《复合材料力学分析》课程教学课件（讲稿）第3章 单向复合材料的刚度分析

Solution0001/E,-V21/E22-V31/E3010001/E2- V12 /El-V32/E3&2020001/ E3- V13 / E,-V23 /E2&303000001/G23Y2323000001/G31Y31T31000001/G12Y12T12沿材料主轴，横观各向同性？二维应力状态，V12 - V21对称性横观各向同性 V13=Vi2E,E262 = 0.013,83 = -0.002810.301V12020.00261Y12 = 0.005, Y31 = 0, Y23 = 020001000EE,16The resulting strains are three-dimensional!

Solution ❖ 二维应力状态，沿材料主轴，横观各向同性 对称性 横观各向同性 1 1 21 2 31 3 1 2 12 1 2 32 3 2 3 13 1 23 2 3 3 23 23 23 31 31 31 12 12 12 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 E E E E E E E E E G G G      −  −            −  −        −  −       =                   12 21 1 2 = E E     13 12 = 1 12 2 1 1 1 1 0.3 0.002 E E 2000 1000     = − = − = 2 3 12 31 23 0.013, 0.0028 0.005, 0, 0      = = − = = = The resulting strains are three-dimensional! 16

Balanced orthotropiclaminaE,=E2Q1i=Q22S.i=S22FIGURE2.10Balanced orthotropic lamina consisting of fibers oriented at 0°and 90°Woven or cross-plied at0°and90°.Threeindependentelasticconstantsbecauseofdoublesymmetry of properties withrespectto1 and2 axes17

Balanced orthotropic lamina ❖ Woven or cross-plied at 0º and 90º. Three independent elastic constants because of double symmetry of properties with respect to 1 and 2 axes. 1 2 11 22 11 22 = = = E E Q Q S S 17

3.2.单层板材料任意方向的应力应变关系LaminateStructure斜铺层合板，螺旋缠绕纤维增强的圆柱壳18

3.2. 单层板材料任意方向的应力 应变关系 斜铺层合板，螺旋缠绕纤维增强的圆柱壳 Laminate Structure 18