采用张量列式的无“自锁”4节点杂交/混合板单元

A Free Locking 4-Node Hybrid/ Mixed Plate Element by Tensorial Formulation

从中厚板的泛函 ΠRP 出发 ,放松了剪切应变、转角和挠度约束 ,建立了一个多变量泛函 ΠRS ,引入了剪力作为变量。然后使用张量插值列式 ,可导出剪应变场 ,利用张量的不变性有助于识别零能模式 ,由“一一对应”原则选择剪力插值函数。由此 ,构造出一个无剪切“自锁”、性能优良的杂交 /混合单元。

A multi-variate functional П RS is derived from plate functional П RP by relaxing the constraint between shear strain, rotation and deflection, with shear force introduced as a variate. Then, by tensorial interpolation formulation, the shear strain field can be derived. Making use of the invariance property of tensor, disadvantages due to coordinate transformation are avoided, thus helpful to identify the zero energy modes. By expressing the shear strain in tensorial form, proper selection of optimal shear force interpolating function is successfully achieved on the basis of “one stress parameter per one deformation mode'. Thus, an efficient free shear locking 4-node hybrid/mixed plate element is constructed. Numerical examination reveals remarkable characteristics of Prs against the existing counterparts.