Probabilistic modeling of crack growth in large structures

Abstract

The allowance for various defects including cracks represents a critical issue related to structural risk analysis. The complexity and the ambiguity involved with such allowance for the amount and growth of defects (cracks) is demonstrated on the real structure of a metallurgical overhead crane. The problem of distribution function conversion must be solved to allow for any variations in defects starting from the point of time when the initial (technological) defectiveness is determined and ending with the estimated time of risk analysis. Due to the lack of data on cyclic resistance to cracking for Вст3сп5 steel, it does not yet seem possible to construct the distribution functions and to determine the estimated theoretical average and dispersion of crack sizes. However, by using the previously obtained calculated data on active stresses and strains, it is now possible to simulate growth of cracks based on Weibull distribution. Different engineering solutions can be accepted at various stages of operating large structures, according to the obtained results.

Nonlinear Dynamics of Heavy Structures

“…𝑁𝑁 � �⃗ is the cycle vector attained by the structure during its operation; 𝜎𝜎 ⃗, 𝜀𝜀 ⃗ are the effective stress and strain vectors. Based on [1][2][3][4][5][6][7][8][9][10][11][12][13] and operational documentation we can assume that the above three vectors are the main ones, which determine the dynamics of the structural load-carrying capability, reliability P and risk of integral failure R for the entire structure.…”

“…It was demonstrated in the previous studies [1,2] that the function of probability density for the number of cycles and the effective stresses and strains of structures operating in heavy-loaded conditions is subject to the normal law of distribution. Thus, the expected value 𝑆𝑆 ̅ , the dispersion 𝑆𝑆 2 and the function of probability density for the load-carrying capability can be represented as follows: Based on [3][4][5], we assume that the structural load-carrying capability will conform to the following rules (wild cards):…”

“…Applicability of risk analysis for heavy structures was demonstrated by the authors in their previous studies [1,2]. As representatives of one of the science departments of the Nosov Magnitogorsk State Technical University, the authors conventionally utilize the resources provided by vector-matrix algebra and structural matrix mechanisms when addressing various process-and equipment-related problems in rolling production [3,4].…”

Stochastic Processes Occurring during the Transition of Technical State of the Structure

“…This particularly applies to the heavy structures operating under different conditions such as cranes of different applications, bridges, pipelines, spaceship masts, etc. [2][3][4][5][6]. For the majority of these structures, the existing technical state is far from perfect [2][3][4][5].…”

“…[2][3][4][5][6]. For the majority of these structures, the existing technical state is far from perfect [2][3][4][5]. The dynamic pattern of their technical state transition can be described by the theory of stochastic processes [1,[6][7][8][9][10][11].…”