Study on the Explicit Formula of the Triangular Flat Shell Element Based on the Analytical Trial Functions for Anisotropy Material

Table 1

The fundamental stress solutions of the anisotropic plane problem.

Item	1	2	3	4	5	6	7
𝜎𝑥	1	0	0	𝐶11𝐶66−𝐶^261 ((𝐶22𝐶66−𝐶^262)𝑥+(𝐶21𝐶62−𝐶61𝐶22)𝑦)	(𝐶11𝐶66−𝐶^261); ((𝐶21𝐶66−𝐶62𝐶61)𝑥; +2(𝐶62𝐶11−𝐶21𝐶61)𝑦)	(𝐶11𝐶66−𝐶^261); ((𝐶61𝐶22−𝐶62𝐶21)𝑥; +(𝐶21𝐶66−𝐶22𝐶11+𝐶^221−𝐶61𝐶62)𝑦)	(𝐶11𝐶66−𝐶^261)^2𝑦
𝜎𝑦	0	1	0	(𝐶21𝐶66−𝐶61𝐶62); (𝐶66𝐶22−𝐶^262)𝑥	(2𝐶^266𝐶^221+𝐶66𝐶^321−4𝐶21𝐶66𝐶61𝐶62−𝐶11𝐶^266𝐶22−𝐶22𝐶21𝐶11𝐶66+𝐶^261𝐶66𝐶22+𝐶11𝐶66𝐶^262+𝐶^261𝐶^262+𝐶62𝐶61𝐶11𝐶22−𝐶62𝐶61𝐶^221)𝑥+(𝐶21𝐶62𝐶11𝐶66−𝐶21𝐶62𝐶^261−𝐶61𝐶22𝐶11𝐶66+𝐶22𝐶^361)𝑦	2(𝐶61𝐶^262𝐶21−𝐶66𝐶62𝐶^221+𝐶21𝐶61𝐶66𝐶22−𝐶22𝐶62𝐶^261)x  + (𝐶22𝐶^266𝐶11−𝐶22𝐶66𝐶^261−𝐶^262𝐶11𝐶66+𝐶^262𝐶^261)𝑦	(2𝐶61𝐶^221𝐶66−𝐶11𝐶66𝐶62𝐶21−3𝐶21𝐶62𝐶^261−𝐶11𝐶61𝐶66𝐶22+𝐶22𝐶^361+2𝐶61𝐶^262𝐶11)𝑥; +(𝐶62𝐶^361−𝐶61𝐶62𝐶11𝐶66+𝐶21𝐶^266𝐶11−𝐶21𝐶66𝐶^261)𝑦
𝜏𝑥𝑦	0	0	1	−(𝐶11𝐶66−𝐶^261); (𝐶66𝐶22−𝐶^262)𝑦	(𝐶11𝐶66−𝐶^261); ((𝐶61𝐶22−𝐶62𝐶21)𝑥; +(𝐶61𝐶62−𝐶21𝐶66)𝑦)	(𝐶^261−𝐶11𝐶66)((𝐶22𝐶66−𝐶^262)𝑥 +(𝐶61𝐶22−𝐶21𝐶62)𝑦)	(𝐶11𝐶66−𝐶^261); (𝐶61𝐶62−𝐶21𝐶66)𝑥