主要期刊论文

作者: P. S. Geng, T.C. Duan and L.X. Li* |

发表/完成日期: 2017-10-01 |

期刊名称: International Journal of Mechanical Sciences |

期卷: |

相关文章: |

论文简介 |

A beam problem is though classical but not well stated theoretically at present. Different
from previous publications, this paper begins with definitions of the generalized displacements. With two assumptions and the shear stress free condition, the axial displacement is first mathematically expanded into two terms and then expressed as an orthogonal form in terms of the generalized displacements. Based on the orthogonal form, the generalized stresses are defined, and the uncoupled constitutive relations are then derived for beam problems after the generalized strains are properly measured. The principle of virtual work is proposed and the variationally consistent higher-order beam theory is eventually established. With these preliminaries, the finite element method is readily formulated like a three-dimensional elastic problem, and then validated through typical examples. The results show that, while accurately simulating the deflection, the higher-order beam element can capture the effect of clamped end and load jump via smoothly modeling the warping of cross section by using a locally refined mesh. It is straightforward to extend the current work to modern beam structures by taking into account the effect of nonlocal elasticity, small scales and material heterogeneities. |