The problem of minimum weight design of laminated circular sandwich plates with axial symmetry is formulated using optimal control theory. A steepest descent algorithm is used to solve the resulting two point boundary value problem. Inequality constraints on minimum face and core thicknesses, maximum stress levels and maximum displacement are included. Both statically determinate and statically indeterminate plates are considered. Several examples are presented illustrating the general configuration of minimum weight designs and the dramatic weight savings attainable.
In the process of running of the blast furnace top gas pressure recovery turbine, abnormal noise and vibration from the gas turbine engine were noticed. One blade was found fractured from the middle during the overhaul inspection of this machine after running. In order to avoid the similar accident from happening again, comprehensive inspections on the failed blade have been carried out with the mechanical property testing, metallographic structure observation, chemical composition analysis, macro-fracture and micro-fracture analysis, and energy spectrum analysis. The analytical results show that many spherical particles are noticed in the area of crack initiation, and these spherical particles are similar to the blade material in chemical composition. After a series of tests, it was thought that these spherical particles are the remnant of molten metal that was firstly cooled in the process of blade casting, and they became the vulnerable part in the blade. When the blade rotates at relatively high speed, the synthesis of centrifugal and aerodynamic stresses may cause the occurrence of stress concentration in the vulnerable part inside of blade, causing the initiation and propagation of crack and subsequently resulting in the blade fracture.
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