【摘要】：本文發(fā)展了一種新型協(xié)同轉(zhuǎn)動(dòng)四節(jié)點(diǎn)四邊形復(fù)合材料殼單元。協(xié)同轉(zhuǎn)動(dòng)法采用了隨單元?jiǎng)傮w轉(zhuǎn)動(dòng)而一起旋轉(zhuǎn)的,并由四邊形兩個(gè)對(duì)角線夾角的平分線定義的局部坐標(biāo)系,并在計(jì)算單元節(jié)點(diǎn)變量時(shí)僅考慮單元變形的影響,故而在排除剛體位移的情況下簡(jiǎn)化了局部坐標(biāo)系下的單元計(jì)算公式。采用的矢量型轉(zhuǎn)動(dòng)變量則大大簡(jiǎn)化了單元的局部節(jié)點(diǎn)變量與整體節(jié)點(diǎn)變量之間的相互轉(zhuǎn)換,并且使得所有節(jié)點(diǎn)變量都可直接用簡(jiǎn)單的加法進(jìn)行更新,因此在更新切線剛度矩陣時(shí)可以提高單元的計(jì)算效率。不同于現(xiàn)有的其他協(xié)同轉(zhuǎn)動(dòng)法,本單元的切線剛度矩陣可以通過(guò)計(jì)算能量混合泛函對(duì)節(jié)點(diǎn)變量的二次微分得到,且其微分次序是可以互換的,從而得到的單元切線剛度矩陣是對(duì)稱的。在分析復(fù)合材料層合板殼結(jié)構(gòu)中的小應(yīng)變、大轉(zhuǎn)動(dòng)問(wèn)題時(shí),采用基于協(xié)同轉(zhuǎn)動(dòng)框架,結(jié)合一階剪切變形理論的單元公式具有很好的計(jì)算性能。閉鎖問(wèn)題會(huì)影響單元的計(jì)算精度與效率,為了減其不利影響,本文采用將降階積分法得到的假定應(yīng)變?nèi)〈鷨卧獎(jiǎng)菽芊汉械哪?yīng)變和剪切應(yīng)變的假定應(yīng)變法來(lái)改善有限單元的計(jì)算效率。在非線性增量計(jì)算過(guò)程中,本文采用了廣義位移控制法跟蹤結(jié)構(gòu)屈曲后的非線性平衡路徑。最后通過(guò)對(duì)一些經(jīng)典復(fù)合材料板殼問(wèn)題的結(jié)構(gòu)分析來(lái)驗(yàn)證該單元具有令人滿意的可靠性、收斂性及計(jì)算效率。
[Abstract]:In this paper, a novel cooperative rotating quadrilateral composite shell element is developed. The cooperative rotation method uses a local coordinate system which rotates with the rotation of the rigid body of the element and is defined by the bisection line of two diagonal angles of the quadrilateral, and only considers the effect of element deformation when calculating the element node variables. Therefore, the element calculation formula in local coordinate system is simplified under the condition that rigid body displacement is excluded. The vector rotation variable greatly simplifies the conversion between the local node variable and the global node variable of the unit, and makes all the node variables can be updated directly by simple addition. Therefore, the computational efficiency of the element can be improved when updating the tangent stiffness matrix. Unlike other cooperative rotation methods, the tangent stiffness matrix of the element can be obtained by calculating the quadratic differential of the energy mixing functional to the nodal variables, and its differential order is interchangeable. The element tangent stiffness matrix obtained is symmetric. In the analysis of small strain and large rotation problem in laminated composite laminated plate and shell structure, the element formula based on cooperative rotation frame and the first order shear deformation theory has good computational performance. The locking problem will affect the calculation accuracy and efficiency of the unit, in order to reduce its adverse effects, In order to improve the computational efficiency of finite elements, the assumed strain method obtained by the reduced order integration method is used to replace the membrane strain and the shear strain in the potential energy functional of the element. In the process of nonlinear incremental calculation, the generalized displacement control method is used to track the nonlinear equilibrium path after buckling. Finally, through the structural analysis of some classical composite plate and shell problems, it is proved that the element has satisfactory reliability, convergence and computational efficiency.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TU599

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本文編號(hào)：2303448