Research on Simplified Analysis Method for Deformation of Two-way Stiffened Plates Based on Orthotropic Equivalent theory
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摘要: 【目的】随着船舶不断向大型化、复杂化发展,舱段级以上的船体结构有限元模型网格数量急剧增加,碰撞、冲击、接触等许多大型非线性力学问题较难求解,针对该问题,提出一种基于正交异性等效的双向加筋板结构变形简化方法已实现船体结构的简化建模。【方法】针对船舶主要构件加筋板进行正交异性简化方法研究,将现行成熟的单向加筋板平面应力简化方法推广至应用更广、更为复杂的双向加筋板的平面弯曲问题中来,引入正交方向上加筋板总惯性矩与板的惯性矩比来反映结构的正交异性,将其代入推广得到的加筋板等效平面弯曲本构方程,实现向材料正交异性的转化,在力学层面上既体现出结构的抗变形能力又考虑了中性轴移轴产生中面力的影响;利用有限元计算,根据不同的位移分布对四边固支加筋板的变形模式分类,将加筋板结果与该方法及传统方法的等效结果对比并进行误差分析。【结果】在船舶双向加筋板结构中,使用该方法可减少84%的网格数量,且三种变形模式下的等效误差均可控制在6%以内,误差值远小于两种传统方法。【结论】该方法精度较高,适用范围更广,且大幅节省计算资源,可为大型船体结构非线性力学问题直接建模仿真计算提供解决方案。Abstract: [Objectives]With the continuous development of large-scale and complex ships, the number of finite element model grids for hull structures above class of hold increases dramatically, and many large non-linear mechanical problems such as collision, impact and contact are difficult to solve. In order to solve this problem, a simplified method for deformation of bi-directional stiffened plate structure based on orthotropic equivalent is proposed, which simplifies the modeling of ship structure. [Methods]The orthotropic simplification method for two-way stiffened panels of main ship members is studied. The current well-established simplification method for plane stress of one-way stiffened plates is extended to the wider and more complex plane bending problem of two-way stiffened plates. The ratio of total moment of inertia of stiffened plates to moment of inertia of plates in the orthogonal direction is introduced to reflect the structural orthotropism. By substituting it into the equivalent constitutive equation for plane bending of stiffened plates extended, physical orthotropism can be transformed. On the mechanical level, it not only reflects the deformation resistance of the structure, but also takes into account the influence of the membrane forces generated by shifting the neutral axis. By finite element calculation, the deformation modes of four-sided fixed stiffened plates are classified according to different displacement distributions. The result of stiffened plate is compared with that of traditional method and the error analysis is also carried out. [Results]In ship two-way stiffened plates
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