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发展了一种新型3节点三边形壳单元。计算单元在局部坐标系下的节点变量时,通过采用协同转动法,预先扣除节点整体变量中的刚体转动成分,从而简化了单元的计算公式。不同于现有的其他协同转动单元,在该单元中采用了增量可以直接累加的矢量型转动变量,单元的切线刚度矩阵可以通过直接计算能量泛函对节点变量的二阶偏微分得到,且对节点变量的偏微分次序是可以互换的,因而在局部和整体坐标系下都得到了对称的单元切线刚度矩阵。为消除单元中可能出现的闭锁现象,引入了Mac Neal提出的线积分法,分别用沿单元边线方向的膜应变和剪切应变构造新的假定应变场。最后,通过对几个产生了大位移与大转角变形的板壳问题进行分析,检验了该单元的可靠性、计算精度和计算效率。
A new 3-node triangular shell element has been developed. When calculating the node variables in the local coordinate system, by using the method of coordinated rotation, the rigid body rotation components in the overall variables of the nodes are deducted in advance, which simplifies the calculation formula of the unit. Different from other existing co-rotating units, a vector-type rotating variable with increment can be added directly in this unit. The element tangent stiffness matrix can be obtained by directly calculating the energy functional of the second-order partial differential of node variables, and The partial differential order of node variables is interchangeable, so symmetric unit tangent stiffness matrix is obtained in both local and global coordinates. In order to eliminate the possible occlusion phenomenon in the cell, a line integral method proposed by Mac Neal was introduced, and a new assumed strain field was constructed by using film strain and shear strain along the edge of the unit. Finally, several panel shells with large displacement and large corner deformation were analyzed to verify the reliability, accuracy and efficiency of the unit.