Stress Field Gradient Analysis Technique Using Lower-Order Elements

Table 1

Stress gradients at point with different meshes and methods.

Mesh-Method-Element	Numerical solution		Exact solution		Error
	/10^8	/10^8	/10^8	/10^8			Average
C-SFG-Q4	−10.3667	4.0309	−10.1284	3.7238	2.3524%	8.2482%	5.3003%
C-SCP-Q8	−8.7140	3.3071			−13.9646%	−11.1893%	12.5769%
C-SFG-Q8	−1.0908	4.1159			7.6936%	10.5311%	9.1123%
C-SFG-T3	−9.2718	4.8073			−8.4575%	29.0992%	18.7783%
C-SCP-T6	−10.1010	3.9277			−0.2813%	5.4765%	2.8789%
C-SFG-T6	−10.2858	3.6292			1.5533%	−2.5402%	2.0467%
F-SFG-Q4	−10.1920	3.6648	−9.9690	3.6431	2.2362%	0.5960%	1.4161%
F-SCP-Q8	−9.54347	3.2959			−4.2689%	−9.5305%	6.8997%
F-SFG-Q8	−10.4925	3.8314			5.2506%	5.1685%	5.2096%
F-SFG-T3	−10.1635	3.7822			1.9511%	3.8174%	2.8842%
F-SCP-T6	−10.2152	3.6521			2.4697%	0.2479%	1.3588%
F-SFG-T6	−10.1343	3.5049			1.6575%	−3.7928%	2.7251%
DF-SFG-Q4	−10.1587	3.6648	−9.8932	3.6050	2.6837%	1.6590%	2.1714%
DF-SCP-Q8	−9.8485	3.3578			−0.4519%	−6.8582%	3.6551%
DF-SFG-Q8	−10.2297	3.5939			3.4010%	−0.3094%	1.8552%
DF-SFG-T3	−9.9612	3.7442			0.6875%	3.8603%	2.2739%
DF-SCP-T6	−10.1757	3.5357			2.8555%	−1.9237%	2.3896%
DF-SFG-T6	−10.1554	3.5479			2.6497%	−1.5834%	2.1166%

Meshes: C: coarse; F: fine; DF: double-fine.
Methods: SFG: stress field gradient; SCP: superconvergent patch.