梁单元与实体单元在分析简支梁振动模态时的差别？？？

学界雏鹰

分别采用梁单元(beam3)和实体单元(solid45)对一两端简支的梁进行模态分析，求得5000Hz以下各阶振动频率
如下所示：
1.beam3单元
23.52739
94.09795
211.67688
376.20626
587.60514
845.76971
1150.57349
1297.18971
1501.86755
1899.48081
2343.22035
2832.87176
3368.19952
3891.65076
3948.94745
4574.83915
2.solid45单元
24.65515
98.50903
221.21670
392.12018
609.85539
870.11901
1142.37217
1314.90913
1598.44489
1993.74231
2442.09875
2932.80131
3447.14439
3849.00369
4178.75387
4751.15324
而理论解是
23.52836
94.11343
211.75521
376.45371
588.20892
847.02085
1152.88949
1297.18630(纵向振动)
1505.81484
1905.79691
2352.83569
2846.93119
3388.08340
3891.55891(纵向振动)
3976.29232
4611.55796

请问：
1.为什么随着阶数的增大，beam3单元的计算结果与理论解的误差越来越大？？？
2.为什么实体单元计算结果与理论解的误差比梁单元计算结果与理论解误差大这么多？？？

程序如下：
1.梁单元-beam3
finish
/clear,nostart
/filname,Modal Analysis With Beam Element
/title,Natural Frequency of Undamping Euler Beam
*set,num,198      !沿梁长度方向划分的单元数量
length=1.0
width=0.01
height=0.01
xsect=width*height
inertiaz=(width*height**3)/12
/prep7
et,1,beam3
r,1,xsect,inertiaz,height,
mp,ex,1,2.1e11
mp,prxy,1,0.3
mp,dens,1,7800
k,1,0,0,0
k,2,length,0,0
l,1,2
lesize,all,1/num,,,      !网格数量
lmesh,all
/eshape,1
/replot
finish
/solu
antype,modal
modopt,lanb,30,0,5000,,off
mxpand,30,0,5000,yes,
dk,1,ux,,,,uy
dk,2,uy,,,
!outres,all,all
allsel,all
solve
finish
2.实体单元-solid45
finish
/clear,nostrat
keyw,pr_set,1
keyw,pr_struc,1
filname,Modal Analysis With Solid Element
/title,Natural Frequency of Undamping Euler Beam
*set,num,198      !沿梁长度方向划分的单元数量
/prep7
et,1,solid45
mp,ex,1,2.1e11
mp,prxy,1,0.3
mp,dens,1,7800
block,0,1,0.005,-0.005,0.005,-0.005
esize,1/num      !设置单元尺寸
mshape,0,3D
mshkey,1
vmesh,all
nsel,all
d,all,uz,0,0
nsel,s,loc,x,0
nsel,r,loc,y,-0.005
d,all,ux,,,,,uy
nsel,s,loc,x,1
nsel,r,loc,y,-0.005
d,all,uy,,,
allsel
finish
/solu
antype,modal
modopt,lanb,30,0,5000,,off
mxpand,30,0,5000
allsel
solve
finish

tonnyw

When you make comparison, it has to be apple-to-apple.
First, the analytical solution is based on the partial differential equation for the beam model. If you use beam element, the finite element solution is the approximation to the partial differential equation for beam model.

If you use brick element, you are solving the partial differential equation to the three-dimensional elasticity, which is -diverge(stress tensor) + second order time derivative = body force. Then you should compare your finite solution to the analytical solution of three-dimensional elasticity.

However, the results should be close to each other even the models are different.

guayigou

我觉得BEAM3结果蛮好的呢。
模态求解一般是一个迭代过程，误差会被放大，具体方式查你用的模态方法。
你这个是ansys的编程么？看看是不是lanczos或者别的方法。

金城肆

你好我想问一下，实体单元模拟简支梁约束条件是一个面全部约束，一个面竖直方向不约束么