Abstract
Using the base forces as fundamental variables to describe the stress state and the displacement gradients that are the conjugate variables of the base forces to describe the deformation state for the two-dimensional elasticity problems, a 4-mid-node plane model of base force element method (BFEM) based on complementary energy principle is proposed. In this chapter, the complementary energy of an element of the BFEM is constructed using the base forces. The equilibrium conditions are released by the Lagrange multiplier method, and a modified complementary energy principle described by the base forces is obtained. The formulation of the 4-mid-node plane element of the BFEM is derived by assuming that the stress is uniformly distributed on each side of the plane element. A procedure of the BFEM on complementary energy principle is developed using MATLAB language. The numerical results of examples show that this model of the BFEM has high precision and is free from mesh sensitivity. This model shows good performances.
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References
Kim, K. D., Liu, G. Z. & Han, S. C. (2005). A resultant 8-node solid-shell element for geometrically nonlinear analysis. Computational Mechanics, 35(5), 315–331.
Liu, Y. H., & Peng, Y. J. (2011). Base force element method (BFEM) on complementary energy principle for linear elasticity problem. Science China-Physics, Mechanics & Astronomy, 54(11), 2025–2032.
Liu, Y. H., Peng, Y. J., Zhang, L. J., & Guo, Q. (2013). A 4-mid-node plane model of base force element method on complementary energy principle. Mathematical Problems in Engineering, 2013, 1–8.
Peng, Y. J., Bai, Y. Q., & Guo, Q. (2017). Analysis of plane frame structure using base force element method. Structural Engineering and Mechanics, 62(4), 11–20.
Santos, H. A. F. A., & de Almeida, J. P. M. (2010). Equilibrium-based finite element formulation for the geometrically exact analysis of planar framed structures. Journal of Engineering Mechanics, 136(12), 1474–1490.
Zienkiewicz, O. C. (1977). The finite element method. New York: McGraw-Hill.
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Peng, Y., Liu, Y. (2019). 2D Base Force Element Method for Linear Elastic Problems. In: Advances in the Base Force Element Method. Springer, Singapore. https://doi.org/10.1007/978-981-13-5776-3_4
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DOI: https://doi.org/10.1007/978-981-13-5776-3_4
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