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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ReisnerMindlin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.
An arbitrary four-node hybrid/hybrid shallow shell finite element was established. Based on the principle of numerical performance optimization, the energy compatibility conditions of the non-coordinated model are introduced, the initial stress of the element is optimized, the non-coordinated displacement field is rationally selected, and the expression is simplified by the functional. The unit considers the transverse shearing effect and approximates the ReisnerMindlin plate theory, which is suitable for medium-thickness flat shells. The numerical study shows that the unit meets the patch test, does not contain the excess zero energy mode, has high precision, is insensitive to elemental distortion, and does not exhibit “self-locking” phenomenon when the thickness approaches the limit, and the bending moment-displacement response is good.