问题描述:
如下所示,面内连接的壳单元和梁单元在竖向荷载作用下,随着壳单元网格密度的增加,悬臂梁自由端的竖向位移值不断增大且毫无收敛于稳定值的趋势,最终数值高达百米以上(见右侧数据)。请问,我们应该如何理解和避免这一结果?
解答:
上述计算结果应该与“壳单元和梁单元之间的单点连接”造成的局部应力集中有关。在壳单元或实体单元的线弹性分析中,随着网格密度的不断增加,应力集中处的应力值将无限增大。基于“应力 → 应变 → 变形 → 挠度”的先后顺序和逻辑关系,悬臂梁自由端的竖向位移必然趋于无穷大。
事实上,应力集中是一种普遍存在的力学现象,而非有限元分析或网格划分引入的计算误差。但是,在实际的工程结构中并不存在无穷大的应力值,部分原因如下:
第一,实际的工程结构中并不存在理想的作用于一个点或仅通过一个点传递的集中力,集中力往往是对作用范围很小的分布力的简化和近似。因此,集中力往往存在于理论推导或数值计算中,包括类似 SAP2000 或 ETABS 的有限元软件。
第二,实际的工程结构在高应力区域往往存在材料的屈服或断裂,由此产生的内力重分布可有效“缓解”应力集中。从这个角度讲,有限元软件在线弹性分析中计算的由应力集中引起“超高”应力值往往缺少实际的参考价值。
在实际的工程结构中,上述墙体与梁的连接区域分布于梁的整个横截面,梁端的位移或内力在整个横截面范围内与墙体发生相互作用。因此,建议采用如下所示的节点约束模拟有限范围内的“墙-梁相互作用”,约束类型选用刚性板(Plate),约束轴平行于梁轴线,约束节点为梁高范围内的壳单元节点和梁端节点。
完成该操作后,对于前文五个不同网格密度的计算模型,悬臂梁自由端的竖向位移不再出现异常的“百米”数值,同时也可以看到“随着网格密度增加,位移解逐步收敛于稳定值”的趋势,详见下图右侧数据。
![](data:image/png;base64,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)