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Interval static analysis of multi-cracked beams with uncertain size and position of cracks

机译：具有不确定尺寸和裂缝位置的多裂梁的区间静态分析

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摘要

This paper deals with beams under static loads, in presence of multiple cracks with uncertain parameters. The crack is modelled as a linearly-elastic rotational spring and, following a non-probabilistic approach, both stiffness and position of the spring are taken as uncertain-but-bounded parameters. A novel approach is proposed to compute the bounds of the response. The key idea is a preliminary monotonicity test, which evaluates sensitivity functions of the beam response with respect to the separate variation of every uncertain parameter within the pertinent interval. Next, two alternative procedures calculate lower and upper bounds of the response. If the response is monotonic with respect to all the uncertain parameters, the bounds are calculated by a straightforward sensitivity-based method making use of the sensitivity functions built in the monotonicity test. In contrast, if the response is not monotonic with respect to even one parameter only, the bounds are evaluated via a global optimization technique. The presented approach applies for every response function and the implementation takes advantage of closed analytical forms for all response variables and related sensitivity functions. Numerical results prove efficiency and robustness of the approach, which provides very accurate bounds even for large uncertainties, avoiding the computational effort required by the vertex method and Monte Carlo simulation.
机译：本文在静载下涉及静态负荷，存在多个具有不确定参数的裂缝。裂缝被建模为线性弹性旋转弹簧，并且在非概​​率方法之后，弹簧的刚度和位置均被视为不确定但有界参数。提出了一种新的方法来计算响应的范围。关键思想是初步单调性测试，其评估光束响应的灵敏度函数相对于在相关间隔内的每个不确定参数的单独变化的单独变化。接下来，两个替代程序计算响应的下限和上限。如果响应是关于所有不确定参数的单调，则通过基于直接的灵敏度的方法计算界限，利用单调性测试中内置的灵敏度函数来计算。相反，如果响应不是甚至一个参数的响应不是单调，则通过全局优化技术评估界限。所提出的方法适用于每个响应函数，实现利用封闭的分析形式进行所有响应变量和相关的灵敏度函数。数值结果证明了这种方法的效率和鲁棒性，即使对于大的不确定性，也提供了非常准确的界限，避免了顶点方法和蒙特卡罗模拟所需的计算工作。

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