问题描述:
请问,在非线性静力分析的【加载控制】选项中,共轭位移与监测位移到底有何不同呢?
解答:
监测位移以某个节点自由度(或广义位移)控制非线性静力分析的求解进程,同时以位移目标值作为非线性静力分析的终止条件。使用监测位移的优点在于,位移目标值可以在分析终止时得到精确满足;缺点则是监测位移值在整个分析过程中只能单调变化。所谓“单调变化”即:只能单调递增或单调递减,但不能先增后减或先减后增。换言之,位移不能“变向”!
监测位移的单调变化在某些情况下可能会导致非线性静力分析的失败。例如,某非对称高层建筑结构的静力 Pushover 分析以顶层位移作为监测位移,但该楼层在侧向荷载作用下极有可能发生扭转。在这种情况下,监测位移在整个推覆过程中很可能会出现一个“先增后减”的变化过程,这将导致非线性静力分析无法收敛,后续自然无法获取完整的 Pushover 曲线。
为了避免上述监测位移导致的收敛性问题,我们可以采用共轭位移来控制非线性静力分析的求解进程。共轭位移是整个结构中全部位移的加权平均值,而权重就是作用于每个节点自由度的荷载值。因此,共轭位移也可以视为外荷载所作的功,只要外荷载持续做正功(即结构的应变能持续增加),非线性分析就能持续进行下去!在整个非线性分析过程中,用户选择的位移分量可增可减可“变向”,但最终结果可能与目标值相去甚远,即目标值无法得到精确满足。
接下来,我们以一个简单的算例验证以上关于监测位移和共轭位移的论述。该算例并非取自实际的工程项目,其目的在于加深读者对监测位移和共轭位移的理解。计算模型的基本情况如以下左图所示,此处不再赘述。值得一提的是,我们在 #11 节点处布置竖向的间隙(Gap)单元并设置 1cm 的初始间隙,这将导致 #10 节点在整个加载过程中的竖向位移先增后减且峰值接近 1cm,如右图所示。
现针对上述模型分别定义四个非线性静力工况,位移控制选项及分析结果如下表所示。从表中数据可以看出,由于 #4 节点的竖向位移在整个加载过程单调递增,故监测位移与共轭位移的结果并无区别且均能收敛。
但是,#10 节点的竖向位移在整个加载过程先增后减,故监测位移无法收敛,共轭位移却可以收敛。注意,第 4 个工况中 #10 节点的最终位移为 -2cm 而非 2cm,这样因为用户在位移控制选项中输入的位移目标值为绝对值,-2cm 同样满足要求。
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)