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This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.
The purpose of this study was to investigate whether sprint performance is related to lower leg musculoskeletal geometry within a homogeneous group of highly trained 100-m sprinters. Using a cluster analysis, eighteen male sprinters were divided into two groups based on their personal best (fast: N = 11, 10.30 ± 0.07 s; slow: N = 7, 10.70 ± 0.08 s). Calf muscular fascicle arrangement and Achilles tendon moment arms (calculated by the gradient of tendon excursion versus ankle joint angle) were analyzed for each athlete using ultrasonography. Achilles tendon moment arm, foot and ankle skeletal geometry, fascicle arrangement as well as the ratio of fascicle length to Achilles tendon moment arm showed no significant (p > 0.05) correlation with sprint performance, nor were there any differences in the analyzed musculoskeletal parameters between the fast and slow sprinter group. Our findings provide evidence that differences in sprint ability in world-class athletes are not a result of differences in the geometrical design of the lower leg even when considering both skeletal and muscular components.