Method for predicting upper and lower bounds of bounded uncertain plane crack stress intensity factors based on fractal theory

Abstract

The invention discloses a method for predicting upper and lower bounds of bounded uncertain plane crack stress intensity factors based on a fractal theory. According to a geometric model including a crack structure, the geometric model is divided into a conventional region and a fractal region of crack tips by using an artificial boundary to establish a bounded uncertain structural static force response solution model in the conventional region; a William's general solution is used as an interpolation function to establish a bounded uncertain structural static force response solution model in the fractal region; then, assembly is performed to obtain a whole bounded uncertain structural static force response solution model including a crack structure, the upper and lower bounds of bounded uncertain generalized coordinates are calculated by adopting a first-order Taylor expansion based interval analysis method, and further the upper and lower bounds of the bounded uncertain plane crack stress intensity factors are calculated. The upper and lower bounds of the bounded uncertain plane crack stress intensity factors are calculated are accurately and efficiently obtained by adopting the method, and objective and effective data is provided for reliability evaluation and design of structures.

Description

technical field [0001] The invention is applicable to the prediction of the upper and lower bounds of the stress intensity factor of a bounded uncertainty plane crack, and specifically relates to a prediction method of the upper and lower bounds of the stress intensity factor of a bounded uncertainty plane crack based on fractal theory and a non-probability interval analysis method. Background technique [0002] In engineering practice, mechanical equipment and metal structure components often have macroscopic cracks caused by manufacturing, use or defects of the material itself. At this time, to determine whether the component can continue to be used safely, the most important thing is to judge whether the crack will expand unstable and cause damage to the structure and equipment. The stress intensity factor reflects the stress field and displacement field near the crack tip, and is a measure of the crack growth tendency and crack growth driving force. From the point of vi...

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Problems solved by technology

The above work enriches the analysis of plane crack stress intensity factors to a certain extent, but ignores the dependence of the probability method on the sample information, which greatly limits the progress of its theory in engineering practice

Due to poor information and little data in actual engineering, it is of great significance to establish a boundary prediction method for stress intensity factors based on a non-probability theoretical framework. At present, the relevant research work is still immature and cannot meet the needs of actual engineering.

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