非线性自然弯扭闭口薄壁复合梁的广义变分原理

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Generalized Variational Principle on Nonlinear Theory of Naturally Curved and Twisted Closed Thin-Walled Composite Beams

Key Laboratory of Solid Mechanics of MOE, Tongji University, Shanghai 200092, P R China

摘要: 对复合材料自然弯扭闭口薄壁细长梁在小应变、大位移和大转动的情况作了研究,建立了两端边界均为完全约束的该梁大变形弹性理论的非完全广义变分原理的泛函。由泛函驻值条件可以导出所给问题的平衡方程及全部边界条件。上述方法可方便地推广到其它各种不完全约束边界的情况。此外,利用上述结果还可以得到该梁在小位移理论中的基本方程和有关公式。
- 广义变分原理 /
- 几何非线性 /
- 大变形
Abstract: Naturally curved and twisted closed thin-walled slender beams of composite material undergoing small strains, large displacements and rotations have been investigated, and an incomplete generalized variational function on theory of elasticity with finite displacement is established for these beams with complete constrained boundaries at two ends. The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition. The above-mentioned method can also be extended to other various incomplete constrained boundaries conveniently. In addition, the fundamental equations and concerned formulas in the small displacement theory of the beams can be derived by using above results.
- generalized variational principle /
- geometric nonlinear /
- finite displacement

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