改进的非协调广义混合单元及性能分析

Improved Noncompatible Generalized Mixed Elements and Performance Analysis

非协调广义混合单元最突出的特点是避免了传统混合单元中系数矩阵主对角线上存在零元素的问题,因此位移和应力结果的收敛是稳定的.以最小势能原理和H-R变分原理为基础,联合增强假设应变理论建立了新的8结点非协调广义混合单元.一方面,该单元保持了已有非协调广义混合单元的全部优点;另一方面,该单元简化了积分计算.数值实例表明,改进的非协调广义混合单元的数值结果精度高,计算速度快并且对单元的几何扭曲敏感度低.

The coefficient matrix of traditional mixed elements has zero values on the principle diagonal. The most prominent feature of noncompatible generalized mixed elements is that they avoid this problem. Thus, the convergences of the displacement and the stress are stable. Combined with the enhanced assumed strain (EAS) method, a new type of 8-node noncompatible generalized mixed elements was established based on the minimum potential energy principle and the H-R variational principle. The element retains all the advantages of existing noncompatible generalized mixed elements. Meanwhile, the integral calculation is more simple. Numerical examples show that, the improved noncompatible generalized mixed element gives highly accurate results, and has a faster computation speed and less sensitivity to the geometric distortions.