Application of non-conforming element in lower-bound shakedown analysis of composites

With the combination of homogenization theory and strain approach, limit and shakedown analysis of composites is investigated on the microscopic level by using stress function method. The admissible 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 mathematical 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.