2005
DOI: 10.1002/nme.1547
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A non‐linear programming approach to kinematic shakedown analysis of composite materials

Abstract: SUMMARYUsing a Representative volume element (RVE) to represent the microstructure of periodic composite materials, this paper develops a non-linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads. The shakedown analysis is performed using homogenization theory and the displacement-based finite element method. With the aid of homogenization theory, the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites.… Show more

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Cited by 10 publications
(1 citation statement)
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“…This was studied further by Collins and Cliffe (1987) in conjunction with kinematic upper bounds for the shakedown limit. The finite element method, in tandem with linear and nonlinear programming techniques, has also been used to compute shakedown limits numerically (see, e.g., Shiau, 2001;Boulbibane and Ponter, 2006;Li and Yu, 2006). When applying Melan's theorem to cohesive-frictional materials, however, considerable confusion exists that may give rise to inaccurate and inconsistent predictions of the shakedown limit.…”
Section: Introductionmentioning
confidence: 98%
“…This was studied further by Collins and Cliffe (1987) in conjunction with kinematic upper bounds for the shakedown limit. The finite element method, in tandem with linear and nonlinear programming techniques, has also been used to compute shakedown limits numerically (see, e.g., Shiau, 2001;Boulbibane and Ponter, 2006;Li and Yu, 2006). When applying Melan's theorem to cohesive-frictional materials, however, considerable confusion exists that may give rise to inaccurate and inconsistent predictions of the shakedown limit.…”
Section: Introductionmentioning
confidence: 98%