A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems
A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems
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DOI：
10.1016/j.enganabound.2019.05.021
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发表时间：
2019-09-01
影响因子：
3.3
通讯作者：
Aliabadi, M. H.
中科院分区：
文献类型：
--
作者：
Morse, Llewellyn;Khodaei, Zahra Sharif;Aliabadi, M. H.
提出了一种使用双边界元法 (DBEM) 确定板弯曲问题的应力强度因子 (SIF) 敏感性的新方法。首次导出板弯曲的 DBEM 积分方程的直导数，并将其用作基于 DBEM 的隐式微分方法（IDM 或 DBEM-IDM）的一部分，用于计算 SIF 对裂纹长度和裂纹旋转角度等不同几何参数变化的敏感性。 SIF 及其灵敏度分别使用 J 积分和 J 积分的导数计算。给出了一个厚板承受膜、弯曲和压力载荷的数值示例。在数值示例的前半部分中，将 IDM 的 SIF 灵敏度与更常见但相对粗糙的有限差分法（FDM 或 DBEM-FDM）获得的 SIF 灵敏度进行了比较。结果表明，IDM 是比 FDM 更高效、更稳健的替代方案。 FDM 的精度显着依赖于所使用的步长，因此需要耗时的优化过程来确定最佳步长。一旦找到最佳步长，两种方法都会提供非常相似的结果。作为数值示例后半部分的一部分，演示了 IDM 的 SIF 灵敏度的一种可能应用。这涉及使用一阶可靠性方法 (FORM) 和大量设计变量进行可靠性分析。
A novel methodology for determining Stress Intensity Factor (SIF) sensitivities for plate bending problems using the Dual Boundary Element Method (DBEM) is presented. The direct derivatives of the DBEM integral equations for plate bending have been derived for the first time and are used as part of a DBEM-based Implicit Differentiation Method (IDM or DBEM-IDM) for calculating the sensitivities of SIFs to changes in different geometric parameters such as crack length and crack rotation angle. The SIFs and their sensitivities are calculated using the J-integral and the derivative of the J-integral respectively. A numerical example featuring a thick plate subjected to membrane, bending, and pressure loads is presented. In the first half of the numerical example, the SIF sensitivities from the IDM are compared with those obtained from the more common, but relatively crude, Finite Difference Method (FDM or DBEM-FDM). Results show that the IDM is a significantly more efficient and robust alternative to the FDM. The accuracy of the FDM showed significant dependence on the step size used, necessitating a time-consuming optimisation procedure to determine the optimal step size. Once this optimal step size was found, both methods provided very similar results. As part of the second half of the numerical example, a demonstration of one possible application of the SIF sensitivities from the IDM is presented. This involved carrying out reliability analyses using the First-Order Reliability Method (FORM) with a large number of design variables.