scholarly journals A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Huiqing Fang ◽  
Zhaohui Qi
Keyword(s):  
Interpolation Method ◽  
Beam Theory ◽  
Small Deformation ◽  
Beam Element ◽  
Patch Tests ◽  
Beam Elements ◽  
Nodal Force ◽  
Geometric Nonlinear ◽  
Geometrically Exact Beam ◽  
Strain Measures

Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

Aerodynamic study of single corrugated variable-camber morphing aerofoil concept

2021 ◽  
pp. 1-29
Author(s):  
K. Dhileep ◽  
D. Kumar ◽  
P.N. Gautham Vigneswar ◽  
P. Soni ◽  
S. Ghosh ◽  
...  
Keyword(s):  
Finite Volume ◽  
Interpolation Method ◽  
Beam Theory ◽  
Small Deformation ◽  
Aerodynamic Characteristics ◽  
Ansys Fluent ◽  
Aerodynamic Efficiency ◽  
Finite Element Software ◽  
Drag Ratio ◽  
Lift To Drag Ratio

Abstract Camber morphing is an effective way to control the lift generated by any aerofoil and potentially improve the range (as measured by the lift-to-drag ratio) and endurance (as measured by $C_l^{3/2}/C_d$ ). This can be especially useful for fixed-wing Unmanned Aerial Vehicles (UAVs) undergoing different flying manoeuvres and flight phases. This work investigates the aerodynamic characteristics of the NACA0012 aerofoil morphed using a Single Corrugated Variable-Camber (SCVC) morphing approach. Structural analysis and morphed shapes are obtained based on small-deformation beam theory using chain calculations and validated using finite-element software. The aerofoil is then reconstructed from the camber line using a Radial Basis Function (RBF)-based interpolation method (J.H.S. Fincham and M.I. Friswell, “Aerodynamic optimisation of a camber morphing aerofoil,” Aerosp. Sci. Technol., 2015). The aerodynamic analysis is done by employing two different finite-volume solvers (OpenFOAM and ANSYS-Fluent) and a panel method code (XFoil). Results reveal that the aerodynamic coefficients predicted by the two finite-volume solvers using a fully turbulent flow assumption are similar but differ from those predicted by XFoil. The aerodynamic efficiency and endurance factor of morphed aerofoils indicate that morphing is beneficial at moderate to high lift requirements. Further, the optimal morphing angle increases with an increase in the required lift. Finally, it is observed for a fixed angle-of-attack that an optimum morphing angle exists for which the aerodynamic efficiency becomes maximum.

A Simple Co-Rotational Finite Planar Beam Element of Geometrical and Material Nonlinearity

2012 ◽  
Vol 268-270 ◽  
pp. 1163-1167
Author(s):  
Song Bai Cai ◽  
Da Zhi Li ◽  
Chang Wan Kim ◽  
Pu Sheng Shen
Keyword(s):  
Stiffness Matrix ◽  
High Efficiency ◽  
Beam Theory ◽  
Yield Function ◽  
Beam Element ◽  
Transformation Matrix ◽  
Material Nonlinearity ◽  
Beam Deflection ◽  
Nodal Force ◽  
Tangential Stiffness

A simple geometrical and material nonlinear co-rotational planar beam element of field consistency is proposed. Herein the element which produces a local stiffness matrix of 3 by 3 other than 6 by 6 is developed. Material nonlinearity is taken into account on the base of yield function of element internal forces. By applying static equilibrium relationship of classic beam theory for the transferring of local element nodal force to global element nodal force, a new transformation matrix different from the nodal displacement transformation matrix is established. Although this results in an asymmetric global tangential stiffness matrix, the new transformation is simpler, and gives rise to field consistency and makes it possible to compute very large beam deflection without remeshing of the deformed structure. Computations of numerical example indicates that formulations for the nonlinear beam element are of validation and high efficiency

Analysis on Coupling of Laminated Elastic Beam Element and the Shock Pressure of Surrounding Rock of Roadway

2012 ◽  
Vol 505 ◽  
pp. 429-433
Author(s):  
Jin Wei ◽  
Zi Ming Kou ◽  
Wang Wang
Keyword(s):  
Characteristic Curve ◽  
Impact Resistance ◽  
Elastic Beam ◽  
Present Situation ◽  
Beam Element ◽  
Tunnel Support ◽  
Beam Elements ◽  
Mine Roadway ◽  
Safety Production ◽  
High Support

Based on the rock pressure tunnel support present situation carries on the analysis, the laminated elastic beams of high support ability and impact resistance was designed.Therefore, through assumptions and establishment of mathematical model, and the application of viscoelastic beam dynamics equation, deformation and energy absorption of the laminated elastic beam elements,under the condition of rock burst, was deduced. According to the load - displacement characteristic curve, the coupling of laminated elastic beam elements and rockburst in coal mine roadway was analysed. This can provide a new method in the field of safety production of mining and roadway.

A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

2016 ◽  
Vol 24 (24) ◽  
pp. 5794-5810 ◽  
Author(s):  
Kemal Mazanoglu ◽  
Elif C Kandemir-Mazanoglu
Keyword(s):  
Beam Theory ◽  
Equivalent Model ◽  
Frame Structures ◽  
Symmetric Mode ◽  
Lumped Mass ◽  
Beam Elements ◽  
Local Flexibility ◽  
Mode Vibration ◽  
Frame Systems ◽  
Lumped Masses

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.

scholarly journals High-Efficiency Dynamic Modeling of a Helical Spring Element Based on the Geometrically Exact Beam Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jian Zhang ◽  
Zhaohui Qi ◽  
Gang Wang ◽  
Shudong Guo
Keyword(s):  
High Efficiency ◽  
Curvature Vector ◽  
Polar Angle ◽  
Beam Theory ◽  
High Frequency Oscillation ◽  
Helical Spring ◽  
Static Stiffness ◽  
Spring Element ◽  
Geometrically Exact Beam ◽  
Geometrically Exact Beam Theory

This paper presents a modeling study of the dynamics of a helical spring element with variable pitch and radius considering both the static stiffness and dynamic response by using the geometrically exact beam theory. The geometrically exact beam theory based on the Euler–Bernoulli beam hypothesis is described, of which the shear deformations are ignored. Unlike the traditional spliced curved beam element method, the helical spring element is described with curvature vector and axial strain by establishing and spline-interpolating a function of the radius, the height, the polar angle, and the torsion angle of the whole spring. In addition, a model smoothing method is developed and applied in the numerical analysis to filter the high-frequency oscillation component of the flexible multibody systems, so as to correct the system dynamic equations and improve the calculation efficiency when solving the static equilibrium of the spring. This study also carries out five numerical trials to validate the above dynamic procedure of the helical spring element. The example of the spring static stiffness design shows that the proposed helical spring procedure enables one to deal with practical engineering applications.

scholarly journals An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2198 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Do Van Thom
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Beam Theory ◽  
Beam Element ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Beam ◽  
Transverse Shear Stresses ◽  
Power Law Index ◽  
Transverse Shear Strains

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

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