请教：应变与位移函数关系

429745315

在看一本有限元书籍时，其中有一段话如下：

从数学角度讲，弹性势能上某种应变的积分，对于平面和实体问题，应变式位移函数的一阶导数，只要在单元边界上位移函数连续，积分则收敛；
对于梁，板和壳问题，应变是位移函数的二阶导数，只要位移函数C1连续，则积分收敛。




上面的对于梁板壳问题，位移与应变的关系不能理解，求高手解惑，谢谢!

tonnyw

在看一本有限元书籍时，其中有一段话如下：

从数学角度讲，弹性势能上某种应变的积分，对于平面和实体问题，应变式位移函数的一阶导数，只要在单元边界上位移函数连续，积分则收敛；
对于梁，板和壳问题，应变是 ...
429745315 发表于 2011-7-17 22:20

The continuity requirements depend on what kind of partial equations we are trying to solve.

For two-dimensional or three dimensional elasticity, you can see that the governing equation (strong form) has the second order derivative of the displacement. In the weak form, we will have first order derivative of the displacement. Even though the derivative is not continuous at the inter-elements edges, but as long as it is square integrable. We are fine.

For thin plate and shell or Euler beam, the governing equation is biharmonic and to have square integrable integral the first order derivative has to be continuous at the inter-element edges.

429745315

多谢 tonnyw

fengrui87

正在学习中！！