Interval uncertainty analysis of elastic bimodular truss structures

Figures & data

Figure 1. Stress–strain relationship of bimodular materials.

Figure 2. An elastic bimodulus truss structure.

Table 1. A comparison of intervals.

Displacement	${\mathit{u}}^{\mathit{c}}$	$\mathrm{\Delta }\mathit{u}$	${\mathit{u}}_{\mathit{r}}^{\mathit{c}}$	$\mathrm{\Delta }{\mathit{u}}_{\mathit{r}}$	$\frac{{\mathit{u}}^{\mathit{c}}}{{\mathit{u}}_{\mathit{r}}^{\mathit{c}}}$ (%)	$\frac{\mathbf{\Delta }\mathit{u}}{{\mathbf{\Delta }\mathit{u}}_{\mathit{r}}}$ (%)
u1	0.00E+00	0.00E+00	0.00E+00	0.00E+00	0.0000	0.0000
v1	0.00E+00	0.00E+00	0.00E+00	0.00E+00	0.0000	0.0000
u2	1.01E−05	1.44E−07	1.01E−05	1.44E−07	0.0179	0.0260
v2	−2.39E−05	3.30E−07	−2.39E−05	3.30E−07	0.0209	0.0264
u3	1.69E−06	2.87E−08	1.70E−06	2.87E−08	0.0295	0.0264
v3	−2.39E−05	3.29E−07	−2.39E−05	3.29E−07	0.0188	0.0173
u4	1.65E−05	2.41E−07	1.65E−05	2.41E−07	0.0242	0.0278
v4	−4.56E−05	6.28E−07	−4.56E−05	6.28E−07	0.0208	0.0167
u5	4.54E−06	7.37E−08	4.54E−06	7.37E−08	0.0275	0.0250
v5	−4.56E−05	6.27E−07	−4.56E−05	6.27E−07	0.0197	0.0233
u6	1.89E−05	2.81E−07	1.89E−05	2.81E−07	0.0212	0.0156
v6	−5.97E−05	8.23E−07	−5.97E−05	8.24E−07	0.0209	0.0234
u7	7.41E−06	1.20E−07	7.41E−06	1.20E−07	0.0277	0.0257
v7	−5.97E−05	8.22E−07	−5.97E−05	8.22E−07	0.0201	0.0198
u8	1.90E−05	2.91E−07	1.90E−05	2.91E−07	0.0263	0.0330
v8	−6.88E−05	9.51E−07	−6.88E−05	9.51E−07	0.0211	0.0209
u9	1.03E−05	1.69E−07	1.03E−05	1.69E−07	0.0339	0.0350
v9	−6.88E−05	9.48E−07	−6.88E−05	9.49E−07	0.0211	0.0253
u10	1.79E−05	2.83E−07	1.79E−05	2.83E−07	0.0280	0.0173
v10	−7.40E−05	1.02E−06	−7.40E−05	1.02E−06	0.0203	0.0225
u11	1.32E−05	2.17E−07	1.32E−05	2.17E−07	0.0264	0.0354
v11	−7.40E−05	1.02E−06	−7.40E−05	1.02E−06	0.0203	0.0216
u12	1.62E−05	2.66E−07	1.62E−05	2.66E−07	0.0278	0.0255
v12	−7.57E−05	1.05E−06	−7.57E−05	1.05E−06	0.0198	0.0210
u13	1.62E−05	2.66E−07	1.62E−05	2.66E−07	0.0278	0.0255
v13	−7.57E−05	1.04E−06	−7.57E−05	1.04E−06	0.0205	0.0192
u14	1.45E−05	2.60E−07	1.45E−05	2.60E−07	0.0277	0.0419
v14	−7.40E−05	1.02E−06	−7.40E−05	1.02E−06	0.0203	0.0225
u15	1.91E−05	3.15E−07	1.91E−05	3.16E−07	0.0288	0.0345
v15	−7.40E−05	1.02E−06	−7.40E−05	1.02E−06	0.0203	0.0216
u16	1.33E−05	2.80E−07	1.33E−05	2.80E−07	0.0300	0.0161
v16	−6.88E−05	9.51E−07	−6.88E−05	9.51E−07	0.0211	0.0209
u17	2.20E−05	3.64E−07	2.20E−05	3.64E−07	0.0250	0.0349
v17	−6.88E−05	9.48E−07	−6.88E−05	9.49E−07	0.0211	0.0253
u18	1.34E−05	3.08E−07	1.34E−05	3.08E−07	0.0335	0.0340
v18	−5.97E−05	8.23E−07	−5.97E−05	8.24E−07	0.0209	0.0234
u19	2.49E−05	4.12E−07	2.49E−05	4.12E−07	0.0261	0.0291
v19	−5.97E−05	8.22E−07	−5.97E−05	8.22E−07	0.0201	0.0198
u20	1.58E−05	3.50E−07	1.58E−05	3.50E−07	0.0285	0.0246
v20	−4.56E−05	6.28E−07	−4.56E−05	6.28E−07	0.0208	0.0167
u21	2.78E−05	4.59E−07	2.78E−05	4.59E−07	0.0288	0.0213
v21	−4.56E−05	6.27E−07	−4.56E−05	6.27E−07	0.0197	0.0232
u22	2.23E−05	4.11E−07	2.23E−05	4.11E−07	0.0314	0.0269
v22	−2.39E−05	3.30E−07	−2.39E−05	3.30E−07	0.0209	0.0263
u23	3.06E−05	5.04E−07	3.06E−05	5.04E−07	0.0277	0.0323
v23	−2.39E−05	3.29E−07	−2.39E−05	3.29E−07	0.0188	0.0173
u24	3.23E−05	5.33E−07	3.23E−05	5.33E−07	0.0278	0.0255
v24	0.00E+00	0.00E+00	0.00E+00	0.00E+00	0.0000	0.0000

Table 2. Numerical comparison of E^c and ΔE (24 sampling points (1–24)).

δ	1%		3%		5%
E^c obtained by the proposed approach	1.20E+08	4.96E+08	1.20E+08	5.04E+08	1.19E+08	5.05E+08
Relative error of E^c (%)	0.00%	−0.80%	0.00%	0.80%	−0.83%	1.00%
ΔE obtained by the proposed approach	4.00E+07	9.92E+07	3.97E+07	1.01E+08	3.95E+07	1.03E+08
Relative error of ΔE (%)	0.00%	−0.80%	−0.75%	1.00%	−1.25%	3.00%

Table 3. Numerical comparison of E^c and ΔE (10 sampling points (1, 2, 5, 8, 11,14, 17, 20, 23, 24)).

δ	1%		3%		5%
E^c obtained by the proposed approach	1.20E+08	5.02E+08	1.20E+08	4.90E+08	1.21E+08	5.11E+08
Relative error of E^c (%)	0.00%	0.40%	0.00%	−2.00%	0.83%	2.20%
ΔE obtained by the proposed approach	4.00E+07	9.98E+07	4.02E+07	1.01E+08	3.98E+07	9.80E+07
Relative error of ΔE (%)	0.00%	−0.20%	0.50%	1.00%	−0.50%	−2.00%

Table 4. Numerical comparison of E^c and ΔE (7 sampling points (1, 3, 8, 13, 18, 23, 24)).

δ	1%		3%		5%
E^c obtained by the proposed approach	1.21E+08	5.00E+08	1.21E+08	4.94E+08	1.22E+08	5.08E+08
Relative error of E^c (%)	0.83%	0.00%	0.83%	−1.20%	1.67%	1.60%
ΔE obtained by the proposed approach	3.99E+07	1.01E+08	4.02E+07	9.79E+07	3.96E+07	1.02E+08
Relative error of ΔE (%)	−0.25%	1.00%	0.50%	−2.10%	−1.00%	2.00%

Table 5. Numerical comparison of E^c and ΔE (5 sampling points (1, 4, 11, 18, 24)).

δ	1%		3%		5%
E^c obtained by the proposed approach	1.19E+08	5.01E+08	1.21E+08	5.06E+08	1.21E+08	4.90E+08
Relative error of E^c (%)	−0.83%	0.20%	0.83%	1.20%	0.83%	−2.00%
ΔE obtained by the proposed approach	4.00E+07	1.00E+08	3.99E+07	1.00E+08	4.00E+07	9.89E+07
Relative error of ΔE (%)	0.00%	0.00%	−0.25%	0.00%	0.00%	−1.10%