新型协同转动四节点四边形复合材料壳单元
发布时间：2018-10-31 20:31
【摘要】：本文发展了一种新型协同转动四节点四边形复合材料壳单元。协同转动法采用了随单元刚体转动而一起旋转的,并由四边形两个对角线夹角的平分线定义的局部坐标系,并在计算单元节点变量时仅考虑单元变形的影响,故而在排除刚体位移的情况下简化了局部坐标系下的单元计算公式。采用的矢量型转动变量则大大简化了单元的局部节点变量与整体节点变量之间的相互转换,并且使得所有节点变量都可直接用简单的加法进行更新,因此在更新切线刚度矩阵时可以提高单元的计算效率。不同于现有的其他协同转动法,本单元的切线刚度矩阵可以通过计算能量混合泛函对节点变量的二次微分得到,且其微分次序是可以互换的,从而得到的单元切线刚度矩阵是对称的。在分析复合材料层合板壳结构中的小应变、大转动问题时,采用基于协同转动框架,结合一阶剪切变形理论的单元公式具有很好的计算性能。闭锁问题会影响单元的计算精度与效率,为了减其不利影响,本文采用将降阶积分法得到的假定应变取代单元势能泛函中的膜应变和剪切应变的假定应变法来改善有限单元的计算效率。在非线性增量计算过程中,本文采用了广义位移控制法跟踪结构屈曲后的非线性平衡路径。最后通过对一些经典复合材料板壳问题的结构分析来验证该单元具有令人满意的可靠性、收敛性及计算效率。
[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.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU599
本文编号：2303448
[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.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU599
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