Analysis of sensitivity and numerical stability in the calculation of factors of tension intensity in a case of fracture mechanics
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Universidad Industrial de Santander
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El artículo aborda el cálculo de factores de intensidad de tensiones en un caso de mecánica de fractura en placas de acero bajo configuración de carga uniforme. Se explora la sensibilidad del factor de primer modo de intensidad de tensiones KI respecto a las relaciones a/w, a/h, h/w (a: tamaño de fractura inicial, w: ancho de placa, h: distancia vertical entre la fractura y la línea de carga). Se realizan comparaciones de los resultados obtenidos por diferentes metodologías como la analítica obtenida de la literatura, el método de colocación del contorno implementado en el software libre MAXIMA y el método de elementos finitos implementado a través de un modelo en ANSYS. Dado que, el método de colocación del contorno incorpora una solución generalizada por mínimos cuadrados, es posible observar algunos problemas de inestabilidad numérica asociados principalmente a casos en los que el tamaño de la fractura inicial es considerable respecto al ancho de la placa cargada. Los aportes más destacados se dan respecto al análisis de sensibilidad particular del caso, el análisis de problemas de inestabilidad numérica en situaciones específicas de cálculo de KI, implementaciones de códigos en software libre como MAXIMA e implementación de modelos de elementos finitos en ANSYS usando elementos Quarter Point. Los resultados obtenidos se reportan mediante comparaciones numéricas y gráficas del comportamiento del factor KI para las diferentes relaciones estudiadas, bajo las diferentes metodologías. El articulo concluye sobre cuáles son las relaciones significativas en la sensibilidad del factor de intensidad de tensiones KI y el origen de los problemas de inestabilidad numérica del método de colocación mediante el estudio paramétrico asociado al número de condición del sistema de la matriz global del mismo método.
The article studies the calculation of stress intensity factors in a case of fracture mechanics in steel plates under uniform load configuration. The sensitivity of the first mode factor of stress intensity KI with respect to the relationships a/w, a/h, h/w (a: initial fracture size, w: plate width, h: vertical distance between fracture and the loading line) is explored. We perform comparisons of the results obtained by different methodologies such as the analytical obtained from the literature, the method of placement of the contour implemented in the free software MAXIMA and the finite element method implemented through a model in ANSYS. Since the method of positioning the contour incorporates a generalized least squares solution, we could observe some problems of numerical instability associated mainly to cases in which the size of the initial fracture is considerable with respect to the width of the loaded plate. The most relevant contributions are given regarding the particular sensitivity analysis of the case, the analysis of problems of numerical instability in specific situations of KI calculation, implementations of free software codes such as MAXIMA and implementation of finite element models in ANSYS using Quarter Elements Point. The results obtained are reported by numerical and graphical comparisons of the behavior of the KI factor for the different relationships studied under different methodologies. The article concludes on what are the significant relations in the sensitivity of the stress intensity factor KI and the origin of the problems of numerical instability of the placement method by the parametric study associated to the condition number of the system of the global matrix of the same method.
The article studies the calculation of stress intensity factors in a case of fracture mechanics in steel plates under uniform load configuration. The sensitivity of the first mode factor of stress intensity KI with respect to the relationships a/w, a/h, h/w (a: initial fracture size, w: plate width, h: vertical distance between fracture and the loading line) is explored. We perform comparisons of the results obtained by different methodologies such as the analytical obtained from the literature, the method of placement of the contour implemented in the free software MAXIMA and the finite element method implemented through a model in ANSYS. Since the method of positioning the contour incorporates a generalized least squares solution, we could observe some problems of numerical instability associated mainly to cases in which the size of the initial fracture is considerable with respect to the width of the loaded plate. The most relevant contributions are given regarding the particular sensitivity analysis of the case, the analysis of problems of numerical instability in specific situations of KI calculation, implementations of free software codes such as MAXIMA and implementation of finite element models in ANSYS using Quarter Elements Point. The results obtained are reported by numerical and graphical comparisons of the behavior of the KI factor for the different relationships studied under different methodologies. The article concludes on what are the significant relations in the sensitivity of the stress intensity factor KI and the origin of the problems of numerical instability of the placement method by the parametric study associated to the condition number of the system of the global matrix of the same method.
Keywords
Sensibility analysis, ANSYS, MAXIMA, method of placement of the contour, finite elements, fracture mechanics, Análisis de sensibilidad, ANSYS, MAXIMA, métodos de colocación del contorno, elementos finitos, fractura