A geometrically nonlinear total Lagrangian meshfree formulation based on the stabilized conforming nodal integration is presented for efficient analysis of shear deformable beam. The incremental equilibrium equation is obtained by the consistent linearization of variational equation. The meshfree shape function is constructed purely based on the initial configuration. Subsequently to accelerate the computation the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation. Both stability and efficiency are gained in the proposed nonlinear meshfree beam formulation. The effectiveness of the present method is validated by two typical numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chen J.S., Wu C.T.,Yoon S., You Y. (2001). A stabilized conforming nodal integration for Galer-kin meshfree methods. Int. J. Numer. Methods Eng., 50: 435–466.
Chen J.S., Wang D. (2006). A constrained reproducing kernel particle formulation for shear de-formable shell in Cartesian coordinates, Int. J. Numer. Methods Eng., 68:151–172.
Li M. (1997). The finite deformation theory for beam, plate and shell. Part I: the two dimensional beam theory. Comput. Methods Appl. Mech. Eng., 146:53–63.
Li S., Liu W.K. (2004). Meshfree Particle Methods, Springer-Verlag.
Mattiasson K. (1981). Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals. Int. J. Numer. Methods Eng., 17:145–153.
Wang D., Chen J.S. (2004). Locking free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation, Comput. Methods Appl. Mech. Eng., 193:1065–1083.
Wang D., Dong S.B., Chen J.S. (2006). Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry, Int. J. Solids Struct., 43:144–171.
Wang D., Chen J.S. (2006). A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration, Computational Mechanics, 39:83–90.
Wang D., Wu Y. (2008). An efficient Galerkin meshfree analysis of shear deformable cylindrical panels, Interaction and Multiscale Mechanics, 1:339–355.
Wang D., Chen J.S. (2008). A Hermite reproducing kernel approximation for thin plate analysis with sub-domain stabilized conforming integration, Int. J. Numer. Methods Eng., 74:368–390.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, D., Sun, Y. (2009). An Efficient Nonlinear Meshfree Analysis of Shear Deformable Beam. In: Yuan, Y., Cui, J., Mang, H.A. (eds) Computational Structural Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2822-8_110
Download citation
DOI: https://doi.org/10.1007/978-90-481-2822-8_110
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2821-1
Online ISBN: 978-90-481-2822-8
eBook Packages: EngineeringEngineering (R0)