[Gmsh] Stress on Gauss Points

Max Orok morok at mevex.com
Thu Feb 14 01:31:51 CET 2019


Hi Gaetano,

Here is a small python script that tries to plot these data along with the
mesh results file.
I assumed the node forces were for the given elements, in the order gmsh is
expecting.

Here are some pictures -> hopefully it is something like you were
predicting.
To an outsider, they look pretty good!

[image: image.png]
[image: image.png]

Sincerely,
Max

On Wed, Feb 13, 2019 at 8:02 AM Gaetano Camarda <gaetano_18 at live.it> wrote:

>
>
> Hello, I have an issue with postprocessing on Gmsh, I created a mesh on
> Gmsh, and I’ve imported it on Matlab, for some analysis,
>
> now I have the displacement of my mesh and I’m able to import it on the
> .msh file and post-processing the view on Gmsh.
>
> I have also 2 matrix, one with stress calculated on Gauss Points (I used
> 2) and one with nodal force of the element in each row.
>
> I would like to view the stress and nodal force in Gmsh, as I do with
> displacement. But I do not know how to do it.
>
> I’ve worked with Hexahedral.
>
> I’m attatching also the file of the mesh, and the files with stress on
> gauss point and nodal forces.
>
>
>
> (please remove .txt from 10cm.msh)
>
> Inviato da Posta <https://go.microsoft.com/fwlink/?LinkId=550986> per
> Windows 10
>
>
> _______________________________________________
> gmsh mailing list
> gmsh at onelab.info
> http://onelab.info/mailman/listinfo/gmsh
>


-- 
Max Orok
Contractor
www.mevex.com
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-18.851	-8.7837	4.0073	-145.67	-651.46	3.1607
44.435	18.122	30.405	-147.59	-1094.8	4.069
32.478	15.592	26.059	-37.014	-1087.5	3.8153
-31.287	-11.518	-0.54382	-34.82	-644.05	2.907
-27.086	-13.167	-19.059	-163.86	-647.52	3.035
36.317	13.855	7.6105	-165.79	-1091	4.2118
24.762	12.265	3.6672	-55.341	-1083.7	4.0356
-39.119	-14.962	-23.207	-53.147	-640.1	2.8589
23.321	-29.186	-39.227	-132.66	-670.22	2.3573
57.916	-14.46	-24.733	-104.37	-1113.7	3.3629
59.45	-10.929	-23.213	8.5271	-1089.1	3.2464
24.798	-25.68	-37.731	-20.5	-645.61	2.2408
-56.041	-165.13	-167.82	-142.6	-670.21	0.63165
-21.317	-150.28	-153.03	-114.31	-1113.7	0.90109
-20.887	-149.32	-152.61	-1.4234	-1089.2	0.86987
-55.667	-164.2	-167.43	-30.451	-645.6	0.60043
-20.905	-149.31	-152.59	79.779	1084.1	0.76755
-55.851	-164.28	-167.56	50.741	641.07	0.50929
-56.654	-165.36	-168.12	160.41	616.5	0.51381
-21.418	-150.27	-153.03	188.75	1059.6	0.77208
59.485	-10.842	-23.093	89.766	1084.2	2.8645
24.557	-25.797	-38.014	60.727	641.19	1.9007
22.697	-29.349	-39.637	170.48	616.62	1.9176
57.913	-14.27	-24.592	198.81	1059.6	2.8814
24.76	12.372	3.8614	25.977	1088.5	3.4033
-39.37	-15.162	-23.788	28.172	645.51	2.2784
-27.322	-13.212	-19.589	139.63	638.33	2.2207
36.053	13.998	7.737	137.7	1081.1	3.3457
32.562	15.783	26.457	44.275	1084.8	2.7784
-31.893	-12.075	-1.949	46.47	641.58	1.9189
-19.446	-9.1963	2.6487	157.71	634.4	1.6451
44.254	18.338	30.731	155.78	1077.4	2.5046
-70.002	-173.55	-174.36	130.32	377.32	0.39262
-69.021	-172.94	-173.3	104.41	99.829	0.14432
-71.061	-174.52	-174.39	381.03	74.421	0.36848
-71.202	-174.77	-175.09	406.26	352.53	0.61677
6.0555	-45.673	-48.715	130.13	377.56	1.4653
7.955	-44.142	-45.51	104.23	100.31	0.53863
4.898	-48.1	-47.615	381.09	74.897	1.3752
3.8378	-49.271	-50.459	406.32	352.77	2.3018
-69.963	-33.075	-37.434	106.67	381.97	1.7666
-82.099	-37.411	-39.752	98.934	105.01	0.63787
-69.538	-35.253	-35.336	376.16	98.096	1.647
-57.579	-30.992	-33.094	384.02	374.92	2.7757
-47.784	4.5774	-1.155	110.57	377.95	1.517
-60.131	0.030011	-3.9661	102.83	100.93	0.51469
-47.38	2.6309	0.63938	380.01	94.024	1.3828
-35.21	7.1025	3.3747	387.87	370.9	2.3851
-9.7832	-146.07	-147.6	329.37	562.14	1.409
-43.348	-159.79	-159.77	302.01	285.51	0.69693
-10.43	-147.72	-146.27	579.19	258.11	1.4707
21.433	-134.73	-134.83	604.6	536.86	2.1827
69.178	-12.383	-18.079	339.29	552.92	5.2584
38.784	-22.934	-22.854	311.93	275.8	2.601
68.783	-17.669	-12.275	588.62	248.4	5.4886
97.476	-7.8473	-8.2284	614.04	527.64	8.1459
57.685	17.106	10.624	280.01	581.96	6.4607
-0.46836	-5.2761	-5.8288	281.81	306.33	3.1224
55.61	9.2194	15.343	558.8	309.02	6.0868
112.64	31.118	31.313	557.09	582.75	9.4251
53.797	9.6144	5.156	297.89	564.83	5.8962
-7.2121	-15.623	-17.961	299.69	288.87	2.6427
48.994	-0.83093	3.3386	576.37	291.57	3.7031
108.88	23.924	25.972	574.65	565.62	6.9566
-56.952	-167.87	-165.26	669.47	143.25	0.59635
-56.843	-167.57	-164.36	644.58	31.246	0.50269
-21.762	-152.8	-149.41	1088	1.9715	0.79983
-22.32	-153.3	-150.49	1112.6	114.79	0.8935
23.075	-38.068	-28.304	669.56	133.32	2.2256
24.401	-36.549	-24.567	644.67	21.182	1.8761
59.099	-22.677	-9.996	1087.9	-8.092	2.985
57.324	-24.388	-13.925	1112.6	104.85	3.3346
-27.315	-17.768	-13.897	647.64	165.11	2.7288
-39.328	-22.095	-16.308	639.86	54.939	2.1616
21.159	2.2073	9.1291	1083.1	60.002	3.1198
33.29	6.5848	11.59	1090.5	168.95	3.6871
-21.395	3.7215	-15.656	651.48	147.55	2.4743
-35.244	-2.4408	-22.348	643.7	37.414	1.5683
24.735	20.676	2.5802	1086.9	42.477	1.303
38.701	26.888	9.3233	1094.4	151.39	2.2091
32.562	15.783	26.457	36.868	1086.4	2.7784
-31.893	-12.075	-1.949	34.673	642.93	1.9189
-19.446	-9.1963	2.6487	145.12	650.11	1.6451
44.254	18.338	30.731	147.05	1093.8	2.5046
24.76	12.372	3.8614	55.167	1082.7	3.4033
-39.37	-15.162	-23.788	52.971	639	2.2784
-27.322	-13.212	-19.589	163.2	646.18	2.2207
36.053	13.998	7.737	165.13	1090.1	3.3457
59.485	-10.842	-23.093	-8.6227	1087.1	2.8645
24.557	-25.797	-38.014	20.416	643.32	1.9007
22.697	-29.349	-39.637	132.35	667.89	1.9176
57.913	-14.27	-24.592	104.02	1111.6	2.8814
-20.905	-149.31	-152.59	1.364	1087.1	0.76755
-55.851	-164.28	-167.56	30.403	643.44	0.50929
-56.654	-165.36	-168.12	142.42	668.01	0.51381
-21.418	-150.27	-153.03	114.09	1111.7	0.77208
-47.784	4.5774	-1.155	92.288	379.13	1.517
-60.131	0.030011	-3.9661	100.02	101.93	0.51469
-47.38	2.6309	0.63938	377.07	108.83	1.3828
-35.21	7.1025	3.3747	369.21	386.18	2.3851
-69.963	-33.075	-37.434	96.188	375.11	1.7666
-82.099	-37.411	-39.752	103.92	97.853	0.63787
-69.538	-35.253	-35.336	380.92	104.76	1.647
-57.579	-30.992	-33.094	373.06	382.16	2.7757
6.0555	-45.673	-48.715	72.724	379.52	1.4653
7.955	-44.142	-45.51	98.633	102.55	0.53863
4.898	-48.1	-47.615	375.99	127.96	1.3752
3.8378	-49.271	-50.459	350.76	404.31	2.3018
-70.002	-173.55	-174.36	72.54	379.75	0.39262
-69.021	-172.94	-173.3	98.449	103.03	0.14432
-71.061	-174.52	-174.39	376.05	128.44	0.36848
-71.202	-174.77	-175.09	350.82	404.55	0.61677
53.797	9.6144	5.156	288.94	576.22	5.8962
-7.2121	-15.623	-17.961	287.14	297.96	2.6427
48.994	-0.83093	3.3386	564.69	295.27	3.7031
108.88	23.924	25.972	566.4	575.43	6.9566
57.685	17.106	10.624	306.83	559.09	6.4607
-0.46836	-5.2761	-5.8288	305.02	280.51	3.1224
55.61	9.2194	15.343	582.25	277.81	6.0868
112.64	31.118	31.313	583.97	558.3	9.4251
69.178	-12.383	-18.079	247.54	588.13	5.2584
38.784	-22.934	-22.854	274.9	311.04	2.601
68.783	-17.669	-12.275	552.43	338.43	5.4886
97.476	-7.8473	-8.2284	527.01	613.41	8.1459
-9.7832	-146.07	-147.6	257.46	578.91	1.409
-43.348	-159.79	-159.77	284.82	301.33	0.69693
-10.43	-147.72	-146.27	561.87	328.72	1.4707
21.433	-134.73	-134.83	536.45	604.19	2.1827
-21.395	3.7215	-15.656	633.03	155.28	2.4743
-35.244	-2.4408	-22.348	640.81	43.729	1.5683
24.735	20.676	2.5802	1084.3	38.667	1.303
38.701	26.888	9.3233	1076.9	151.44	2.2091
-27.315	-17.768	-13.897	636.87	137.72	2.7288
-39.328	-22.095	-16.308	644.66	26.204	2.1616
21.159	2.2073	9.1291	1088.2	21.142	3.1198
33.29	6.5848	11.59	1080.8	133.88	3.6871
23.075	-38.068	-28.304	614.95	169.51	2.2256
24.401	-36.549	-24.567	639.84	59.961	1.8761
59.099	-22.677	-9.996	1083.3	89.235	2.985
57.324	-24.388	-13.925	1058.7	197.98	3.3346
-56.952	-167.87	-165.26	615.04	159.58	0.59635
-56.843	-167.57	-164.36	639.93	49.897	0.50269
-21.762	-152.8	-149.41	1083.3	79.172	0.79983
-22.32	-153.3	-150.49	1058.7	188.04	0.8935
22.636	-134.32	-134.35	-536.48	605.14	-2.1455
-9.1654	-147.34	-145.95	-561.8	329.56	-1.4204
-42.536	-159.57	-159.63	-284.97	302.35	-0.70924
-9.3577	-145.96	-147.44	-257.68	579.87	-1.4344
98.517	-7.8062	-7.9272	-527.09	614.6	-8.0071
69.629	-17.912	-12.725	-552.4	339.41	-5.3009
39.23	-23.208	-23.433	-275.19	312.2	-2.6469
69.494	-12.512	-18.046	-247.89	589.33	-5.3531
115.24	31.722	31.552	-583.65	557.58	-9.9922
58.813	10.342	16.714	-582.16	279.6	-6.6493
0.40106	-5.1405	-5.4541	-305.61	281.38	-3.3783
58.409	16.916	10.061	-307.35	559.1	-6.7212
110.72	24.201	23.986	-566.13	575.25	-9.5543
53.901	2.435	8.2486	-564.63	297.72	-6.4529
-4.873	-13.893	-14.282	-287.63	299.5	-3.4389
53.52	8.5494	2.1322	-289.37	576.77	-6.5403
-21.024	-152.84	-150.23	-1058.6	188.83	-0.87699
-20.578	-152.43	-149.31	-1083.2	79.905	-0.81203
-55.583	-167.25	-164.25	-640.02	51.015	-0.55379
-55.926	-167.61	-165.14	-615.22	160.64	-0.61874
58.184	-24.39	-14.659	-1058.6	198.83	-3.273
59.688	-22.92	-11.261	-1083.2	89.934	-3.0305
24.95	-37.115	-25.941	-640.01	61.045	-2.0668
23.548	-38.542	-29.295	-615.21	170.64	-2.3092
36.957	8.2456	13.703	-1080.7	137.12	-4.0831
25.22	4.1714	11.86	-1088.1	25.824	-3.7452
-38.808	-22.304	-15.291	-644.89	28.093	-2.6298
-26.682	-18.063	-13.282	-637.39	139.09	-2.9677
45.125	31.259	17.915	-1076.9	155.44	-3.9005
32.95	26.748	15.053	-1084.3	44.263	-3.4793
-30.952	0.56429	-11.973	-640.95	46.531	-2.6552
-18.39	5.2416	-8.9441	-633.44	157.42	-3.0763
-21.317	-150.28	-153.03	-114.31	1113.7	-0.90109
-56.041	-165.13	-167.82	-142.6	670.21	-0.63165
-55.667	-164.2	-167.43	-30.451	645.6	-0.60043
-20.887	-149.32	-152.61	-1.4234	1089.2	-0.86987
57.916	-14.46	-24.733	-104.37	1113.7	-3.3629
23.321	-29.186	-39.227	-132.66	670.22	-2.3573
24.798	-25.68	-37.731	-20.5	645.61	-2.2408
59.45	-10.929	-23.213	8.5271	1089.1	-3.2464
36.317	13.855	7.6105	-165.79	1091	-4.2118
-27.086	-13.167	-19.059	-163.86	647.52	-3.035
-39.119	-14.962	-23.207	-53.147	640.1	-2.8589
24.762	12.265	3.6672	-55.341	1083.7	-4.0356
44.435	18.122	30.405	-147.59	1094.8	-4.069
-18.851	-8.7837	4.0073	-145.67	651.46	-3.1607
-31.287	-11.518	-0.54382	-34.82	644.05	-2.907
32.478	15.592	26.059	-37.014	1087.5	-3.8153
-70.303	-174.46	-174.64	-351.02	406.92	-0.72287
-69.813	-174.05	-173.76	-376.16	131.06	-0.44955
-68.64	-172.76	-173.03	-98.479	105.54	-0.21463
-69.726	-173.43	-174.16	-72.595	382.04	-0.48796
4.7269	-49.153	-49.849	-351.06	406.87	-2.6978
6.1793	-47.779	-46.722	-376.2	130.85	-1.6777
8.4724	-43.882	-44.865	-98.689	105.32	-0.80102
6.4238	-45.511	-48.248	-72.804	381.99	-1.8211
-57.74	-31.574	-32.536	-373.62	383.81	-3.4963
-69.941	-35.836	-34.543	-381.19	106.84	-2.1704
-81.747	-37.107	-38.466	-104	99.333	-1.0427
-69.677	-32.901	-36.516	-96.34	376.35	-2.3686
-35.196	6.1082	4.9279	-369.65	387.79	-3.7028
-47.331	1.9119	3.0749	-377.22	110.78	-2.2883
-59.004	0.95089	-0.7153	-100.07	103.27	-1.1166
-47	5.0912	1.0816	-92.408	380.33	-2.5312
110.72	24.201	23.986	-574.92	565.81	-9.5543
53.901	2.435	8.2486	-576.42	289.11	-6.4529
-4.873	-13.893	-14.282	-299.2	287.34	-3.4389
53.52	8.5494	2.1322	-297.46	564.29	-6.5403
115.24	31.722	31.552	-557.4	583.48	-9.9922
58.813	10.342	16.714	-558.9	307.23	-6.6493
0.40106	-5.1405	-5.4541	-281.23	305.46	-3.3783
58.409	16.916	10.061	-279.49	581.96	-6.7212
98.517	-7.8062	-7.9272	-613.96	526.46	-8.0071
69.629	-17.912	-12.725	-588.65	247.42	-5.3009
39.23	-23.208	-23.433	-311.65	274.64	-2.6469
69.494	-12.512	-18.046	-338.94	551.73	-5.3531
22.636	-134.32	-134.35	-604.57	535.91	-2.1455
-9.1654	-147.34	-145.95	-579.26	257.27	-1.4204
-42.536	-159.57	-159.63	-301.86	284.48	-0.70924
-9.3577	-145.96	-147.44	-329.16	561.18	-1.4344
45.125	31.259	17.915	-1094.4	147.39	-3.9005
32.95	26.748	15.053	-1086.9	36.881	-3.4793
-30.952	0.56429	-11.973	-643.56	34.612	-2.6552
-18.39	5.2416	-8.9441	-651.07	145.41	-3.0763
36.957	8.2456	13.703	-1090.5	165.72	-4.0831
25.22	4.1714	11.86	-1083.1	55.319	-3.7452
-38.808	-22.304	-15.291	-639.62	53.05	-2.6298
-26.682	-18.063	-13.282	-647.12	163.74	-2.9677
58.184	-24.39	-14.659	-1112.6	104	-3.273
59.688	-22.92	-11.261	-1088	-8.7903	-3.0305
24.95	-37.115	-25.941	-644.5	20.099	-2.0668
23.548	-38.542	-29.295	-669.3	132.19	-2.3092
-21.024	-152.84	-150.23	-1112.7	114	-0.87699
-20.578	-152.43	-149.31	-1088	1.2389	-0.81203
-55.583	-167.25	-164.25	-644.49	30.128	-0.55379
-55.926	-167.61	-165.14	-669.29	142.19	-0.61874
44.435	18.122	30.405	-155.24	1076.4	-4.069
-18.851	-8.7837	4.0073	-157.16	633.05	-3.1607
-31.287	-11.518	-0.54382	-46.324	640.46	-2.907
32.478	15.592	26.059	-44.13	1083.8	-3.8153
36.317	13.855	7.6105	-137.05	1080.2	-4.2118
-27.086	-13.167	-19.059	-138.97	636.99	-3.035
-39.119	-14.962	-23.207	-27.996	644.41	-2.8589
24.762	12.265	3.6672	-25.802	1087.6	-4.0356
57.916	-14.46	-24.733	-198.46	1057.6	-3.3629
23.321	-29.186	-39.227	-170.17	614.29	-2.3573
24.798	-25.68	-37.731	-60.643	638.9	-2.2408
59.45	-10.929	-23.213	-89.671	1082.1	-3.2464
-21.317	-150.28	-153.03	-188.52	1057.6	-0.90109
-56.041	-165.13	-167.82	-160.23	614.3	-0.63165
-55.667	-164.2	-167.43	-50.692	638.91	-0.60043
-20.887	-149.32	-152.61	-79.72	1082.1	-0.86987
-35.196	6.1082	4.9279	-387.43	369.29	-3.7028
-47.331	1.9119	3.0749	-379.86	92.08	-2.2883
-59.004	0.95089	-0.7153	-102.79	99.584	-1.1166
-47	5.0912	1.0816	-110.45	376.75	-2.5312
-57.74	-31.574	-32.536	-383.46	373.27	-3.4963
-69.941	-35.836	-34.543	-375.89	96.021	-2.1704
-81.747	-37.107	-38.466	-98.861	103.53	-1.0427
-69.677	-32.901	-36.516	-106.52	380.73	-2.3686
4.7269	-49.153	-49.849	-406.02	350.2	-2.6978
6.1793	-47.779	-46.722	-380.88	72.013	-1.6777
8.4724	-43.882	-44.865	-104.17	97.537	-0.80102
6.4238	-45.511	-48.248	-130.05	375.09	-1.8211
-70.303	-174.46	-174.64	-406.06	350.16	-0.72287
-69.813	-174.05	-173.76	-380.92	71.795	-0.44955
-68.64	-172.76	-173.03	-104.38	97.319	-0.21463
-69.726	-173.43	-174.16	-130.26	375.04	-0.48796
-------------- next part --------------
import gmsh
import math

model = gmsh.model
factory = model.occ

# spin up gmsh API
gmsh.initialize()
gmsh.option.setNumber("General.Terminal", 1)

# read in the stresses as arrays of floats
# -> assume 15 sigdigs is enough
with open("gauss-stress.txt") as file:
    six_stresses = [[float(val) for val in line.split()] for line in file]

# have to repeat stress values to properly call the addModelData function
# -> it expects vector of length 9 instead of the vector of length six we've
#    read in so far
#
# want to take the each array in six_stresses ([sx, sy, sz, sxy, sxz, syz])
# and transform it to an array like this: [sx, sxy, sxz, sxy, sy, syz, sxz, syz, sz]
# there is probably a better way to do this...
stress_tensor = []
for stress_line in six_stresses:
    (sx, sy, sz, sxy, sxz, syz) = tuple(stress_line)
    stress_tensor.append([sx, sxy, sxz, sxy, sy, syz, sxz, syz, sz])

# read in the node forces
node_forces = []
data_stride = 3

with open("nodal-forces.txt") as file:
    elt_forces = [[float(val) for val in line.split()] for line in file]
    # remove elt number (not needed here)
    for sublist in elt_forces:
        sublist.pop(0)
    # transpose elt forces (array of arrays of 24 elts)
    # to node forces (array of arrays of 3 elts)
    flat_elt_forces = [forces for sublist in elt_forces for forces in sublist]
    i = 0
    while i < len(flat_elt_forces):
            node_forces.append(flat_elt_forces[i:i + data_stride])
            i = i + data_stride


# --

# import the mesh
gmsh.open("10cm.msh")

# find element & node tags
# -> exit if the type isn't hexa (5) as a quick precaution
(elt_types, elt_tags, node_tags) = gmsh.model.mesh.getElements()

hexa_type = 5 # (c.f. section 9.1 gmsh documentation)

if len(elt_types) != 1 or elt_types[0] != hexa_type:
    quit()

# comes back as array of arrays, get the nodes as a bare array of ints
elt_tags = elt_tags[0]
node_tags = node_tags[0]

# --

# get the model name
model_names = gmsh.model.list()
curr_model = model_names[0]


# add the stress data
#   make a stress view tag
stress_view_tag = gmsh.view.add("node stresses")
# (c.f. the gmsh.py header)
#    >> def addModelData(tag, step, modelName, dataType, tags, data, time=0., numComponents=-1, partition=0)
gmsh.view.addModelData(stress_view_tag, 0, curr_model, "NodeData", node_tags, stress_tensor)


# make a view for the node forces
force_view_tag = gmsh.view.add("node forces")
# add the forces
gmsh.view.addModelData(force_view_tag, 0, curr_model, "NodeData", node_tags, node_forces)


# --

# output the data

out_filename = "10cm_data.msh"

# save as new mesh file
# first we save the stresses
# @arg False -> don't want to append for first view
gmsh.view.write(stress_view_tag, out_filename, False)

# node force output
# @arg True -> want to append (otherwise would overwrite the stress data)
gmsh.view.write(force_view_tag, out_filename, True)

# close gmsh
gmsh.finalize();
-------------- next part --------------
1	240.35	-46679	2954.6	-69667	1399	27953	9709	-23286	76483	79916	-71743	51212	-9502.5	12194	-37756	-79674	32524	-62639	-677.85	58345	-41234	69656	37247	-16974
2	9819.7	-29227	20174	-65597	-20238	45829	8565.6	-44803	55326	83906	-53598	29917	-11479	23837	-26542	-83990	24641	-50924	-6844	49962	-49245	65619	49425	-24536
3	-1.0991e+05	-26831	94364	-1.6481e+05	15694	1.3606e+05	1.3941e+05	6034.3	1.7851e+05	1.3455e+05	-36806	1.3952e+05	-1.1347e+05	-1098.3	-1.2614e+05	-1.6026e+05	11288	-1.6418e+05	1.4376e+05	22412	-1.4944e+05	1.3074e+05	9306.9	-1.0869e+05
4	-1.0066e+05	-10978	1.1286e+05	-1.6944e+05	-11177	1.5623e+05	1.3001e+05	-20355	1.5539e+05	1.3856e+05	-20005	1.1702e+05	-1.0875e+05	10503	-1.1516e+05	-1.6265e+05	10082	-1.519e+05	1.3957e+05	20603	-1.5816e+05	1.3337e+05	21327	-1.163e+05
5	1.0007e+05	-1.3539e+05	-6943.8	-1.3508e+05	-90320	3087.6	-1.3045e+05	-1.3129e+05	45912	1.6499e+05	-1.7376e+05	35551	96342	1.038e+05	-20882	-1.3894e+05	1.2088e+05	-30443	-1.2629e+05	1.6035e+05	-17525	1.6935e+05	1.4573e+05	-8758.4
6	1.1007e+05	-1.1685e+05	7938.1	-1.305e+05	-1.1293e+05	19107	-1.3978e+05	-1.5424e+05	19514	1.6062e+05	-1.5391e+05	8758.4	1.0132e+05	1.1472e+05	-10462	-1.3622e+05	1.1356e+05	-19363	-1.3144e+05	1.5222e+05	-17754	1.6591e+05	1.5743e+05	-7738.7
7	-9174.8	-71388	38490	-1.3941e+05	-30879	64993	6.9122e-11	-56147	1.0377e+05	1.3045e+05	-94905	79008	-7474.8	44370	-65508	-1.3021e+05	55769	-88748	16293	81972	-77887	1.3952e+05	71210	-54119
8	-271.17	-55160	54421	-1.4357e+05	-57825	82796	-16293	-81972	77887	1.2654e+05	-77327	52130	2979.6	55133	-55078	-1.2638e+05	54392	-76829	13951	79995	-80393	1.4303e+05	82764	-54933
9	11479	-26159	23455	-66000	-25356	49069	6844	-50031	50749	84371	-50568	25461	-9819.7	20770	-29823	-84393	29759	-54164	-8565.6	55190	-44667	66084	46396	-20079
10	9502.5	-37803	12241	-70316	-17473	37354	677.85	-41649	58760	80334	-62746	33023	-240.35	3317.7	-47042	-80323	51396	-72041	-9709	76707	-23510	70074	28250	1215.8
11	-1.0124e+05	-9495.9	1.1483e+05	-1.6732e+05	-9916.8	1.5808e+05	1.3041e+05	-19394	1.5182e+05	1.3662e+05	-18670	1.1369e+05	-1.0932e+05	9020.9	-1.1712e+05	-1.6054e+05	8821.8	-1.5375e+05	1.3997e+05	19642	-1.5459e+05	1.3142e+05	19992	-1.1296e+05
12	-96518	-21097	1.0385e+05	-1.6972e+05	-8710.9	1.458e+05	1.2622e+05	-17585	1.6054e+05	1.3925e+05	-30690	1.2129e+05	-1.0008e+05	-6832.4	-1.3562e+05	-1.6516e+05	35693	-1.7392e+05	1.3057e+05	46032	-1.3147e+05	1.3543e+05	3191.4	-90467
13	1.0866e+05	-1.1527e+05	9536.8	-1.3377e+05	-1.1642e+05	20634	-1.3854e+05	-1.5776e+05	22244	1.6407e+05	-1.5255e+05	12260	99914	1.1313e+05	-12061	-1.3948e+05	1.1705e+05	-20891	-1.3021e+05	1.5574e+05	-20483	1.6935e+05	1.5607e+05	-11240
14	1.1364e+05	-1.2619e+05	-882.85	-1.3104e+05	-1.091e+05	9554.6	-1.437e+05	-1.4963e+05	22472	1.6062e+05	-1.6425e+05	11240	1.0991e+05	94594	-26942	-1.349e+05	1.3967e+05	-36910	-1.3953e+05	1.7869e+05	5915	1.6499e+05	1.3622e+05	15553
15	-2979.6	-54860	54915	-1.4361e+05	-55601	83160	-13951	-79995	79596	1.2695e+05	-77225	55060	271.17	54833	-55572	-1.2642e+05	52167	-77194	16293	78018	-82102	1.4344e+05	82663	-57863
16	7474.8	-65623	44485	-1.3978e+05	-54224	71241	-16293	-78018	82102	1.3046e+05	-88780	55874	9174.8	38604	-71503	-1.3057e+05	79114	-94997	-2.5466e-11	1.0384e+05	-56218	1.3953e+05	65085	-30985
17	-1.6499e+05	1.3627e+05	-15704	1.3953e+05	1.7865e+05	-6061.3	1.3461e+05	1.3961e+05	36752	-1.1018e+05	94596	26815	-1.6034e+05	-1.6426e+05	-11257	1.44e+05	-1.4961e+05	-22454	1.31e+05	-1.0904e+05	-9294.7	-1.1363e+05	-1.2623e+05	1203.4
18	-1.6964e+05	1.565e+05	11257	1.299e+05	1.555e+05	20281	1.3861e+05	1.168e+05	19985	-1.0086e+05	1.1311e+05	11142	-1.6267e+05	-1.5173e+05	-9999.3	1.3974e+05	-1.5819e+05	-20832	1.3365e+05	-1.169e+05	-21507	-1.0874e+05	-1.1508e+05	-10327
19	-1.3953e+05	65115	30844	1.3426e-10	1.0379e+05	56099	1.303e+05	79061	94790	-9407.3	38601	71320	-1.3013e+05	-88787	-55774	16607	-78006	-81911	1.3965e+05	-54171	-71089	-7498.4	-65603	-44279
20	-1.4377e+05	82900	57947	-16607	78006	81911	1.2619e+05	51969	77084	-667.74	54705	55298	-1.2623e+05	-76792	-54163	14365	-79995	-79995	1.4363e+05	-55850	-83119	3085.3	-54943	-54962
21	-69810	28296	-1534.4	9932.5	76651	23159	79858	51325	71574	-240.35	3317.3	46580	-79720	-62645	-32458	-180.6	-41609	-58329	69979	-17537	-37097	-9819.1	-37798	-11894
22	-65773	46382	20112	8741.3	55311	44475	84064	29597	53690	9501.9	20683	29476	-84071	-50490	-24671	-6650.1	-49741	-50360	65818	-25530	-49267	-11630	-26212	-23455
23	-1.3513e+05	3195.6	90179	-1.303e+05	46011	1.3112e+05	1.6481e+05	35640	1.7356e+05	99717	-6869	1.3527e+05	-1.3879e+05	-30602	-1.2085e+05	-1.2591e+05	-17495	-1.6028e+05	1.6938e+05	-8751	-1.4552e+05	96226	-21130	-1.0349e+05
24	-1.3121e+05	20042	1.13e+05	-1.3993e+05	19696	1.5428e+05	1.6032e+05	8640.1	1.5347e+05	1.0913e+05	8861	1.1698e+05	-1.363e+05	-18399	-1.1315e+05	-1.3029e+05	-19145	-1.5187e+05	1.6714e+05	-10082	-1.5808e+05	1.0114e+05	-9614	-1.1463e+05
25	-1.6731e+05	1.5825e+05	9999.3	1.3024e+05	1.5179e+05	19165	1.3633e+05	1.1308e+05	18490	-1.0125e+05	1.1491e+05	9672.1	-1.6034e+05	-1.5348e+05	-8741.9	1.4008e+05	-1.5448e+05	-19717	1.3137e+05	-1.1319e+05	-20012	-1.0913e+05	-1.1687e+05	-8856.3
26	-1.6964e+05	1.4572e+05	8741.9	1.2598e+05	1.6037e+05	17544	1.3898e+05	1.2094e+05	30703	-96360	1.0376e+05	21202	-1.6499e+05	-1.7371e+05	-35702	1.3046e+05	-1.3133e+05	-46059	1.3538e+05	-90370	-3245.7	-99808	-1.3539e+05	6816.2
27	-1.4375e+05	83198	55830	-14365	79995	79995	1.2635e+05	54143	76870	-3085.3	55050	55031	-1.2621e+05	-77090	-52046	16607	-81984	-78078	1.4379e+05	-58024	-82906	667.74	-55288	-54695
28	-1.3985e+05	71202	54219	-16607	81984	78078	1.3033e+05	55822	88900	7498.4	44390	65713	-1.3046e+05	-94875	-79149	-1.3927e-11	-56201	-1.0389e+05	1.3968e+05	-30932	-65199	9407.3	-71391	-38673
29	-65919	49504	25326	6650.1	50252	49633	84173	24467	50726	11630	23785	26542	-84217	-53611	-29885	-8741.3	-44682	-55519	65926	-20400	-46303	-9501.9	-29314	-20521
30	-70270	37349	17539	180.6	58385	41664	80011	32459	62897	9819.1	12198	38102	-80181	-71698	-51531	-9932.5	-23343	-76835	70132	1328.5	-28420	240.35	-46679	-3417.1
31	-1.3368e+05	21599	1.1683e+05	-1.3969e+05	20852	1.5811e+05	1.6284e+05	9916.8	1.519e+05	1.0884e+05	10385	1.1536e+05	-1.3877e+05	-19955	-1.1699e+05	-1.3005e+05	-20301	-1.557e+05	1.6966e+05	-11359	-1.5651e+05	1.0085e+05	-11138	-1.1301e+05
32	-1.3119e+05	9395.7	1.0913e+05	-1.4407e+05	22503	1.497e+05	1.606e+05	11248	1.6446e+05	1.1376e+05	-1131.2	1.2649e+05	-1.3485e+05	-36802	-1.3981e+05	-1.3968e+05	6013.4	-1.7886e+05	1.6516e+05	15641	-1.3642e+05	1.1027e+05	-26868	-94710
33	1.6516e+05	-35693	-1.7392e+05	1.0008e+05	6832.4	-1.3562e+05	-1.3543e+05	-3191.4	-90467	-1.3057e+05	-46032	-1.3147e+05	1.6972e+05	8710.9	1.458e+05	96518	21097	1.0385e+05	-1.3925e+05	30690	1.2129e+05	-1.2622e+05	17585	1.6054e+05
34	1.6054e+05	-8821.8	-1.5375e+05	1.0932e+05	-9020.9	-1.1712e+05	-1.3142e+05	-19992	-1.1296e+05	-1.3997e+05	-19642	-1.5459e+05	1.6732e+05	9916.8	1.5808e+05	1.0124e+05	9495.9	1.1483e+05	-1.3662e+05	18670	1.1369e+05	-1.3041e+05	19394	1.5182e+05
35	80323	-51396	-72041	240.35	-3317.7	-47042	-70074	-28250	1215.8	9709	-76707	-23510	70316	17473	37354	-9502.5	37803	12241	-80334	62746	33023	-677.85	41649	58760
36	84393	-29759	-54164	9819.7	-20770	-29823	-66084	-46396	-20079	8565.6	-55190	-44667	66000	25356	49069	-11479	26159	23455	-84371	50568	25461	-6844	50031	50749
37	1.3057e+05	-79114	-94997	-9174.8	-38604	-71503	-1.3953e+05	-65085	-30985	-4.1837e-11	-1.0384e+05	-56218	1.3978e+05	54224	71241	-7474.8	65623	44485	-1.3046e+05	88780	55874	16293	78018	82102
38	1.2642e+05	-52167	-77194	-271.17	-54833	-55572	-1.4344e+05	-82663	-57863	-16293	-78018	-82102	1.4361e+05	55601	83160	2979.6	54860	54915	-1.2695e+05	77225	55060	13951	79995	79596
39	1.349e+05	-1.3967e+05	-36910	-1.0991e+05	-94594	-26942	-1.6499e+05	-1.3622e+05	15553	1.3953e+05	-1.7869e+05	5915	1.3104e+05	1.091e+05	9554.6	-1.1364e+05	1.2619e+05	-882.85	-1.6062e+05	1.6425e+05	11240	1.437e+05	1.4963e+05	22472
40	1.3948e+05	-1.1705e+05	-20891	-99914	-1.1313e+05	-12061	-1.6935e+05	-1.5607e+05	-11240	1.3021e+05	-1.5574e+05	-20483	1.3377e+05	1.1642e+05	20634	-1.0866e+05	1.1527e+05	9536.8	-1.6407e+05	1.5255e+05	12260	1.3854e+05	1.5776e+05	22244
41	1.6265e+05	-10082	-1.519e+05	1.0875e+05	-10503	-1.1516e+05	-1.3337e+05	-21327	-1.163e+05	-1.3957e+05	-20603	-1.5816e+05	1.6944e+05	11177	1.5623e+05	1.0066e+05	10978	1.1286e+05	-1.3856e+05	20005	1.1702e+05	-1.3001e+05	20355	1.5539e+05
42	1.6026e+05	-11288	-1.6418e+05	1.1347e+05	1098.3	-1.2614e+05	-1.3074e+05	-9306.9	-1.0869e+05	-1.4376e+05	-22412	-1.4944e+05	1.6481e+05	-15694	1.3606e+05	1.0991e+05	26831	94364	-1.3455e+05	36806	1.3952e+05	-1.3941e+05	-6034.3	1.7851e+05
43	83990	-24641	-50924	11479	-23837	-26542	-65619	-49425	-24536	6844	-49962	-49245	65597	20238	45829	-9819.7	29227	20174	-83906	53598	29917	-8565.6	44803	55326
44	79674	-32524	-62639	9502.5	-12194	-37756	-69656	-37247	-16974	677.85	-58345	-41234	69667	-1399	27953	-240.35	46679	2954.6	-79916	71743	51212	-9709	23286	76483
45	1.2638e+05	-54392	-76829	-2979.6	-55133	-55078	-1.4303e+05	-82764	-54933	-13951	-79995	-80393	1.4357e+05	57825	82796	271.17	55160	54421	-1.2654e+05	77327	52130	16293	81972	77887
46	1.3021e+05	-55769	-88748	7474.8	-44370	-65508	-1.3952e+05	-71210	-54119	-16293	-81972	-77887	1.3941e+05	30879	64993	9174.8	71388	38490	-1.3045e+05	94905	79008	-5.2751e-11	56147	1.0377e+05
47	1.3622e+05	-1.1356e+05	-19363	-1.0132e+05	-1.1472e+05	-10462	-1.6591e+05	-1.5743e+05	-7738.7	1.3144e+05	-1.5222e+05	-17754	1.305e+05	1.1293e+05	19107	-1.1007e+05	1.1685e+05	7938.1	-1.6062e+05	1.5391e+05	8758.4	1.3978e+05	1.5424e+05	19514
48	1.3894e+05	-1.2088e+05	-30443	-96342	-1.038e+05	-20882	-1.6935e+05	-1.4573e+05	-8758.4	1.2629e+05	-1.6035e+05	-17525	1.3508e+05	90320	3087.6	-1.0007e+05	1.3539e+05	-6943.8	-1.6499e+05	1.7376e+05	35551	1.3045e+05	1.3129e+05	45912
49	8.0945e-11	56201	-1.0389e+05	1.3046e+05	94875	-79149	-9407.3	71391	-38673	-1.3968e+05	30932	-65199	16607	-81984	78078	1.3985e+05	-71202	54219	-7498.4	-44390	65713	-1.3033e+05	-55822	88900
50	-16607	81984	-78078	1.2621e+05	77090	-52046	-667.74	55288	-54695	-1.4379e+05	58024	-82906	14365	-79995	79995	1.4375e+05	-83198	55830	3085.3	-55050	55031	-1.2635e+05	-54143	76870
51	-1.3046e+05	1.3133e+05	-46059	1.6499e+05	1.7371e+05	-35702	99808	1.3539e+05	6816.2	-1.3538e+05	90370	-3245.7	-1.2598e+05	-1.6037e+05	17544	1.6964e+05	-1.4572e+05	8741.9	96360	-1.0376e+05	21202	-1.3898e+05	-1.2094e+05	30703
52	-1.4008e+05	1.5448e+05	-19717	1.6034e+05	1.5348e+05	-8741.9	1.0913e+05	1.1687e+05	-8856.3	-1.3137e+05	1.1319e+05	-20012	-1.3024e+05	-1.5179e+05	19165	1.6731e+05	-1.5825e+05	9999.3	1.0125e+05	-1.1491e+05	9672.1	-1.3633e+05	-1.1308e+05	18490
53	1.3968e+05	-6013.4	-1.7886e+05	1.3485e+05	36802	-1.3981e+05	-1.1027e+05	26868	-94710	-1.6516e+05	-15641	-1.3642e+05	1.4407e+05	-22503	1.497e+05	1.3119e+05	-9395.7	1.0913e+05	-1.1376e+05	1131.2	1.2649e+05	-1.606e+05	-11248	1.6446e+05
54	1.3005e+05	20301	-1.557e+05	1.3877e+05	19955	-1.1699e+05	-1.0085e+05	11138	-1.1301e+05	-1.6966e+05	11359	-1.5651e+05	1.3969e+05	-20852	1.5811e+05	1.3368e+05	-21599	1.1683e+05	-1.0884e+05	-10385	1.1536e+05	-1.6284e+05	-9916.8	1.519e+05
55	9932.5	23343	-76835	80181	71698	-51531	-240.35	46679	-3417.1	-70132	-1328.5	-28420	-180.6	-58385	41664	70270	-37349	17539	-9819.1	-12198	38102	-80011	-32459	62897
56	8741.3	44682	-55519	84217	53611	-29885	9501.9	29314	-20521	-65926	20400	-46303	-6650.1	-50252	49633	65919	-49504	25326	-11630	-23785	26542	-84173	-24467	50726
57	-14365	79995	-79995	1.2623e+05	76792	-54163	-3085.3	54943	-54962	-1.4363e+05	55850	-83119	16607	-78006	81911	1.4377e+05	-82900	57947	667.74	-54705	55298	-1.2619e+05	-51969	77084
58	-16607	78006	-81911	1.3013e+05	88787	-55774	7498.4	65603	-44279	-1.3965e+05	54171	-71089	1.819e-11	-1.0379e+05	56099	1.3953e+05	-65115	30844	9407.3	-38601	71320	-1.303e+05	-79061	94790
59	-1.3974e+05	1.5819e+05	-20832	1.6267e+05	1.5173e+05	-9999.3	1.0874e+05	1.1508e+05	-10327	-1.3365e+05	1.169e+05	-21507	-1.299e+05	-1.555e+05	20281	1.6964e+05	-1.565e+05	11257	1.0086e+05	-1.1311e+05	11142	-1.3861e+05	-1.168e+05	19985
60	-1.44e+05	1.4961e+05	-22454	1.6034e+05	1.6426e+05	-11257	1.1363e+05	1.2623e+05	1203.4	-1.31e+05	1.0904e+05	-9294.7	-1.3953e+05	-1.7865e+05	-6061.3	1.6499e+05	-1.3627e+05	-15704	1.1018e+05	-94596	26815	-1.3461e+05	-1.3961e+05	36752
61	1.3029e+05	19145	-1.5187e+05	1.363e+05	18399	-1.1315e+05	-1.0114e+05	9614	-1.1463e+05	-1.6714e+05	10082	-1.5808e+05	1.3993e+05	-19696	1.5428e+05	1.3121e+05	-20042	1.13e+05	-1.0913e+05	-8861	1.1698e+05	-1.6032e+05	-8640.1	1.5347e+05
62	1.2591e+05	17495	-1.6028e+05	1.3879e+05	30602	-1.2085e+05	-96226	21130	-1.0349e+05	-1.6938e+05	8751	-1.4552e+05	1.303e+05	-46011	1.3112e+05	1.3513e+05	-3195.6	90179	-99717	6869	1.3527e+05	-1.6481e+05	-35640	1.7356e+05
63	6650.1	49741	-50360	84071	50490	-24671	11630	26212	-23455	-65818	25530	-49267	-8741.3	-55311	44475	65773	-46382	20112	-9501.9	-20683	29476	-84064	-29597	53690
64	180.6	41609	-58329	79720	62645	-32458	9819.1	37798	-11894	-69979	17537	-37097	-9932.5	-76651	23159	69810	-28296	-1534.4	240.35	-3317.3	46580	-79858	-51325	71574
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