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Buckling and post-buckling analysis of frame structures using a free-locking beam-SPH model
Thanh Hai Tuan Tran, Jamila Rahmoun, Hakim Naceur, Nguyen Dinh Son

Last modified: 2020-07-31


This work deals with the numerical modeling of buckling and post-buckling of thin frame structures using a newly developed Timoshenko beam-SPH model. Modeling of thin flexible structures using the 3D continuum SPH [1] formulation is not convenient, since several particles need to be used through the cross section, which results in an excessive increase of computational CPU time. A new extension of the Lagrangian Smoothed Particle Hydrodynamics (SPH) method has been introduced [2] to develop a geometrically nonlinear beam-SPH formulation valid for large displacements and rotations.

This is an improvement of the standard stabilized SPH [1] commonly used for continua, in the framework of Timoshenko beam theory, for the modeling of thick frame structures by using only one layer of particles in the beam mid-curve [3]. The proposed new Timoshenko beam-SPH model is efficient and very fast compared to the standard continuum SPH model. The Total Lagrangian Formulation valid for large deformations was adopted using a strong formulation of the differential equilibrium equations based on the principle of collocation.

The resulting nonlinear dynamic problem was solved incrementally using the Newmark time integration scheme, commonly used for structural dynamics applications. To validate the reliability and accuracy of the proposed Timoshenko beam-SPH model in solving buckling and post-buckling of frame structure problems, several numerical applications were solved and the results were compared with reference solutions from the literature or obtained using ABAQUS code.

Keywords: SPH, Timoshenko Beam, Frame Structures, Total Lagrangian Formulation, Newmark integration scheme.


1. LIU M.B., LIU G.R. (2010). Smoothed particle hydrodynamics (SPH): an overview and recent developments. Arch. Comput. Method. E., 17(1): 25-76.

2. LIN J., NACEUR H., COUTELLIER D., LAKSIMI A. (2015). Geometrically Nonlinear Analysis of two-dimensional structures using an improved Smoothed Particle Hydrodynamics Method. Engineering Computations, 32(3), pp. 779-805.

3. LI J., GUAN Y., WANG G., ZHAO G., LIN J., NACEUR H., COUTELLIER D. (2018). Meshless modeling of bending behavior of bi-directional functionally graded beam structures. Composites Part B: Engineering, 155, pp. 104-111.


SPH; Timoshenko Beam; Frame Structures; Total Lagrangian Formulation; Newmark integration scheme

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