四节点中厚扁壳杂交优化应力元

建立了一种任意形状的四节点杂交/混合扁壳有限元。基于数值性能优化原理，引入非协调模型的能量相容条件，对单元初始应力进行优化，合理地选择非协调位移场，通过简化泛函进行列式。单元考虑了横向剪切效应，近似采用了Reissner-Mindlin板理论，适用于中厚扁壳。数值研究表明，单元满足分片检验，不含多余零能模式，精度高，对单元畸变不敏感，厚度趋于极限时不出现“自锁”现象，且弯矩-位移响应良好。

A 4 Node Moderate Shallow Shell Hybrid Optimized Stress Finite Element

An arbitrary shallow shell hybrid/mixed finite element with 4 node is developed. Based on the optimization principle of numerical property, an energy compatible condition is introduced and an optimization is given to the initial stress terms. The finite element equations are derived by simplifying Hellinger Reissner functional and carefully choosing appropriate incompatible displacement field. Taking account of transverse shear and according to Reissner Mindlin plate theory, the element can be used for moderate thick and thin shell. Numerical study demonstrates that the patch test is passed. Superfluous zero energy deformation modes and shear locking in thin plate limit are free. The accuracy is good.