退化，剪切锁定，减缩积分

pyyp2

本人有一下几个问题：

1. “degenerated concepts in the formulation of element properties reducing those requiring C1 to C0" 退化的概念是把C1连续降到C0连续，但是后面讲的高阶位移模式，减缩积分，假定应变场都与插值多项式的次数的升降有关？那里能体现连续性的降低？插值多项式的次数和连续性没有什么必然的联系吧（如C0用不同次数的拉格朗日构造）
>>Could you provide the book or paper so we can take a closer look? The way I understand continuity is that at the interelement edges if we want to enforce the continuity of values, we just need C0 type functions. If we want the continuity of derivative, we need C1 type functions.
2. 为了防止剪切锁定的方法：1. 高阶位移模式 2. 减缩积分 3.假定应变场 这三种有什么理论根据吗？还就是发现有剪切锁定现象有试出来的？
>>I think at first people found the locking phenonma in computations. Then they did the investigation later and found the theories that explain why locking happens.
3. assumed strain field中队剪切应变进行单独插值，而且次数要比位移和转角低一阶，为什么要低一阶设置？
>>Strain is the first order derivative of displacement or rotation. So assumed strain has to be one order lower than displacement or rotation to make sure the compatibility.

4. 对plate的假定应变场方法中，需要对剪切应变的插值函数选取sample points，这个有什么规定，我看基本就是边界上布置，和按照高斯积分点布置，这个是剪切应变的sample points 布置，为什么有时遵循高斯积分点呢？
>>The choice of sampling points or tying points is not a random thing. You need the strain vlaues at sampling points to construct the assumed strain field. You definitely want the sampling strains to be a good one. The values at the Gauss integration points can exhibit superconvergent properties. Of course, this could be a mesh-dependent matter.