| Recently, topology optimization is the hottest problems in international structure optimization filed, through which better schemes can be chosen in concept design stage. Development becoming ripe with its theory, grow from pure theoretical research to project practice terms of the application stage ripe becoming appropriate. This text study the topological basic theories and discuss the application in the field of hydraulic engineering on the basis of reading a large number of foreign reports, the most works are:1. This thesis investigates the design problems of hydraulic engineering using homogenization method, which is the most mature method in topology optimization. It explains the mathematics homogenization method model and formulaon the base of microstructures.2. Alternative hydraulic engineering structural design are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain, Small-strain integration algorithms for general two-material mixtures of solids are developed for the Voigt-Reuss assumption, and the number of calculations is cut short. This text empoldered topology optimization program using APDL language of ANSYS, and it realized topology optimization of hydraulic engineering form the point of the view of technique.3. Form the point view of inverse PDE, the essence of numerical instabilities in the topology optimization is given, including checkerboard pattern and mesh-dependence. Based on this explanation, a novel method-Gaussian method and multi-grid method are proposed, then extended radius of filter wave are introduced to reduce the influence of local extremum phenomena.4. After decreasing the computation scale and solving the numerical instabilities, we use the continuum topology optimization to design hydraulic engineering, and compared the results in topology optimization with the results in traditional optimization, the outcome showed that topology optimization is better and the it is widely use.
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