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Example of Acutual Model for Elastic Static Analysis

Actual Model Examples for Elastic Static Analysis

Analysis Model

A list of actual model verification examples for elastic static analysis are presented in Table 9.2.1. The different shapes of the models are shown in Figs. 9.2.1–9.2.5 (some models are excluded). The examples of the element types 731 and 741 require a separate direct method solver.

Table 9.2.1: Actual model verification examples for elastic static analysis
Case name Element type Verification model Number of nodes Freedom freequency
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 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 (coarse) 7,240 43,440
EX05B 731 Wine glass (midium) 48,803 292,818
EX05C 731 Wine glass (fine) 100,602 603,612

Connecting Rod (EX01A)

Fig. 9.2.1: Connecting Rod (EX01A)

Perforated block (EX02)

Fig. 9.2.2: Perforated block (EX02)

Turbine blade (EX03, EX06)

Fig. 9.2.3: Turbine blade (EX03, EX06)

Cylindrical shell (EX04, EX09)

Fig. 9.2.4: Cylindrical shell (EX04, EX09)

Wine Glass (EX05, EX10A)

Fig. 9.2.5: Wine Glass (EX05, EX10A)

Analysis results

Example of analysis results

Examples of the analysis results are shown in Figs. 9.2.6–9.2.9.

EX01 analysis results (Mises stress and deformation diagram (10 times))

Fig. 9.2.6: EX01 analysis results (Mises stress and deformation diagram (10 times))

EX02 analysis results (Mises stress and deformation diagram (100 times))

Fig. 9.2.7: EX02 analysis results (Mises stress and deformation diagram (100 times))

EX03 analysis results (deformation diagram (10 times))

Fig. 9.2.8: EX03 analysis results (deformation diagram (10 times))

EX04 analysis results (deformation diagram (100 times))

Fig. 9.2.9: EX04 analysis results (deformation diagram (100 times))

Verification Results of Analysis Performance with Example EX02

An analysis was performed with the commercial software ABAQUS using a model equivalent to the verification example model EX02 (perforated block). A comparison of the maximum and minimum values of the stress components with the results of FrontISTR is shown in Fig. 9.2.10. It can be seen that the stress components are very close to each other.

The effect of area division on stress distribution was also analyzed. The division was performed according to the RCB method, i.e., the model was halved in each of the X, Y, and Z axial directions, creating eight areas in total. Fig. 9.2.11 shows the division, while Fig. 9.2.12 shows the stress distribution of the analysis results with a single area and with the area divided into eight areas.

Comparison of the stress components of EX02 with the commercial software

Fig. 9.2.10: Comparison of the stress components of EX02 with the commercial software

Result of the division of EX02 in eight areas by the RCB method

Fig. 9.2.11: Result of the division of EX02 in eight areas by the RCB method

No difference between the stress distribution of the analysis results with a single area and with the area divided into eight areas

Fig. 9.2.12: No difference between the stress distribution of the analysis results with a single area and with the area divided into eight areas

Furthermore, a comparison of the execution time with the settings of the HEC-MW solver used is presented in Table 9.2.2. Fig. 9.2.13 shows the convergence history until the solution was found.

Table 9.2.2: Comparison of execution time with HEC-MW solvers
Solver Execution Time(s)
CGI 38.79
CGscale 52.75
BCGS 60.79
CG8 6.65

Comparison of convergence history with the HEC-MW solver (convergence threshold: 1.0 \times 10^{-8} )

Fig. 9.2.13: Comparison of convergence history with the HEC-MW solver (convergence threshold: )

Comparison of calculation time with verification example EX01A

The increase rate of the calculation speed because of area division was verified with the example EX01A (connecting rod.) The test was conducted with a Xeon 2.8 GHz 24 node cluster computer, and the results are shown in Fig. 9.2.14. This figure shows that the calculation speed increases proportionally to the number of areas.

The difference in the calculation time because of the computer environment was also analyzed. The results are presented in Table 9.2.3.

Speed-increasing effect because of area division

Fig. 9.2.14: Speed-increasing effect because of area division

Table 9.2.3: Comparison of calculation time with different computers (one 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