Transient dynamic analysis of cracked structures with multiple contact pairs using generalized HSNC
Transient dynamic analysis of cracked structures with multiple contact pairs using generalized HSNC
复制标题
使用广义 HSNC 对具有多个接触对的裂纹结构进行瞬态动态分析
作者：
Meng;Kiran D’Souza
由于裂纹对结构动力学的影响在设计、预测和健康监测中起着重要的作用，因此发展有效的裂纹结构计算方法在土木、机械和航空航天工程领域是至关重要的。裂纹表面的间歇性接触所引起的非线性通常排除了快速线性方法的使用，没有快速线性方法，复杂裂纹结构的动力学计算变得非常具有挑战性。本文介绍了一种计算含裂纹多接触结构瞬态和稳态响应的有效方法。新算法被称为广义混合符号-数值计算（HSNC）方法。广义HSNC方法扩展了原来的HSNC方法，这是最近开发的双线性系统，一般的分段线性非线性系统。本文还将HSNC与$$hbox {X}-hbox {X}_{r}$$X-Xr方法（一种裂纹结构的降阶建模技术）相结合，有效地预测了含裂纹复杂结构的动力学行为。广义HSNC方法是基于这样的思想，即多个接触对的裂纹结构的非线性响应可以通过组合系统在其每个线性状态下的线性响应来获得。这些线性响应可以象征性地表示为系统线性行为的每个时间范围内开始时间点处初始条件的函数。系统从一个线性状态切换到另一个线性状态的过渡时间，发现使用非线性优化求解器与增量搜索过程提供的初始值。该方法能够单独跟踪每个接触对的状态，因此，它可以用来预测系统的动态时，裂纹表面不完全打开或关闭。此外，新方法可以捕捉到复杂裂纹结构在各种加载条件下的瞬态和稳态响应。广义HSNC方法提供了一个灵活的计算框架，比传统的数值积分方法快几个数量级。用该方法研究了含单裂纹和多裂纹的弹簧-质量系统和悬臂梁模型的动力学问题。
The development of efficient computational methods for cracked structures is critical in the fields of civil, mechanical, and aerospace engineering since the influence of cracks on structural dynamics can play an important role in design, prognosis, and health monitoring. The nonlinearity caused by the intermittent contact on the crack surfaces typically excludes the use of fast linear methods, without which the computation of the dynamics of complex cracked structures becomes very challenging. In this paper, an efficient computational scheme for predicting both the transient and steady-state responses of cracked structures with multiple contact pairs is introduced. The new algorithm is referred to as the generalized hybrid symbolic–numeric computational (HSNC) method. The generalized HSNC method extends the original HSNC method, which was recently developed for bilinear systems, to general piecewise-linear nonlinear systems. This work also combines the HSNC with the $$hbox {X}-hbox {X}_{r}$$X-Xr method, a reduced-order modeling technique for cracked structures, to efficiently predict the dynamics of complex structures with cracks. The generalized HSNC approach is based on the idea that the nonlinear response of a cracked structure with multiple contact pairs can be obtained by combining linear responses of the system in each of its linear states. These linear responses can be symbolically expressed as functions of the initial conditions at starting time points in each time range where the system behaves linearly. The transition time where the system switches from one linear state to another is found using a nonlinear optimization solver with the initial values provided by an incremental search process. The method is able to individually track status of each contact pair; therefore, it can be used to predict the dynamics of the system when the crack surfaces are not completely open or closed. Moreover, both the transient and steady-state responses of complex cracked structures under various forcing conditions can be captured by the new method. The generalized HSNC method provides a flexible computational framework that is several orders of magnitude faster than traditional numerical integration methods. The dynamics of a spring–mass system and cantilever beam models that contain one crack and multiple cracks are investigated using the proposed method.