荷载作用在四边形单元上怎么向节点等效

momo仿真

当集中荷载作用在四边形单元上怎么向节点等效，以及在ansys中怎么实现，各位大侠们会的给点指导，谢谢！学ansys的女生伤不起:Q

tonnyw

The answer to your question can be found in almost all the finite element books. Just find one and read it.

momo仿真

tonnyw 发表于 2012-9-13 08:50
The answer to your question can be found in almost all the finite element books. Just find one and r ...

有限元书上介绍的一般都是三节点单元的节点荷载等效，版主能推荐一本好书么 感谢

tonnyw

For concentrated loads, it depends on what kind of elements you are using. It is okay for shell or plate elements. For 2D plane element, point load is not admissible. It is better to convert the point load into some kind of line load.

ggbbggb

tonnyw 发表于 2012-9-18 11:04
For concentrated loads, it depends on what kind of elements you are using. It is okay for shell or p ...

Could you elaborate on why "for 2D plane element, point load is not admissible."?

penultimate

1. 精确方法
点荷载作用点处的位移模式叠加是已知的，用虚功原理求出等效节点力。该原理在有限元书上都有介绍。
该方法在理论上是严谨的，但在使用上不太方便
2.简化方法
可以用简化的静力平衡方法，将四边形分成两个三角形对，对每对三角形进行静力平衡等效，每次分配一半点荷载的值（点荷载必定位于其中的一个三角形内）
3.更简化的方法
1/4分配即可

你采用的单元只要在理论上是收敛的，当网格密到一定程度时，以上3种方法的结果也会收敛到相同的值

tonnyw

ggbbggb 发表于 2012-9-18 11:10
Could you elaborate on why "for 2D plane element, point load is not admissible."?

The finite element formulation is based on the assumption that the strain energy is finite. If you have point load on 2D plane element, the strain energy is not finite.

ggbbggb

tonnyw 发表于 2012-9-19 00:02
The finite element formulation is based on the assumption that the strain energy is finite. If you ...

This also applies in theory of elasticity. At the point of concentrated load, there is no closed-form solution. However, we distract the interest, e.g. using St.Venant. If this is the case, there is no problem in  transforming the concentrated  load to nodal load using "work equivalence", which is exactly what  is assumed in using FEM?

tonnyw

ggbbggb 发表于 2012-9-19 10:12
This also applies in theory of elasticity. At the point of concentrated load, there is no closed-f ...

It has nothing to do with St. Venant principle.

ggbbggb

tonnyw 发表于 2012-9-20 21:58
It has nothing to do with St. Venant principle.

Maybe you misunderstand the role of S.V. in my last comment.