一种基于张量列式的高性能平面4节点杂交/混合单元

An Efficient 4-Node Plane Hybrid/Mixed Element with Tensorial Formulation

采用张量形式,从HellingerReissner变分原理出发,建立一种列式杂交/混合有限单元的有效方法。该方法利用了张量的不变性,剔除了坐标系转换的影响,通过应力参数与独立变形模式一一对应的方法,选择并优化应力场,由此建立高性能的杂交/混合单元。据此方法,建立了一个4节点杂交/混合单元。数值算例表明,该单元具有不变性、普适性、不含零能模式。

The paper is mainly concerned with developing a kind of tensorial formulation scheme for low order hybrid/mixed finite elements based on Hellinger Reisser variational principle. By making use of the invariance properties of tensors, the disadvantages due to coordinates transformation are totally avoided. Also, in matching the derived strain field, which is in tensorial form, a proper selection of the optimal stress field is successfully achieved on the basis of “the consistency of one stress parameter with one independent deformation mode”. Thus, a 4 node plane quadrilateral element is obtained. Numerical simulations reveal the remarkable characteristics of the present elements, such as invariance, robustness, having no zero energy, etc .