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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 physically coupled finite element method (FEM) model is developed to study the response behavior of a calorimetric gas sensor. The modeled sensor serves as a monitoring device of the concentration of gaseous hydrogen peroxide (H2 O2) in a high temperature mixture stream in aseptic sterilization processes. The principle of operation of a calorimetric H2 O2 sensor is analyzed and the results of the numerical model have been validated by using previously published sensor experiments. The deviation in the results between the FEM model and experimental data are presented and discussed.
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.
Using results from an 8 m2 instrumented force plate we describe field measurements of normal and shear stresses, and fluid pore pressure for a debris flow. The flow depth increased from 0.1 to 1 m within the first 12 s of flow front arrival, remained relatively constant until 100 s, and then gradually decreased to 0.5 m by 600 s. Normal and shear stresses and pore fluid pressure varied in-phase with the flow depth. Calculated bulk densities are ρb = 2000–2250 kg m−3 for the bulk flow and ρf = 1600–1750 kg m−3 for the fluid phase. The ratio of effective normal stress to shear stress yields a Coulomb basal friction angle of ϕ = 26° at the flow front. We did not find a strong correlation between the degree of agitation in the flow, estimated using the signal from a geophone on the force plate, and an assumed dynamic pore fluid pressure. Our data support the idea that excess pore-fluid pressures are long lived in debris flows and therefore contribute to their unusual mobility.
A field-effect biosensor employing tobacco mosaic virus (TMV) particles as scaffolds for enzyme immobilization is presented. Nanotubular TMV scaffolds allow a dense immobilization of precisely positioned enzymes with retained activity. To demonstrate feasibility of this new strategy, a penicillin sensor has been developed by coupling a penicillinase with virus particles as a model system. The developed field-effect penicillin biosensor consists of an Al-p-Si-SiO₂-Ta₂O₅-TMV structure and has been electrochemically characterized in buffer solutions containing different concentrations of penicillin G. In addition, the morphology of the biosensor surface with virus particles was characterized by scanning electron microscopy and atomic force microscopy methods. The sensors possessed a high penicillin sensitivity of ~ 92 mV/dec in a nearly-linear range from 0.1 mM to 10 mM, and a low detection limit of about 50 µM. The long-term stability of the penicillin biosensor was periodically tested over a time period of about one year without any significant loss of sensitivity. The biosensor has also been successfully applied for penicillin detection in bovine milk samples.