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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 12/2018

02-08-2018 | Original

Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method

Authors: Chao Fu, Xiao Yang

Published in: Archive of Applied Mechanics | Issue 12/2018

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Abstract

In this paper, the Kant higher-order beam theory is applied to model each segment of the partial-interaction composite beams, aiming to capture as possible fidelity as the plane stress model. On this basis, the weak-form equation is obtained through the principle of virtual work. Besides, the weak-form quadrature element (WQE), as a counterpart of the conventional finite element (CFE), is derived and implemented to more efficiently solve problems, including free vibration eigenvalue analysis and dynamic responses prediction to moving loads. After the verification of all the programs developed, a series of numerical examples are given to investigate the WQE’s superiority on convergence rate and numerical smoothness over the CFE. At the end of the paper, the influences of structural damping and loads’ moving speed on impact factor of two-span continuous beams are analyzed. Numerical results show that the proposed WQE, due to the variable-order interpolation of the element, possesses overwhelmingly higher computational efficiency than the CFE, and the numerical smoothness problem in the internal force analysis is significantly alleviated by WQE method.
previous article A comparative study of the principal methods for the analytical formulation and the numerical solution of the equations of motion of rigid multibody systems
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Literature
1.
Newmark, N.M., Siess, C.P., Viest, I.M.: Tests and analysis of composite beams with incomplete interaction. Proc. Soc. Exp. Stress Anal. 9(1), 75–92 (1951)
2.
Xu, R., Wang, G.: Variational principle of partial-interaction composite beams using Timoshenko’s beam theory. Int. J. Mech. Sci. 60(1), 72–83 (2012)CrossRef
3.
Xu, R., Wang, G.: Bending solutions of the Timoshenko partial-interaction composite beams using Euler–Bernoulli solutions. J. Eng. Mech., ASCE 139(12), 1881–1885 (2013)CrossRef
4.
Ecsedi, I., Baksa, A.: Analytical solution for layered composite beams with partial shear interaction based on Timoshenko beam theory. Eng. Struct. 115, 107–117 (2016)CrossRef
5.
Schnabl, S., Saje, M., Turk, G., Planinc, I.: Analytical solution of two-layer beam taking into account interlayer slip and shear deformation. J. Struct. Eng., ASCE 133(6), 886–894 (2007)CrossRef
6.
Ranzi, G., Bradford, M.A.: Direct stiffness analysis of a composite beam-column element with partial interaction. Comput. Struct. 85(15–16), 1206–1214 (2007)CrossRef
7.
Nguyen, Q.-H., Martinelli, E., Hjiaj, M.: Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction. Eng. Struct. 33(2), 298–307 (2011)CrossRef
8.
Hou, H., He, G.: Static and dynamic analysis of two-layer Timoshenko composite beams by weak-form quadrature element method. Appl. Math. Model. 55, 466–483 (2018)MathSciNetCrossRef
9.
Chakrabarti, A., Sheikh, A.H., Griffith, M., Oehlers, D.J.: Dynamic response of composite beams with partial shear interaction using a higher order beam theory. J. Struct. Eng., ASCE 139(1), 47–56 (2013)CrossRef
10.
Chakrabarti, A., Sheikh, A.H., Griffith, M., Oehlers, D.J.: Analysis of composite beams with partial shear interactions using a higher order beam theory. Eng. Struct. 36, 283–291 (2012)CrossRef
11.
Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51(4), 745–752 (1984)CrossRef
12.
He, G., Yang, X.: Dynamic analysis of two-layer composite beams with partial interaction using a higher order beam theory. Int. J. Mech. Sci. 90, 102–112 (2015)CrossRef
13.
He, G., Yang, X.: Analysis of higher order composite beams by exact and finite element methods. Struct. Eng. Mech. 53(4), 625–644 (2015)CrossRef
14.
He, G., Yang, X.: Finite element analysis for buckling of two-layer composite beams using Reddy’s higher order beam theory. Finite Elem. Anal. Des. 83, 49–57 (2014)CrossRef
15.
Manjunatha, B.S., Kant, T.: New theories for symmetric/unsymmetric composite and sandwich beams with C\(^{0}\) finite elements. Compos. Struct. 23(1), 61–73 (1993)CrossRef
16.
Kant, T., Owen, D.R.J., Zienkiew, O.C.: A refined higher-order C\(^{0}\) plate bending element. Compos. Struct. 15(2), 177–183 (1982)MathSciNetCrossRef
17.
Kant, T., Gupta, A.: A finite element model for a higher-order shear-deformable beam theory. J. Sound Vib. 125(2), 193–202 (1988)CrossRef
18.
Kroker, A.M.: Becker W Closed-form analysis of a higher-order composite box beam theory. Proc. Appl. Math. Mech. 9(1), 213–214 (2009)MathSciNetCrossRef
19.
Kroker, A.M.: Becker W A higher-order composite beam theory for closed-form analysis of beams with box and I cross-section. Proc. Appl. Math. Mech. 10(1), 179–180 (2010)MathSciNetCrossRef
20.
Carrera, E., Pagani, A.: Analysis of reinforced and thin-walled structures by multi-line refined 1D/beam models. Int. J. Mech. Sci. 75, 278–287 (2013)CrossRef
21.
Carrera, E., Cinefra, M., Petrolo, M., Zappino, E.: Finite Element Analysis of Structures Through Unified Formulation. Wiley, New Delhi (2014)CrossRef
22.
Carrera, E., Giunta, G., Petrolo, M.: Beam Structures Classical and Advanced Theories. Wiley, London (2011)CrossRef
23.
Szabo, B.A., Mehta, A.K.: \(p\)-convergent finite element approximations in fracture mechanics. Int. J. Numer. Methods Eng. 12(3), 551–560 (1978)CrossRef
24.
Pozrikidis, C.: Introduction to Finite and Spectral Element Methods Using Matlab. CRC Press, New York (2014)MATH
25.
Wang, X.: Differential Quadrature and Differential Quadrature Based Element Methods Theory and Applications. Butterworth-Heinemann, Oxford (2015)MATH
26.
Shu, C., Richards, B.E.: Application of generalized differential quadrature to solve two-dimensional incompressible Navier–Stokes equations. Int. J. Numer. Methods Fluids 15(15), 791–798 (1992)CrossRef
27.
Zhong, H., Wang, Y.: Weak form quadrature element analysis of Bickford Beams. Eur. J. Mech. A-Solid 29(5), 851–858 (2010)CrossRef
28.
Zhang, R., Zhong, H.: Weak form quadrature element analysis of planar slender beams based on geometrically exact beam theory. Arch. Appl. Mech. 83(9), 1309–1325 (2013)CrossRef
29.
Zhong, H., Zhang, R., Xiao, N.: A quaternion-based weak form quadrature element formulation for spatial geometrically exact beams. Arch. Appl. Mech. 84(12), 1825–1840 (2014)CrossRef
30.
Zhang, R., Zhong, H.: Weak form quadrature element analysis of spatial geometrically exact shear-rigid beams. Finite Elem. Anal. Des. 87, 22–31 (2014)MathSciNetCrossRef
31.
Jin, C., Wang, X.: Accurate free vibration analysis of Euler functionally graded beams by the weak form quadrature element method. Compos. Struct. 125, 41–50 (2015)CrossRef
32.
Wang, Y., Wang, X.: Free vibration analysis of soft-core sandwich beams by the novel weak form quadrature element method. J. Sandw. Struct. Mater. 18(3), 294–320 (2016)CrossRef
33.
Wang, X., Yuan, Z.: A novel weak form three-dimensional quadrature element solution for vibrations of elastic solids with different boundary conditions. Finite Elem. Anal. Des. 141, 70–83 (2018)MathSciNetCrossRef
34.
Shen, Z., Zhong, H.: Static and vibrational analysis of partially composite beams using the weak-form quadrature element method. Math. Probl. Eng. 2012, 1–23 (2012)MathSciNetMATH
35.
Zhong, H., Yue, Z.: Analysis of thin plates by the weak form quadrature element method. Sci. China Ser. G. 55(5), 861–871 (2012)CrossRef
36.
Liao, M., Zhong, H.: Application of a weak form quadrature element method to nonlinear free vibrations of thin rectangular plates. Int. J. Struct. Stab. Dyn. 16(1), 1–12 (2016)MathSciNetCrossRef
37.
Zhang, R., Zhong, H.: Weak form quadrature element analysis of geometrically exact shells. Int. J. Nonlinear Mech. 71, 63–71 (2015)CrossRef
38.
Yuan, S., Zhong, H.: Consolidation analysis of non-homogeneous soil by the weak form quadrature element method. Comput. Geotech. 62, 1–10 (2014)CrossRef
39.
Yuan, S., Zhong, H.: A weak form quadrature element formulation for coupled analysis of unsaturated soils. Comput. Geotech. 76, 1–11 (2016)CrossRef
40.
Liu, B., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A.: Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Compos. Struct. 136, 546–553 (2016)CrossRef
41.
Liu, B., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A.: Analysis of composite plates using a layerwise theory and a differential quadrature finite element method. Compos. Struct. 156, 393–398 (2016)CrossRef
42.
Wang, X., Yuan, Z., Jin, C.: Weak form quadrature element method and its applications in science and engineering: A state-of-the-art review. ASME Appl. Mech. Rev. 69(3), 030801 (2017)CrossRef
43.
Bellman, R., Kashef, B.G., Casti, J.: Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. 10, 40–52 (1972)MathSciNetCrossRef
44.
Bellman, R.E., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl. 34(2), 235–238 (1971)MathSciNetCrossRef
45.
Jin, C., Wang, X., Ge, L.: Novel weak form quadrature element method with expanded Chebyshev nodes. Appl. Math. Lett. 34, 51–59 (2014)MathSciNetCrossRef
46.
Bathe, K.J.: Finite Element Procedures. Prentice-Hall, Upper Saddle River (1996)MATH
47.
Huang, C.W., Su, Y.H.: Dynamic characteristics of partial composite beams. Int. J. Struct. Stab. Dyn. 8(4), 665–685 (2008)CrossRef
Metadata
Title
Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method
Authors
Chao Fu
Xiao Yang
Publication date
02-08-2018
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 12/2018
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-018-1443-1

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