Actual Model Examples for Elastic Static Analysis

Analysis Model

Table 9.2.1 lists actual-model verification examples for elastic static analysis. The shapes of the models, with some exceptions, are also shown in Figures 9.2.1 through 9.2.5. A separate direct solver is required to run the examples using element types 731 and 741.

Table 9.2.1 Actual model verification examples for elastic static analysis

Case Name	Element Type	Verification Model	Number of Nodes	Degrees of Freedom
EX01A	342	Connecting rod (100,000 nodes)	94,074	282,222
EX01B	342	Connecting rod (330,000 nodes)	331,142	993,426
EX02	361	Block with a hole	37,386	112,158
EX03	342	Turbine blade	10,095	30,285
EX04	741	Cylindrical shell	10,100	60,600
EX05A	731	Wine glass (coarce)	7,240	43,440
EX05B	731	Wine glass (midium)	48,803	292,818
EX05C	731	Wine glass (fine)	100,602	603,612

Figure 9.2.1 Connecting rod (EX01A)

Figure 9.2.2 Block with a hole (EX02)

Figure 9.2.3 Turbine blade (EX03, EX06)

Figure 9.2.4 Cylindrical shell (EX04, EX09)

Figure 9.2.5 Wine glass (EX05, EX10A)

Analysis Results

Example Analysis Results

Examples of analysis results are shown in Figures 9.2.6 through 9.2.9.

Figure 9.2.6 EX01A analysis result (Mises stress and deformation plot (10x))

Figure 9.2.7 EX02 analysis result (Mises stress and deformation plot (100x))

Figure 9.2.8 EX03 analysis result (deformation plot (10x))

Figure 9.2.9 EX04 analysis result (deformation plot (100x))

Verification Results of Analysis Performance Using Example EX02

An analysis was performed with general-purpose commercial software using a model equivalent to the EX02 block-with-hole verification model. Figure 9.2.10 shows a comparison of the maximum and minimum stress-component values with those from FrontISTR. The figure shows that the stress components agree very closely.

Next, the effect of domain partitioning on the stress distribution was investigated. Domain partitioning was performed using the RCB method, dividing the model into two in each of the X, Y, and Z directions for a total of eight domains. Figure 9.2.11 shows the partitioning. Figure 9.2.12 shows the stress distributions from analyses using a single domain and eight partitioned domains.

Figure 9.2.10 Comparison of stress components in EX02 with general-purpose software

Figure 9.2.11 EX02 partitioned into eight domains by the RCB method

Figure 9.2.12 Difference in Mises stress distribution due to domain partitioning

Figure 9.2.12 shows no difference between the two results; they agree completely.

Table 9.2.2 compares execution times for the HEC-MW solver settings used. Figure 9.2.13 also shows the convergence history up to the solution.

Table 9.2.2 Comparison of execution times using HEC-MW solvers

Solver	Execution Time (s)
CGI	38.79
CGscale	52.75
BCGS	60.79
CG8	6.65

Figure 9.2.13 Comparison of convergence histories using HEC-MW solvers (convergence threshold: 1.0x10^-8^)

Comparison of Calculation Time Using Verification Example EX01A

Using verification example EX01A (connecting rod), the speedup in calculation due to domain partitioning was evaluated. A 24-node cluster computer with Xeon 2.8 GHz processors was used for the calculation. The results are shown in Figure 9.2.14. The figure shows that calculation speed increases in proportion to the number of domains.

Differences in calculation time due to the computer environment were also investigated. The results are shown in Table 9.2.3.

Figure 9.2.14 Speedup effect of domain partitioning

Table 9.2.3 Comparison of calculation times by computer (1 CPU)

CPU	Frequancy [GHz]	OS	CPU Time [sec]	solver time [sec]
Xeon	2.8	Linux	850	817
Pentium III	0.866	Win2000	2008	1980
Pentium M	0.760	WinXP	1096	1070
Pentium 4	2.0	WinXP	802	785
Pentium 4	2.8	WinXP	738	718
Celeron	0.700	Win2000	2252	2215
Pentium 4	2.4	WinXP	830	804