北航计算固体力学大作业,网格收敛性分析

Homework of Computational Solid Mechanics

Element Type : PLANE 183 with 8 nodes

Thick of the plane : 0.01m

Material Properties :

EX=2×105Mpa PRXY=0.3 Density=7800kg/m3

Case1:

Concentrated loads F respectively applied on A and B ,F=10kN Case2:

Uniformly distributed load q applied on line AB ,q=20kN/m

1、1×1 meshing

A and

B have the same displacements .Displacements of A、B is shown in table 1 .

Table 1

Figure 1: X-Component of displacement in Case 1

Figure 2: X-Component of displacement in Case 2 2、5×5 meshing

Displacements of A、B is shown in table 2 .

Table 2

Figure 3: X-Component of displacement in Case 1

Figure 4: X-Component of displacement in Case 2 3、10×10 meshing

Displacements of A、B is shown in table 3.

Table 3

4、The first 10 frequencies

We also get the first 10 frequencies shown in table 4 .

Table 4

Figure 5: X-Component of displacement in Case 1

Figure 6: X-Component of displacement in Case 2

Reorganize the data in table 1 ,table 2 and table 3 we get a new table shown as table 5 .Data in table 5 is the displacements in X direction of A,B in different cases and meshings .

Table 5

Analysis:

1、Analyze the data in table 5 ,we can know ,the displacement of A ,B is larger in case 1 than that in case 2 .That means it has a larger displacement when a concentrate load is applied .

2、Analyze the data in table 5 , we can also know that the numbers with more meshes are a little larger .In fact , the data will be more accurate if we use more meshes .

3、Look at figure 3, figure 4,figure 5and figure 6,we can know that the nodes on line AB have the same displacements when a uniformly distributed load is applied .It’s not suitable for case 1 when a concentrate load is applied .

4、Analyze the data in table 4,the frequencies get smaller when the number of meshes is bigger .