纤维缠绕不等极孔椭球类容器应力分析和优化.PDF

纤维缠绕不等极孔椭球类容器的应力分析及优化 王　 荣　 　 何钦象　 　 祖　 磊 (西安理工大学工程力学系,西安　 710054) 文　 摘　 基于微分几何推导出了不等极孔椭球类容器纤维缠绕的非测地线稳定缠绕方程,并根据薄膜理 - 论、层合板理论、蔡 吴失效准则得到了赤道处纤维层的最小厚度1.2817 mm,计算出的纤维方向的应力小于 纤维的极限强度3.92 GPa。 发现纤维缠绕椭球容器的应力状态是赤道处最先发生破坏,且会出现局部失效现 - 象。 以缠绕层最小质量M 为目标函数,蔡 吴失效准则为约束条件,在给定内压5 MPa 的情况下,得到了优化 后的容器质量为34.072 kg。 相比于等极孔的容器而言,非测地线缠绕具有高度非线性、不稳定性及精度难以 控制等问题。 关键词　 不等极孔,纤维缠绕,非测地线,优化 - 中图分类号:TB332 DOI:10.3969/ j.issn.1007 2330.2014.04.004 Stress Analysis and Optimization for Filament Wound Ellipsoidal Pressure Vessels With Unequal Polar Openings WANG Rong　 　 HE Qinxiang　 　 ZU Lei (Department of Engineering Mechanics,Xi’an University of Technology,Xi’an　 710054) Abstract　 Mechanical propertyof ellipsoidpressurevesselswithunequalpolaropeningsisstudiedinthispaper. The steady formulasfor filament on a surface of revolution are derivedfrom differential geometry. Based on the mem- brane theory,laminate theory and Tsai-Wu failure criterion,the thickness of the equator is 1.2817 mm,the stress value of the fiber direction islessthan thefiber strength3.92 GPa. The stress state of thefilament wound ellipsoidal vessel is that the damage happensfirst in equator,and local failure phenomenon is happened. To minimum winding layersweightM asthe objectivefunction,Tsai-Wufailure criterion asthe constraint condition,under the condition of 5 MPa internal pressure,we achieve the optimized weight is34.072 kg. Compared to ellipsoid pressure vesselswith equal polar openings,it has highly non-linear,instability and high precision. Key words　 Unequal polar openings,Filament winding,Non-geodesic,Optimization 0　 引言 线方程显得十分重要。 国内外的研究人员已经对常