例2-2：由碳纤维增强聚合物制得的正交各向异性材料的工程弹性常数为：E1=175 GPa E2=32GPa E3=83GPa G23=57GPa G12=G13=12Gpa V23=031V12=V13=025求其刚度矩阵C1和柔度矩阵S。

刚度矩阵[C1]的计算公式为： [C1] = 1 / (1 - V12V21 - V13V31 - V23V32) * [E1/(1-V12V21), V21E2/(1-V12V21), V31E3/(1-V12V21), 0, 0, 0; V12E1/(1-V12V21), E2/(1-V12V21), V32E3/(1-V12V21), 0, 0, 0; V13E1/(1-V12V21), V23E2/(1-V12V21), E3/(1-V12V21), 0, 0, 0; 0, 0, 0, G23, 0, 0; 0, 0, 0, 0, G13, 0; 0, 0, 0, 0, 0, G12]

代入已知的数值： [C1] = 1 / (1 - 0.250.25 - 0.250.25 - 0.310.31) * [175/(1-0.250.25), 0.2532/(1-0.250.25), 0.258.3/(1-0.250.25), 0, 0, 0; 0.25175/(1-0.250.25), 32/(1-0.250.25), 0.318.3/(1-0.250.25), 0, 0, 0; 0.25175/(1-0.250.25), 0.3132/(1-0.250.25), 8.3/(1-0.250.25), 0, 0, 0; 0, 0, 0, 5.7, 0, 0; 0, 0, 0, 0, 12, 0; 0, 0, 0, 0, 0, 12]

简化后得到： [C1] = [148.9362, 10, 10, 0, 0, 0; 10, 32, 10.5505, 0, 0, 0; 10, 10.5505, 8.3, 0, 0, 0; 0, 0, 0, 5.7, 0, 0; 0, 0, 0, 0, 12, 0; 0, 0, 0, 0, 0, 12]

柔度矩阵[S]是刚度矩阵的逆矩阵： [S] = [0.0065, -0.0015, -0.0015, 0, 0, 0; -0.0015, 0.0323, -0.0042, 0, 0, 0; -0.0015, -0.0042, 0.1205, 0, 0, 0; 0, 0, 0, 0.1754, 0, 0; 0, 0, 0, 0, 0.0833, 0; 0, 0, 0, 0, 0, 0.0833]