An optimized approach for tracing pre- and post-buckling equilibrium paths of space trusses. (English) Zbl 1535.74590
Summary: In this paper, a novel optimization-based method is proposed to analyze steel space truss structures undergoing large deformations. The geometric nonlinearity is considered using the total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to the displacement-type constraints. The proposed approach can fully follow the equilibrium path of the geometrically nonlinear space truss structures not only before the limit point, but also after it, namely, including both the pre- and post-buckling paths. Moreover, a direct estimation of the buckling loads and their corresponding displacements is possible by using the method. Particularly, it has been shown that the equilibrium path of a structure with highly nonlinear behavior, multiple limit points, snap-through, and snap-back phenomena can be traced via the proposed algorithm. To demonstrate the accuracy, validity, and robustness of the proposed procedure, four benchmark truss
examples are analyzed and the results compared with those by the modified arc-length method and those reported in the literature.
MSC:
| 74P10 | Optimization of other properties in solid mechanics |
| 74G60 | Bifurcation and buckling |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
geometric nonlinearity; buckling; nonlinear analysis; limit point; post-buckling path; trussReferences:
| [1] | Yang, Y. B., Lin, S. P. and Leu, L. J., Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation, Eng. Struct.29(6) (2007) 1189-1200. |
| [2] | Rezaiee-Pajand, M., Salehi-Ahmadabad, M. and Ghalishooyan, M., Structural geometrical nonlinear analysis by displacement increment, Asian J. Civil Eng. (BHRC)15(5) (2014) 633-653. |
| [3] | Izadpanah, M. and Habibi, A., Evaluating the spread plasticity model of IDARC for inelastic analysis of reinforced concrete frames, Struct. Eng. Mech.56(2) (2015) 169-188. |
| [4] | Jiang, G., Li, F. and Li, X., Nonlinear vibration analysis of composite laminated trapezoidal plates, Steel Compos. Struct.21(2) (2016) 395-409. |
| [5] | Wan, C.-Y. and Zha, X.-X., Nonlinear analysis and design of concrete-filled dual steel tubular columns under axial loading, Steel Compos. Struct.20(3) (2016) 571-597. |
| [6] | Habibi, A. and Izadpanah, M., Improving the linear flexibility distribution model to simultaneously account for gravity and lateral loads, Comp. Concrete Int. J.20(1) (2017) 11-22. |
| [7] | Lee, J. K. and Lee, B. K., Large deflections and buckling loads of cantilever columns with constant volume, Int. J. Struct. Stab. Dyn.17(8) (2017) 1750091. · Zbl 1535.74119 |
| [8] | Liu, A., Bradford, M. A. and Pi, Y.-L., In-plane nonlinear multiple equilibria and switches of equilibria of pinned-fixed arches under an arbitrary radial concentrated load, Arch. Appl. Mech.87(11) (2017) 1909-1928. |
| [9] | Oveisi, A., Nestorović, T. and Nguyen, N. L., Semi-analytical modeling and vibration control of a geometrically nonlinear plate, Int. J. Struct. Stab. Dyn.17(4) (2017) 1771003. · Zbl 1535.74082 |
| [10] | Pi, Y.-L., Bradford, M. A. and Liu, A., Nonlinear equilibrium and buckling of fixed shallow arches subjected to an arbitrary radial concentrated load, Int. J. Struct. Stab. Dyn.17(8) (2017) 1750082. · Zbl 1535.74131 |
| [11] | Rezaiee-Pajand, M. and Naserian, R., Nonlinear frame analysis by minimization technique, Iran Univ. Sci. Technol.7(2) (2017) 291-318. |
| [12] | Shamass, R., Alfano, G. and Guarracino, F., On elastoplastic buckling analysis of cylinders under nonproportional loading by differential quadrature method, Int. J. Struct. Stab. Dyn.17(7) (2017) 1750072. · Zbl 1535.74138 |
| [13] | Habibi, A. and Bidmeshki, S., A dual approach to perform geometrically nonlinear analysis of plane truss structures, Steel Compos. Struct.27(1) (2018) 13-25. |
| [14] | Crisfield, M. A., Nonlinear Finite Element Analysis of Solids and Structures. Vol. 1: Essentials (John Wiley & Sons, New York, 1991). · Zbl 0809.73005 |
| [15] | Torkamani, M. A. and Sonmez, M.. Solution techniques for nonlinear equilibrium equations, in Proc. 18th Analysis and Computation Specialty Conf. (ASCE) (2008). |
| [16] | Thai, H.-T. and Kim, S.-E., Large deflection inelastic analysis of space trusses using generalized displacement control method, J. Construct. Steel Res.65(10-11) (2009) 1987-1994. |
| [17] | Chen, W.-F. and Lui, E. M., Stability Design of Steel Frames (CRC Press, United States, 1991). |
| [18] | Yang, Y.-B. and Kuo, S.-R., Theory and Analysis of Nonlinear Framed Structures (Prentice Hall, New York, 1994). |
| [19] | Hamdaoui, A., Braikat, B. and Damil, N., Solving elastoplasticity problems by the asymptotic numerical method: Influence of the parameterizations, Finite Elem. Anal. Des.115 (2016) 33-42. |
| [20] | Mahdavi, S. H.et al., A comparative study on application of Chebyshev and spline methods for geometrically non-linear analysis of truss structures, Int. J. Mech. Sci.101 (2015) 241-251. |
| [21] | Mansouri, I. and Saffari, H., An efficient nonlinear analysis of 2D frames using a Newton-like technique, Arch. Civil Mech. Eng.12(4) (2012) 485-492. |
| [22] | Saffari, H. and Mansouri, I., Non-linear analysis of structures using two-point method, Int. J. Non-Linear Mech.46(6) (2011) 834-840. |
| [23] | Saffari, H.et al., Elasto-plastic analysis of steel plane frames using homotopy perturbation method, J. Construct. Steel Res.70 (2012) 350-357. |
| [24] | Wempner, G. A., Discrete approximations related to nonlinear theories of solids, Int. J. Solids Struct.7(11) (1971) 1581-1599. · Zbl 0222.73054 |
| [25] | Riks, E., The application of Newton’s method to the problem of elastic stability, J. Appl. Mech.39(4) (1972) 1060-1065. · Zbl 0254.73047 |
| [26] | Riks, E., An incremental approach to the solution of snapping and buckling problems, Int. J. Solids Struct.15(7) (1979) 529-551. · Zbl 0408.73040 |
| [27] | Crisfield, M. A., A fast incremental/iterative solution procedure that handles “snap-through”, Comp. Struct.13(1) (1981) 55-62. · Zbl 0479.73031 |
| [28] | Ramm, E., Strategies for tracing the nonlinear response near limit points, in Nonlinear Finite Element Analysis in Structural Mechanics (Springer, Berlin, Heidelberg, 1981), pp. 63-89. · Zbl 0474.73043 |
| [29] | Crisfield, M., An arc-length method including line searches and accelerations, Int. J. Numer. Methods Eng.19(9) (1983) 1269-1289. · Zbl 0516.73084 |
| [30] | Schweizerhof, K. H. and Wriggers, P., Consistent linearization for path following methods in nonlinear FE analysis, Comp. Methods Appl. Mech. Eng.59(3) (1986) 261-279. · Zbl 0588.73138 |
| [31] | Bellini, P. and Chulya, A., An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations, Comp. Struct.26(1) (1987) 99-110. · Zbl 0609.73070 |
| [32] | Forde, B. W. and Stiemer, S. F., Improved arc length orthogonality methods for nonlinear finite element analysis, Comp. Struct.27(5) (1987) 625-630. · Zbl 0623.73079 |
| [33] | Geers, M.-A., Enhanced solution control for physically and geometrically non-linear problems. Part I — The subplane control approach, Int. J. Numer. Methods Eng.46(2) (1999) 177-204. · Zbl 0957.74034 |
| [34] | Hellweg, H.-B. and Crisfield, M., A new arc-length method for handling sharp snap-backs, Comp. Struct.66(5) (1998) 704-709. · Zbl 0933.74080 |
| [35] | Baguet, S. and Cochelin, B., On the behaviour of the ANM continuation in the presence of bifurcations, Commun. Numer. Methods Eng.19(6) (2003) 459-471. · Zbl 1022.65062 |
| [36] | Damil, N. and Potier-Ferry, M., A new method to compute perturbed bifurcations: Application to the buckling of imperfect elastic structures, Int. J. Eng. Sci.28(9) (1990) 943-957. · Zbl 0721.73018 |
| [37] | Elhage-Hussein, A., Potier-Ferry, M. and Damil, N., A numerical continuation method based on Padé approximants, Int. J. Solids Struct.37(46) (2000) 6981-7001. · Zbl 0980.74021 |
| [38] | Leahu-Aluas, I. and Abed-Meraim, F., A proposed set of popular limit-point buckling benchmark problems, Struct. Eng. Mech.38(6) (2011) 767-802. |
| [39] | Yang, Y.-B. and Shieh, M.-S., Solution method for nonlinear problems with multiple critical points, AIAA J.28(12) (1990) 2110-2116. |
| [40] | Kuo, S.-R. and Yang, Y.-B., Tracing postbuckling paths of structures containing multi-loops, Int. J. Numer. Methods Eng.38(23) (1995) 4053-4075. · Zbl 0835.73092 |
| [41] | Bonopera, M.et al., Compressive column load identification in steel space frames using second-order deflection-based methods, Int. J. Struct. Stab. Dyn.18(7) (2018) 1850092. |
| [42] | Rehlicki, L. Z.et al., On post-critical behavior of a beam on an elastic foundation, Int. J. Struct. Stab. Dyn.18(6) (2018) 1850082. · Zbl 1535.74454 |
| [43] | Shaterzadeh, A., Behzad, H. and Shariyat, M., Stability analysis of composite perforated annular sector plates under thermomechanical loading by finite element method, Int. J. Struct. Stab. Dyn.18(7) (2018) 1850100. · Zbl 1535.74377 |
| [44] | Xu, Y. L.et al., Experimental and numerical study on lateral-torsional buckling behavior of high performance steel beams, Int. J. Struct. Stab. Dyn.18(7) (2018) 1850090. |
| [45] | Liang, K., Ruess, M. and Abdalla, M., Co-rotational finite element formulation used in the Koiter-Newton method for nonlinear buckling analyses, Finite Elem. Anal. Des.116 (2016) 38-54. |
| [46] | Bathe, K.-J., Finite Element Procedures (Klaus-Jurgen Bathe, United States of America, 2006). |
| [47] | Planinc, I. and Saje, M., A quadratically convergent algorithm for the computation of stability points: The application of the determinant of the tangent stiffness matrix, Comp. Methods Appl. Mech. Eng.169(1) (1999) 89-105. · Zbl 1161.74494 |
| [48] | Rao, S. S., Engineering Optimization: Theory and Practice (John Wiley & Sons, Hoboken, New Jersey, 2009). |
| [49] | Arora, J. S., Introduction to Optimum Design, 3rd edn. (Academic Press, Boston, 2012). |
| [50] | Papadrakakis, M., Inelastic post-buckling analysis of trusses, J. Struct. Eng.109(9) (1983) 2129-2147. |
| [51] | Yang, Y.-B. and Leu, L.-J., Constitutive laws and force recovery procedures in nonlinear analysis of trusses, Comp. Methods Appl. Mech. Eng.92(1) (1991) 121-131. · Zbl 0743.73003 |
| [52] | Hill, C. D., Blandford, G. E. and Wang, S. T., Post-buckling analysis of steel space trusses, J. Struct. Eng.115(4) (1989) 900-919. |
| [53] | Ramesh, G. and Krishnamoorthy, C., Inelastic post-buckling analysis of truss structures by dynamic relaxation method, Int. J. Numer. Methods Eng.37(21) (1994) 3633-3657. · Zbl 0814.73063 |
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