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The structure of the female pelvic floor (PF) is an inter-related system of bony pelvis,muscles, pelvic organs, fascias, ligaments, and nerves with multiple functions. Mechanically, thepelvic organ support system are of two types: (I) supporting system of the levator ani (LA) muscle,and (II) the suspension system of the endopelvic fascia condensation [1], [2]. Significantdenervation injury to the pelvic musculature, depolimerization of the collagen fibrils of the softvaginal hammock, cervical ring and ligaments during pregnancy and vaginal delivery weakens thenormal functions of the pelvic floor. Pelvic organ prolapse, incontinence, sexual dysfunction aresome of the dysfunctions which increases progressively with age and menopause due toweakened support system according to the Integral theory [3]. An improved 3D finite elementmodel of the female pelvic floor as shown in Fig. 1 is constructed that: (I) considers the realisticsupport of the organs to the pelvic side walls, (II) employs the improvement of our previous FEmodel [4], [5] along with the patient based geometries, (III) incorporates the realistic anatomy andboundary conditions of the endopelvic (pubocervical and rectovaginal) fascia, and (IV) considersvarying stiffness of the endopelvic fascia in the craniocaudal direction [3]. Several computationsare carried out on the presented computational model with healthy and damaged supportingtissues, and comparisons are made to understand the physiopathology of the female PF disorders.
This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
FEM shakedown analysis of structures under random strength with chance constrained programming
(2022)
Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play a significant role in mechanical and civil engineering design. The concept of direct methods aims to determine the ultimate load carrying capacity of structures beyond the elastic range. In practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and constraints. If strength and loading are random quantities, the shakedown analysis can be formulated as stochastic programming problem. In this paper, a method called chance constrained programming is presented, which is an effective method of stochastic programming to solve shakedown analysis problems under random conditions of strength. In this study, the loading is deterministic, and the strength is a normally or lognormally distributed variable.
A new formulation to calculate the shakedown limit load of Kirchhoff plates under stochastic conditions of strength is developed. Direct structural reliability design by chance con-strained programming is based on the prescribed failure probabilities, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem. We restrict uncertainty to strength, the loading is still deterministic. A new formulation is derived in case of random strength with lognormal distribution. Upper bound and lower bound shakedown load factors are calculated simultaneously by a dual algorithm.
Diese Studie beschäftigte sich mit der Dämpfungswirkung von Schienbeinschonern, wie sie beim Fußball zum Einsatz kommen. Sie wurde mit Hilfe eines Pendelhammers durchgeführt, der verschiedene Aufschlagkräfte auf die Schoner ermöglichte. Dabei wurde deutlich, dass Schienbeinschoner die beste Wirkung bei Maximalkräften unterhalb von 5kN erreichen können, dass bei größerer Belastung allerdings Verbesserungsbedarf besteht. Hierfür konnte, u.a. durch den Einsatz neuer Materialien, ein guter Ansatzpunkt im „adäquaten Zusammenspiel von Schale und Polsterung“ der Schoner gefunden werden. Die Untersuchung hat weiterhin gezeigt, dass zumindest teilweise eine deutliche Verbesserung der Dämpfungswirkung der Schienbeinschoner in den letzten Jahren erreicht werden konnte.