Meshfree Method for Inelastic Frame Analysis
Publication: Journal of Structural Engineering
Volume 135, Issue 6
Abstract
The feasibility of using meshfree methods in nonlinear structural analysis is explored in an attempt to establish a new paradigm in structural engineering computation. A blended finite-element and meshfree Galerkin approximation scheme is adopted to solve the inelastic response of plane frames. In the proposed method, moving least-squares shape functions represent the displacement field, a plane stress approximation of the two-dimensional domain simulates beam bending, plasticity characterizes material behavior, and stabilized nodal integration yields the discrete equations. The particular case of steel frames composed of wide flange sections is investigated, though the concepts introduced can be extended to other structural materials and systems. Results of numerical simulations are compared with analytical solutions, finite-element simulations, and experimental data to validate the methodology. The findings indicate that meshfree methods offer an alternative approach with enhanced capabilities for nonlinear structural analysis. The proposed method can be integrated with finite elements so that a structural system is composed of meshfree regions and finite-element regions to facilitate simulations of large-scale systems.
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Acknowledgments
Helpful discussions with Dr. Michael Puso of Lawrence Livermore National Laboratory are gratefully acknowledged. Research support provided by the National Science Foundation, through Contract Grant Nos. NSFCMMI-0626481 and CMMI-0826513, is also acknowledged.
References
Atluri, S. N., Cho, J., and Kim, H. (1999). “Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations.” Comput. Mech., 2, 334–347.
Atluri, S. N., and Zhu, T. (1998). “A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics.” Comput. Mech., 22, 117–127.
Baker, J. F., and Roderick, J. W. (1952). “Tests on full-scale portal frames.” Proceedings of the Institution of Civil Engineers, Vol. 1, Institution of Civil Engineers, London, 71–94.
Beedle, L. S., and Christopher, R. (1964). “Tests of steel moment connections.” Eng. J., 1(4), 116–125.
Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., and Krysl, P. (1996). “Meshless methods: An overview and recent developments.” Comput. Methods Appl. Mech. Eng., 139, 3–47.
Belytschko, T., Lu, Y. Y., and Gu, L. (1994). “Element-free Galerkin methods.” Int. J. Numer. Methods Eng., 37, 229–256.
Chen, J. S., Wu, C. T., Yoon, S., and You, Y. (2001). “A stabilized conforming nodal integration for Galerkin meshfree methods.” Int. J. Numer. Methods Eng., 50, 435–466.
Chen, J. S., Yoon, S., and Wu, C. T. (2002). “Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods.” Int. J. Numer. Methods Eng., 53, 2587–2615.
Donning, B. M., and Liu, W. K. (1997). “Meshless methods for shear deformable beams and plates.” Comput. Methods Appl. Mech. Eng., 152(1–2), 47–71.
Fernández-Méndez, S., and Huerta, A. (2004). “Imposing essential boundary conditions in mesh-free methods.” Comput. Methods Appl. Mech. Eng., 193, 1257–1275.
Fries, T. P., and Matthies, H. G. (2004). “Classification and overview of meshfree methods.” Technical Rep. Informatikbericht-Nr. 2003-03, Institute of Scientific Computing, Technical Univ. Braunschweig, Braunschweig, Germany.
Gosz, M. R. (2006). Finite element method—Applications in solids, structures, and heat transfer, CRC, Boca Raton, Fla.
Huerta, A., and Fernández-Méndez, S. (2004). “A comparison of two formulations to blend finite elements and mesh-free methods.” Comput. Methods Appl. Mech. Eng., 193, 1105–1117.
Johnston, B. G., Yang, C. H., and Beedle, L. S. (1953). “Progress report no. 8, an evaluation of plastic analysis as applied to structural design.” Weld. J. (Miami, FL, U.S.), 32, 224s–239s.
Lancaster, P., and Salkauskas, K. (1992). “Surfaces generated by moving least-squares methods.” Math. Comput., 37, 141–158.
Li, S., and Liu, W. K. (2002). “Meshfree and particle methods and their applications.” Appl. Mech. Rev., 55(1), 1–34.
Liu, W. K., Jun, S., and Zhang, Y. F. (1995). “Reproducing kernel particle methods.” Int. J. Numer. Methods Eng., 20, 1081–1106.
Mazzoni, S., McKenna, F., Scott, M. H., and Fenves, G. L. (2007). OpenSees command language manual, The Regents of the Univ. of California, Berkeley, Calif., ⟨http://opensees.berkeley.edu/index.php⟩.
Nayroles, B., Touzot, G., and Villon, P. (1992). “Generalizing the finite element method: Diffuse approximation and diffuse elements.” Comput. Mech., 10, 307–318.
Phillips, A. (1956). Introduction to plasticity, Ronald Press, New York.
Puso, M. A., Chen, J. S., Zywicz, E., and Elmer, W. (2008). “Meshfree and finite element nodal integration methods.” Int. J. Numer. Methods Eng., 74, 416–446.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer, New York.
Simo, J. C., and Taylor, R. L. (1986). “Return mapping algorithm for plane stress elastoplasticity.” Int. J. Numer. Methods Eng., 22, 649–670.
Suetake, Y. (2002). “Element-free method based on Lagrange polynomial.” J. Eng. Mech., 128(2), 231–239.
Sukumar, N., and Wright, R. W. (2007). “Overview and construction of meshfree basis functions: From moving least squares to entropy approximants.” Int. J. Numer. Methods Eng., 70(2), 181–205.
Timoshenko, S. P., and Goodier, J. N. (1951). Theory of elasticity, 2nd Ed., McGraw-Hill, New York.
Weitzmann, R. (2004). “Limit state design of hybrid structures with meshless methods using mathematical optimization.” Institute of Structural Engineering, Bauhaus-University, Weimar, Germany, ⟨http://e-pub.uni-weimar.de/volltexte/2004/7/pdf/M_113.pdf⟩.
Yu, T. X., and Zhang, L. C. (1996). Plastic bending—Theory and applications, World Scientific, Singapore.
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© 2009 ASCE.
History
Received: May 21, 2007
Accepted: Dec 1, 2008
Published online: May 15, 2009
Published in print: Jun 2009
Notes
Note. Associate Editor: Keith D. Hjelmstad
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