Upper Bound Limit Analysis of 2D Structures Using Lagrange Extraction-Based Isogeometric Analysis
Corressponding author's email:
hiendv@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.79.2023.1372Keywords:
Limit analysis, Isogeometric analysis, SOCP, Upper bound method, Lagrange extractionAbstract
This work presents a new approach that uses Lagrange extraction-based isogeometric analysis and Second Order Cone Programming (SOCP) to determine the limit load factor in two-dimensional problems. This methodology makes use of an upper-bound limit approach and a rigid-perfectly plastic material model. Lagrange extraction is used to link a C0 nodal basis to a smooth B-spline basis. This enables the use of straightforward methods for isogeometric analysis in conventional finite element systems. A SOCP problem is created from the limit analysis problem, which may then be solved using Mosek optimization software. The numerical results indicate the correctness and effectiveness of the current technique by contrasting it with other approaches mentioned in the literature.
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References
F. A. Gaydon and A. W. McCrum, "A theoretical investigation of the yield point loading of a square plate with a central circular hole," Journal of Mechanics and Physics Solids, vol. 2, pp. 156-169, 1951, doi: 10.1016/0022-5096(54)90022-8.
R. Casciaro and L. Cascini, "A mixed formulation and mixed finite elements for limit analysis," International Journal for Numerical Methods in Engineering, vol. 18, pp. 211-243, 1982, doi: 10.1002/nme.1620180206.
T. Belytschko, "Plane stress shakedown analysis by finite elements," International Journal of Mechanic Sciences, vol. 14, pp. 619–625, 1972, doi: 10.1016/0020-7403(72)90061-6.
J. G. Weege, "On the numerical assessment of the safety factor of elasto-plastic structures under variable loading," International Journal of Mechanics and Sciences, vol. 39, pp. 417–433, 1997, doi: 10.1016/S0020-7403(96)00039-2.
G. Garcea, G. Armentano, S. Petrolo, and R. Casciaro, "Finite element shakedown analysis of two-dimensional structures," International Journal for Numerical Methods in Engineering, vol. 63, pp. 1174–1202, 2005, doi: 10.1002/nme.1316.
A. Makrodimopoulos and C. M. Martin, "Upper bound limit analysis using simplex strain elements and second-order cone programming," Int. J. Numer. Anal. Meth. Geomech., vol. 31, pp. 835-865, 2007, doi: https://doi.org/10.1002/nag.567.
J. S. Chen, C. T. Wu, S. Yoon, and Y. You, "A stabilized conforming nodal integration for Galerkin mesh-free methods," International Journal for Numerical Methods in Engineering, vol. 50, pp. 435–466, 2001, doi: 10.1002/1097-0207(20010120)50:2.
S. Chen, Y. Liu, and Z. Cen, "Lower-bound limit analysis by using the EFG method and non-linear programming," International Journal for Numerical Methods in Engineering, vol. 74, pp. 391–4157, 2008, doi: 10.1002/nme.2177.
Z. Zhang, Y. Liu, and Z. Cen, "Boundary element methods for lower bound limit and shakedown analysis," Engineering Analysis with Boundary Elements, vol. 28, pp. 905–917, 2004, doi: 10.1016/S0955-7997(03)00117-6.
H. V. Do and H. N. Xuan, "Limit and shakedown isogeometric analysis of structures based on Bézier extraction," European Journal Mechanics and Solid, vol. 63, pp. 149–164, 2017, doi: 10.1016/j.euromechsol.2017.01.004.
H. V. Do and H. N. Xuan, "Computation of limit and shakedown loads for pressure vessel components using isogeometric analysis based on Lagrange extraction," International Journal of Pressure Vessels and Piping, vol. 169, pp. 57–70, 2019, doi: 10.1016/j.ijpvp.2018.11.012.
V. Gupta et al., "An Insight on NURBS Based Isogeometric Analysis, Its Current Status and Involvement in Mechanical Applications," Arch. Computat. Methods Eng., vol. 30, pp. 1187–1230, 2023, doi: https://doi.org/10.1007/s11831-022-09838-0.
X. Wei, D. Liu, and S. Yin, "An Isogeometric Bézier Finite Element Method for Vibration Optimization of Functionally Graded Plate with Local Refinement," Crystals, vol. 12, no. 6, p. 830, 2022, doi: https://doi.org/10.3390/cryst12060830.
V. H. Do, "Application of isogeometric analysis to free vibration of truss structures," Journal of Technical Education Science, no. 42, pp. 20–27, 2021. [Online]. Available: https://jte.edu.vn/index.php/jte/article/view/373.
D. V. Hien, H. N. Bon, and V. H. Thinh, "Limit analysis for plane stress problem by using nurbs based on bézier extraction in combination with second order cone program," Journal of Technical Education Science, no. 52, pp. 17–24, 2019. [Online]. Available: https://jte.edu.vn/index.php/jte/article/view/200.
T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs, "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement," Computer Methods in Applied Mechanics and Engineering, vol. 194, pp. 4135–4195, 2005, doi: 10.1016/j.cma.2004.10.008.
M. J. Borden, M. A. Scott, J. A. Evans, and T. J. R. Hughes, "Isogeometric finite element data structures based on Bézier extraction of NURBS," International Journal for Numerical Methods in Engineering, vol. 86, pp. 15 – 47, 2011, doi: 10.1002/nme.2968.
D. Schillinger, P. K. Ruthal, and L. H. Nguyen, "Lagrange extraction and projection for NURBS basis functions: a direct link between isogeometric and standard nodal finite element formulations," International Journal for Numerical Methods in Engineering, vol. 108, pp. 515–534, 2016, doi: 10.1002/nme.5216.
Z. Zouain, L. Borges, and J. L. Silveira, "An algorithm for shakedown analysis with nonlinear yield functions," Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 2463–2481, 2002, doi: 10.1016/S0045-7825(01)00374-7.
F. A. Gaydon and A. W. McCrum, "A theoretical investigation of the yield point loading of a square plate with a central circular hole," Journal of Mechanics and Physics Solids, vol. 2, pp. 156-169, 1951, doi: 10.1016/0022-5096(54)90022-8.
P. L. H. Ho, C. V. Le, and T. Q. Chu, "The equilibrium cell-based smooth finite element method for shakedown analysis of structures," International Journal Computational Methods, vol. 16, no. 6, p. 1840013, 2017, doi: 10.1142/S0219876218400133.
H. N. Xuan, T. Rabczuk, T. N. Thoi, T. N. Tran, and N. N. Thanh, "Computation of limit and shakedown loads using a node-based smoothed finite element method," International Journal for Numerical Methods in Engineering, vol. 90, pp. 287–310, 2012, doi: 10.1002/nme.3317.
D. H. Nguyen and L. Palgen, "Shakedown analysis by displacement method and equilibrium finite elements," in Proceedings of SMIRT-5, Berlin, German, 1979, doi: 10.1139/tcsme-1980-0006.
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