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Constitutive relation error formalism applied to the solution of inverse problems using the BEM

机译：本构关系误差形式主义应用于利用边界元法求解反问题

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摘要

Mechanical connections are crucial for describing appropriately the global behaviour of structural systems. It is observed in real structures that connections are subjected to nonlinear effects such as damages, cracks, adherence losses and friction. These phenomena are complex to handle in terms of modelling. As alternative, connections can often be admitted as perfectly rigid which may prove to be conservative in many cases. A more realistic approach is considering connections as semi-rigid. In this case, a new difficulty arises even assuming linear elastic behaviour, i.e., which values should be specified for the elastic parameters in order to represent as accurate as possible the reality? The present study proposes an innovative numerical procedure for answering this question. For sake of compactness, the analysis is limited to plane elasticity assuming Hookean behaviour for connections and static loading conditions. The formulation is based on a set of reference boundary fields representative of the current static loading state. Then, the complementary mechanical unknowns are predicted using the Boundary Element Method. The Constitutive Relation Error formalism is applied to write the interface parameters search as non-linear inverse problem. The results show good agreement with the reference cases.
机译：机械连接对于正确描述结构系统的整体行为至关重要。在实际结构中观察到，连接会受到非线性影响，例如损坏，裂纹，附着力损失和摩擦。这些现象在建模方面很难处理。作为替代方案，通常可以认为连接是完全刚性的，这在许多情况下可能是保守的。一种更现实的方法是将连接视为半刚性。在这种情况下，即使假设线性弹性行为，也将出现新的困难，即，应为弹性参数指定哪些值，以便尽可能准确地表示实际情况？本研究提出了一种创新的数值程序来回答这个问题。为了紧凑起见，假设连接和静态载荷条件为Hookean行为，则分析仅限于平面弹性。该公式基于代表当前静态载荷状态的一组参考边界场。然后，使用边界元方法预测互补的机械未知数。应用本构关系误差形式主义将接口参数搜索写为非线性反问题。结果表明与参考案例吻合良好。

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