scholarly journals Analysis of the effect of the secondary moment on curved beams of full cross section

2021 ◽  
Vol 14 (2) ◽  
Author(s):  
Thiago Cunha da Silva ◽  
Emil de Souza Sánchez Filho
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Structural Model ◽  
Paper Analysis ◽  
Opening Angle ◽  
Curved Beam ◽  
Curved Beams ◽  
Straight Beam ◽  
Full Cross Section

abstract This paper analysis the effect of the secondary moment on curved beams using the equivalent nodal loads method. A case study was carried out applying the equivalent nodal loads method to a two-span prestressed curved beam, using a curved finite element as the structural model, analyzing the effect of the secondary moment for each case and comparing it with its equivalent in straight beam. It was found that the stiffness parameters E I and G J influence the secondary moment. The results demonstrates that the beam opening angle reduces the effect of secondary moment, and that the greater the angle, the greater is the reduction that occurs in its secondary moment compared to its equivalent straight beam.

Finite Element Technique for the Curved Beam Analysis: In-Plate Vibration of Curved Beam With Varying Cross Section

1991 ◽  
Author(s):  
Michihiko Tanaka ◽  
Motoki Kobayashi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Element Formulation ◽  
Curved Beam ◽  
Curved Beams ◽  
Finite Element Technique ◽  
Beam Analysis ◽  
Power Series Expansions ◽  
Element Technique

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].

scholarly journals Free vibrations of circular curved beams

2018 ◽  
Vol 211 ◽  
pp. 04006
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fem Simulation ◽  
Free Vibrations ◽  
Opening Angle ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Governing Equations ◽  
Simulation Results

The study of free vibrations of curved beams has relevance in engineering applications like modeling turbo machinery blades, propellers, arch design, etc. Vibration characteristics of structures are generally evaluated using the Finite Element Method. The governing equations for the curved beam using the inextensional theory are available in the literature. These equations are solved analytically for two different boundary conditions, namely (a) simplysupported, (b) cantilever. The results obtained for all the cases are compared against the FEM simulation results. It is found that the present solutions are in agreement with the FEM solutions up to an opening angle of 40°.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

Natural frequencies of a rotating curved cantilever beam: A perturbation method-based approach

2020 ◽  
Vol 234 (9) ◽  
pp. 1706-1719
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Perturbation Method ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Analytical Formula ◽  
Industrial Applications ◽  
Curved Beam ◽  
Straight Beam ◽  
Element Method

The blades of propellers, fans, compressor and turbines can be modeled as curved beams. In general, for industrial application, finite element method is employed to determine the modal characteristics of these structures. In the present work, a novel formula for determining the natural frequencies of a rotating circularly curved cantilever beam is derived. Rayleigh–Ritz approach is used along with perturbation method to obtain the analytical formula. In the first part of the work, a formula for natural frequencies of a non-rotating curved beam vibrating in its plane of curvature is presented. This formula is derived as a correction to the natural frequencies of its straight counterpart. The curvature is treated as a perturbation parameter. In the next part of the work, the effect of rotation on the curved beam is captured as an additional perturbation. Thus, the formula for a curved rotating beam is derived as a correction (involving two perturbation parameters) to the non-rotating straight beam. The results obtained using the derived formula are compared with the finite element method results. It is found that the frequency estimates from the formula are valid over a fairly large range of curvature and rotation speed. Thus, the derived formula can provide a faster alternative for design iterations in industrial applications.

A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

scholarly journals The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhibo Yang ◽  
Xuefeng Chen ◽  
Yumin He ◽  
Zhengjia He ◽  
Jie Zhang
Keyword(s):  
Finite Element ◽  
Polynomial Interpolation ◽  
Physical Space ◽  
Curved Beam ◽  
Approximation Properties ◽  
Curved Beams ◽  
Spline Wavelet ◽  
B Spline ◽  
Wavelet Space ◽  
Interval Finite Element Method

A B-spline wavelet on interval (BSWI) finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch) are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.

scholarly journals Structural model updating based on metamodel using modal frequencies

2021 ◽  
Vol 15 (58) ◽  
pp. 114-127
Author(s):  
Jutao Wang ◽  
Zhenzhong Liu ◽  
Liju Xue
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Structural Model ◽  
Model Updating ◽  
Element Model ◽  
Kriging Model ◽  
Frame Structure ◽  
Updating Procedure ◽  
The Finite Element Model

Modal frequencies are often used in structural model updating based on the finite element model, and metamodel technique is often applied to the corresponding optimization process. In this work, the Kriging model is used as the metamodel. Firstly, the influence of different correlation functions of Kriging model is inspected, and then the approximate capability of Kriging model is investigated via inspecting the approximate accuracy of nonlinear functions. Secondly, a model updating procedure is proposed based on the Kriging model, and the samples for constructing Kriging model are generated via the method of Optimal Latin Hypercube. Finally, a typical frame structure is taken as a case study and demonstrates the feasibility and efficiency of the proposed approach. The results show the Kriging model can match the target functions very well, and the finite element model can achieve accurate frequencies and can reliably predict the frequencies after model updating.

Analytical Solutions at Three Freedom Direction for Curved Beams with Clamped-Pinned Ends under Thermal Load

2011 ◽  
Vol 94-96 ◽  
pp. 322-325
Author(s):  
Xiao Fei Li ◽  
Ying Hua Zhao ◽  
De Hai Yu
Keyword(s):  
Thermal Expansion ◽  
Cross Section ◽  
Analytical Solutions ◽  
Thermal Load ◽  
Virtual Work ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Internal Forces ◽  
Scientific Base

The purpose of the paper is to present analytical solution of curved beam with clamped-pinned ends under thermo load based on the principle of thermal expansion and theory of virtual work. A class of equations for in-plane displacements at three freedom direction and internal forces in the cross-section of statically indeterminate curved beams under thermo load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

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