采用应力函数法，结合均匀化理论和应变法，在细观层次上研究了复合材料的极限和安定分析，获取复合材料代表性体积元在载荷加载历史未知下的容许承载域。利用8节点非协调等参元离散结构，获取弹性应力场和自平衡残余应力场，建立复合材料在细观层次上安定下限的优化格式。在满足计算精度的同时，大大降低了优化规模。以周期性纤维增强金属基复合材料为例，验证了该单元在安定下限分析中的有效性和可靠性。%With the combination of homogenization theory and strain approach, limit and shakedown anal- ysis of composites is investigated on the microscopic level by using stress function method. The admissi- ble loading domain of representative volume element can be obtained under the unknown loading history. An eight node non-conforming isoparametric finite element is used to discritize the physical model, and the self-equilibrated residual stresses as well as the local stresses are obtained to establish the mathemat- ical programming of lower-bound shakedown problem. The application of non-conforming element not only achieves the qualified accuracy as the second order element, but also reduces the computational scale. Limit and shakedown analysis of fiber reinforced metal matrix periodic composites is done to prove the validity and reliability of application of the non-conforming element.
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