam-Shaping Metasurfaces." In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf35879.2020.9329853.

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Pane, Ivransa Z., and Tanemasa Asano. "Fabrication of Bistable Prestressed Curved-Beam." In 2007 Digest of papers Microprocesses and Nanotechnology. IEEE, 2007. http://dx.doi.org/10.1109/imnc.2007.4456268.

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Kim, Nam-Il, Anh-Tuan Luu, and Jaehong Lee. "Refined Assumed Strain Curved Beam Elements." In 10th Pacific Structural Steel Conference (PSSC 2013). Singapore: Research Publishing Services, 2013. http://dx.doi.org/10.3850/978-981-07-7137-9_108.

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Medina, Lior. "Bistability Condition for Electrostatically Actuated Initially Curved Micro-Beams in the Presence of Curved Electrodes." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-89669.

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Abstract Following increasing interest in electrostatic actuation of curved beams via curved electrodes. A rigorous limit point analysis is carried out to view how the beam reacts as a function of its geometry, as well as that of the electrode. The culmination of the study is in a bistability condition that describes what geometry both beam and electrode must have in order for bistability to be present. The study is based on a single-degree-of-freedom (DOF) reduced order (RO) model of a curved beam, derived from Galerkin’s decomposition. The extraction of a condition is based on the existence of a vanishing discriminant of a cubic equation, which formed a boundary in the parameters space of both beam and electrode geometries. The boundary describes a shift in behaviour, from mono- to bistability. Such a model and subsequent analysis have been used before for the study of curved beams, especially when it is on the verge of bistability, with high degree of fidelity. The condition shows that while actuation voltages will increase or decrease as a function of electrode curvature, as well as operational range, the curvature of an electrode plays a key role in determining the behaviour of the beam. Such results can serve researchers and engineers alike in designing curved beam-electrode configurations for usage in future studies, thus promoting their usage in micro-electro-mechanical (MEMS) based applications.

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Jansen Sheng, J. Renner, and W. S. Levine. "A Ball and Curved Offset Beam Experiment." In 2010 American Control Conference (ACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/acc.2010.5530776.

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Rodyoo, Itsawat, Nattawoot Depaiwa, and Unnat Pinsopon. "Active Vibration Absorber with Curved Beam Design." In 2023 9th International Conference on Engineering, Applied Sciences, and Technology (ICEAST). IEEE, 2023. http://dx.doi.org/10.1109/iceast58324.2023.10157855.

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Chen, Guimin, Fulei Ma, Guangbo Hao, and Weidong Zhu. "Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85515.

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Understanding and analyzing large and nonlinear deflections is one of the major challenges of designing compliant mechanisms. Initially curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross-sections, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

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Reports on the topic "Curved Beam"

1

Zhang. L52052 Control of Horizontal Beam Width with Phased Array Transducers. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), January 2008. http://dx.doi.org/10.55274/r0010945.

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Accurate defect sizing is becoming more and more critical in pipeline welds due to the application of Engineering Critical Assessment, demanding deep sea applications, the arrival of high performance piping, and increased public safety demands. This project improved horizontal beam focusing for automated ultrasonic testing; curved arrays, focused lenses and electronic focusing using phased arrays were investigated. Two target applications were selected: thickwalled risers and tendons, and thinner walled high performance pipes for onshore. Extensive computer modeling was performed to optimize the focusing. The recommended array for thick-walled pipes has 360 elements in three rows, and is mechanically curved. The results from this 1.5D and a standard 1D array on a thick-wall calibration block showed that the 1.5D array had significantly better sizing. Also important, side lobes were significantly reduced. Computer modeling showed that a 60 element, 1 mm pitch array with a 100 mm curvature gave significant improvements over the standard unfocused array. The experimental results showed a significant improvement; the curved array oversized FBH reflectors by only ~1 mm, instead of the 4�6 mm from the unfocused array. These curved arrays can be used on PipeWIZARD with no modifications to the general mechanics or software.

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Woloshun, Keith, Shuprio Ghosh, Carlos Miera, Patrick Lance, Taylor Roybal, and Bhavini Singh. Pulsed Beam Heating Analysis of Curved Inconel Window with Pressurized Helium Gas Cooling. Office of Scientific and Technical Information (OSTI), December 2022. http://dx.doi.org/10.2172/1906022.

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Ziemann, V. Beam-beam deflection and signature curves for elliptic beams. Office of Scientific and Technical Information (OSTI), October 1990. http://dx.doi.org/10.2172/6431631.

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Eberle, C. C. Interfacial Properties of Electron Beam Cured Composites. Office of Scientific and Technical Information (OSTI), December 1999. http://dx.doi.org/10.2172/816161.

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Brown, B. Excitation Curves of small quadrupoles for tev I Beam Line Use. Office of Scientific and Technical Information (OSTI), February 1985. http://dx.doi.org/10.2172/948887.

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Du, Xinlong, and Jerome F. Hajjar. Structural Performance Assessment of Electrical Transmission Networks for Hurricane Resilience Enhancement. Northeastern University, August 2022. http://dx.doi.org/10.17760/d20460693.

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Hurricanes are one of the main causes for blackouts and related infrastructure damage in the United States. Electrical transmission towers, which are key parts of the electrical transmission networks, are vulnerable to high wind speeds during storms. Collapse of transmission towers may lead to a loss of functionality of transmission lines. This research focuses on regional analysis of electrical transmission networks under hurricane hazards through developing beam elements for analyzing transmission towers, selection of hurricane wind records that incorporate uncertainty quantification, generating collapse fragility curves for transmission towers, and regional damage assessment of transmission networks.

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Friedsam, H., and W. Oren. The Application of the Principal Curve Analysis Technique to Smooth Beam Lines. Office of Scientific and Technical Information (OSTI), August 2005. http://dx.doi.org/10.2172/878884.

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Morgan, Roger J. The Characterization of the Structure-Property Relations of Electron Beam Cured Composites. Fort Belvoir, VA: Defense Technical Information Center, March 2004. http://dx.doi.org/10.21236/ada422141.

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Farmer, J. D., C. J. Janke, and V. J. Lopata. The electron beam cure of epoxy paste adhesives. Office of Scientific and Technical Information (OSTI), July 1998. http://dx.doi.org/10.2172/638207.

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Janke, C. J. CRADA Final Report for CRADA No. ORNL99-0544, Interfacial Properties of Electron Beam Cured Composites. Office of Scientific and Technical Information (OSTI), October 2005. http://dx.doi.org/10.2172/885946.

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