﻿ 复合材料夹层板架结构在组合载荷作用下的极限强度研究
 舰船科学技术  2019, Vol. 41 Issue (1): 14-19 PDF

Investigations on the ultimate strength of composite sandwich frame structure under combined loads
PAN Kang-hua, TIAN A-li, YE Ren-chuan, REN Peng, JIANG Wen-an
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: With the increase of the sizes of composite ships, the assessment of the ultimate strength of ship hulls in composite materials is overwhelmingly significant. The ultimate strength of composite sandwich frame structures under combined loads is predicted by a progressive failure analysis based on post-buckling theory. Compared with the published results about composite laminated plates tested by the experiments and simulated by the finite element method, the accuracy of the progressive failure method in this paper is verified. Considering the mechanical properties of composite sandwich frame structures as the ship superstructure, the first ply failure strength and last ply failure strength are obtain when composite structures with initial imperfection are subjected to in-plane loads and transverse pressure together, then the failure location is also predicted.
Key words: sandwich frame structures     combine loads     first ply failure     ultimate strength
0 引　言

1 有限元屈曲理论

 $\begin{array}{l} {{{ K}_T}} d\left\{ \Delta \right\} = d\left\{ P \right\},\\ {{{{K}}_T}} = \int_\varOmega {{{\mathord{\buildrel{\hbox{$\scriptscriptstyle\frown$}} \over B} }^{\rm T}}{{\mathord{\buildrel{\hbox{$\scriptscriptstyle\frown$}} \over D} }_T}\mathord{\buildrel{\hbox{$\scriptscriptstyle\frown$}} \over B} {\rm {\rm{d}}}V \!+\! } \int_\varOmega {\frac{{\partial {{\mathord{\buildrel{\hbox{$\scriptscriptstyle\frown$}} \over B} }^{\rm T}}}}{{\partial \tilde u}}S{\rm{d}}V - } \frac{{\partial f}}{{\partial \tilde u}} \!=\! {{{{K}}_{{L}}}} \!+\!{{{{K}}_{{\sigma}} }} \!+\! {{{{K}}_{NL}}} \text{。} \end{array}$ (1)

2 失效模型及破坏分析 2.1 本构关系

 $\left\{\! {\begin{array}{*{20}{c}} {{\sigma _1}} \\ {{\sigma _2}} \\ {{\tau _{12}}} \\ {{\tau _{23}}} \\ {{\tau _{13}}} \end{array}}\! \right\} = \left[ \!{\begin{array}{*{20}{c}} {{Q_{11}}}&{{Q_{12}}}&0&0&0 \\ {{Q_{12}}}&{{Q_{22}}}&0&0&0 \\ 0&0&{{Q_{66}}}&0&0 \\ 0&0&0&{{Q_{44}}}&0 \\ 0&0&0&0&{{Q_{55}}} \end{array}}\! \right]\left\{\! {\begin{array}{*{20}{c}} {{\varepsilon _1}} \\ {{\varepsilon _2}} \\ {{\gamma _{12}}} \\ {{\gamma _{23}}} \\ {{\gamma _{13}}} \end{array}}\! \right\}{\text{。}}\!\!\!\!\!\!\!$ (2)

 $\begin{array}{l} {Q_{11}} = \displaystyle\frac{{{E_1}}}{{1 - {\nu _{12}}{\nu _{21}}}},\;\;{Q_{12}} = \displaystyle\frac{{{\nu _{12}}{E_2}}}{{1 - {\nu _{12}}{\nu _{21}}}},\;\;{Q_{22}} = \displaystyle\frac{{{E_2}}}{{1 - {\nu _{12}}{\nu _{21}}}}\\ \;\;\;\;\;{Q_{66}} = {G_{12}},\;\;\;\;\;{Q_{44}} = {G_{23}},\;\;\;\;\;{Q_{55}} = {G_{13}}\;{\text{。}} \end{array}$ (3)

2.2 失效准则

Shokrieh等[20]改进了三维的Hashin失效准则，考虑了7种失效模式。

 ${\left( {\frac{{{\sigma _{11}}}}{{{X_T}}}} \right)^2} + {\left( {\frac{{{\tau _{12}}}}{{{S_{12}}}}} \right)^2} + {\left( {\frac{{{\tau _{13}}}}{{{S_{13}}}}} \right)^2} \geqslant 1{\text{；}}$ (4)

 ${\left( {\frac{{{\sigma _{11}}}}{{{X_C}}}} \right)^2} \geqslant 1{\text{；}}$ (5)

 ${\left( {\frac{{{\sigma _{22}}}}{{{Y_T}}}} \right)^2} + {\left( {\frac{{{\tau _{12}}}}{{{S_{12}}}}} \right)^2} + {\left( {\frac{{{\tau _{23}}}}{{{S_{23}}}}} \right)^2} \geqslant 1{\text{；}}$ (6)

 ${\left( {\frac{{{\sigma _{22}}}}{{{Y_c}}}} \right)^2} + {\left( {\frac{{{\tau _{12}}}}{{{S_{12}}}}} \right)^2} + {\left( {\frac{{{\tau _{23}}}}{{{S_{23}}}}} \right)^2} \geqslant 1{\text{；}}$ (7)

 ${\left( {\frac{{{\sigma _{11}}}}{{{X_c}}}} \right)^2} + {\left( {\frac{{{\tau _{12}}}}{{{S_{12}}}}} \right)^2} + {\left( {\frac{{{\tau _{13}}}}{{{S_{13}}}}} \right)^2} \geqslant 1{\text{，}} {{\sigma _{11}} < 0} {\text{；}}$ (8)

 ${\left( {\frac{{{\sigma _{22}}}}{{{Z_T}}}} \right)^2} + {\left( {\frac{{{\tau _{13}}}}{{{S_{13}}}}} \right)^2} + {\left( {\frac{{{\tau _{23}}}}{{{S_{23}}}}} \right)^2} \geqslant 1{\text{；}}$ (9)

 ${\left( {\frac{{{\sigma _{33}}}}{{{Z_C}}}} \right)^2} + {\left( {\frac{{{\tau _{13}}}}{{{S_{13}}}}} \right)^2} + {\left( {\frac{{{\tau _{23}}}}{{{S_{23}}}}} \right)^2} \geqslant 1{\text{。}}$ (10)
2.3 材料退化模型

 ${p^ * } = k \cdot p{\text{，}}\;\;\;\;\; {k = 0 \sim 1}{\text{。}}$ (11)

3 方法验证

3.1 结构参数以及边界条件

3.2 有限元模型

 图 1 一阶弹性屈曲模态 Fig. 1 The first-order elastic buckling mode
3.3 分析比较

4 复合材料夹层板架结构极限强度

4.1 夹层板架结构模型

 图 2 结构布置图及局部示意图 Fig. 2 Structural layout and local schematic diagram

4.2 载荷工况与边界约束

 图 3 板架结构的组合载荷 Fig. 3 Load modes of frame structure

 图 4 边界条件 Fig. 4 Boundary conditions
4.3 结果与讨论

 图 5 板架结构纵向在组合载荷作用下的载荷位移曲线 Fig. 5 The load-displacement curve along the longtitude direction

 图 6 板架结构横向在组合载荷作用下的载荷位移曲线 Fig. 6 The load-displacement curve along the tranverse direction

1）随着纵向载荷的比例减少，纵向首层失效载荷呈现降低趋势，然而对比Nxx:Nyy=1.0:0.0和Nxx:Nyy=0.7:0.3，二者首层失效铺层角度相同，后者首层失效强度大于前者；

2）垂向均布载荷的施加影响了板架结构的纵向极限强度，载荷模式在Nxx:Nyy=1.0:0.0，Nxx:Nyy=0.7:0.3，Nxx:Nyy=0.5:0.5时分别减小了6.00%，5.51%，.56%，随着纵向载荷比例的减少，垂向载荷影响减小；

3）加载方式的不同，复合材料首层失效位置和最终失效位置也发生改变，一般来看往往是垂直于载荷方向的铺层角度最先失效，与载荷方向相同的铺层失效往往是导致结构失去承载能力的主要因素。

1）P=0时随着横向载荷比例增加，横向失效载荷增大，但是其他因素使Nxx:Nyy=0.0:1.0的首层失效载荷有所降低；

2）垂向载荷的施加减低了加筋板的横向极限强度，载荷模式在Nxx:Nyy=0.7:0.3，Nxx:Nyy=0.5:0.5，Nxx:Nyy=0.0:1.0时分别减小了5.51%，1.56%，5.40%。

5 结　语

1）随着纵向载荷的降低、横向载荷的提高，结构主要承载方向将随提高边转移。侧向均布压力的存在，对结构承载能力影响十分显著，导致结构较快的达到满足失效条件。

2）复合材料首层失效铺层与承载方式相关，一般来看往往是垂直于载荷方向的铺层角度最先失效，与载荷方向相同的铺层失效往往是导致结构失去承载能力的主要因素。

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