非对称楔形重力坝受重力和液体压力的弹性力学解

ELASTICITY SOLUTION FOR NONSYMMETRIC WEDGE DAMS UNDER GRAVITY AND HYDROSTATIC PRESSURE

  • 摘要: 弹性力学教材给出了楔形重力坝的应力场理论解,但假定坝体受液压边界与重力方向平行且下端无限延伸,这与实际工程重力坝不符。本文针对更加贴近实际工程的非对称楔形重力坝,采用叠加原理和半逆解法推导了应力场的理论解,并与有限元分析进行了对比。理论解与有限元数值结果在远离坝底区域吻合,说明了理论解的准确性。本文研究结果不仅对重力坝的工程设计具有一定的指导意义,还为弹性力学提供了具体的教学实践。

     

    Abstract: The textbook of Elasticity presents a theoretical solution to the stress filed of a wedge dam. This model assumes that the boundary subjected to hydrostatic pressure is parallel to the gravity and that the lower end extends infinitely, which does not align with engineering design. In the current work, we establish a mechanics model for a nonsymmetric wedge dam that is more practically relevant, and derive the analytical solution to the stress field by virtue of the principle of superposition and the semi-inverse method. Finite element analysis is performed to obtain numerical results for the stress field, demonstrating the accuracy of the theoretical solution in regions far from the dam base. This work provides valuable insights for the engineering design of gravity dams and contributes a concrete example to the theory of elasticity.

     

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