In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3)...In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.展开更多
The most critical issue in the steel catenary riser design is to evaluate the fatigue damage in the touchdown zone accurately. Appropriate modeling of the riser-soil resistance in the touchdown zone can lead to signif...The most critical issue in the steel catenary riser design is to evaluate the fatigue damage in the touchdown zone accurately. Appropriate modeling of the riser-soil resistance in the touchdown zone can lead to significant cost reduction by optimizing design. This paper presents a plasticity model that can be applied to numerically simulate riser-soil interaction and evaluate dynamic responses and the fatigue damage of a steel catenary riser in the touchdown zone. Utilizing the model, numerous riser-soil elements are attached to the steel catenary riser finite elements, in which each simulates local foundation restraint along the riser touchdown zone. The riser-soil interaction plasticity model accounts for the behavior within an allowable combined loading surface. The model will be represented in this paper, allowing simple numerical implementation. More importantly, it can be incorporated within the structural analysis of a steel catenary riser with the finite element method. The applicability of the model is interpreted theoretically and the results are shown through application to an offshore 8.625 steel catenary riser example. The fatigue analysis results of the liner elastic riser-soil model are also shown. According to the comparison results of the two models, the fatigue life analysis results of the plasticity framework are reasonable and the horizontal effects of the riser-soil interaction can be included.展开更多
文摘In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.
文摘The most critical issue in the steel catenary riser design is to evaluate the fatigue damage in the touchdown zone accurately. Appropriate modeling of the riser-soil resistance in the touchdown zone can lead to significant cost reduction by optimizing design. This paper presents a plasticity model that can be applied to numerically simulate riser-soil interaction and evaluate dynamic responses and the fatigue damage of a steel catenary riser in the touchdown zone. Utilizing the model, numerous riser-soil elements are attached to the steel catenary riser finite elements, in which each simulates local foundation restraint along the riser touchdown zone. The riser-soil interaction plasticity model accounts for the behavior within an allowable combined loading surface. The model will be represented in this paper, allowing simple numerical implementation. More importantly, it can be incorporated within the structural analysis of a steel catenary riser with the finite element method. The applicability of the model is interpreted theoretically and the results are shown through application to an offshore 8.625 steel catenary riser example. The fatigue analysis results of the liner elastic riser-soil model are also shown. According to the comparison results of the two models, the fatigue life analysis results of the plasticity framework are reasonable and the horizontal effects of the riser-soil interaction can be included.
