Optimal hole shape for arrest of longitudinal shear crack

Рассматривается задача об отыскании оптимальной формы отверстия в вершине трещины продольного сдвига. Искомая форма отверстия удовлетворяет условию минимальной концентрации напряжений на его контуре. Исследуется влияние отверстия оптимальной формы на торможение трещины. Дается критерий и метод решения задачи по предотвращению хрупкого разрушения тела, ослабленного прямолинейной трещиной продольного сдвига. Используется минимаксный критерий. Получено условие хрупкого разрушения. The problem of finding optimal hole shape at the tip of a longitudinal shear crack is considered. The desired hole shape satisfies the condition of the minimum stress concentration on the contour. The effect of the optimal hole shape on deceleration of a crack is studied. A criterion and solution method for the problem of preventing brittle fracture of the solid weakened by rectilinear longitudinal shear crack is given. The minimax criterion is used. The brittle fracture condition is obtained.

Autonomous Large Eddy Simulations Setup for Cooling Hole Shape Optimization

Film cooling is a common technique to manage turbine blade thermal environment. The geometry of the holes which are used to generate the cooling film is known to play a very important role on thermal performances and finding the most optimized shape involves rigorous experimental as well as numerical investigations to probe the many parameters at play. For the current study an automatic optimization tool is developed and then probed with the capability of performing hole shape optimization based on Large Eddy Simulation (LES) predictions. To do so, the particular geometry called shaped cooling hole is chosen as a baseline geometry for this optimization process. Relying on the response surface evaluation based on a reduced model approach, the use of a Design of Experiments (DOE) method allows probing a discrete set of values from the parameter space used to define the present shaped cooling hole. At first only two parameters are chosen out of the seven parameters defining the hole shape. This is followed by the automatic generation of the hole geometry, the corresponding computational domain and the associated meshes. Once the geometries and meshes are created, the numerical setup is autonomously completed for each of the cases including a first guess of the flow field to increase convergence of the simulation towards an exploitable solution. To finish, the LES fluid flow prediction is used to evaluate the discrete value of the problem response function which can then participate in the reduced model construction from which the optimization is derived.