SUMMARYNon-probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non-probabilistic convex modeling. However, the former can only deal with independent variables, while the latter can only deal with dependent variables. This paper presents a more general non-probabilistic convex model, the multidimensional parallelepiped model. This model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex 'multi-source uncertainty' problems in which dependent variables and independent variables coexist. For any two parameters, the concepts of the correlation angle and the correlation coefficient are defined. Through the marginal intervals of all the parameters and also their correlation coefficients, a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters. Through the introduction of affine coordinates, the parallelepiped model in the original parameter space is converted to an interval model in the affine space, thus greatly facilitating subsequent structural uncertainty analysis. The parallelepiped model is applied to structural uncertainty propagation analysis, and the response interval of the structure is obtained in the case of uncertain initial parameters. Finally, the method described in this paper was applied to several numerical examples.
The excellent mechanical properties of graphene have enabled it as appealing candidate in the field of impact protection or protective shield. By considering a monolayer graphene membrane, in this work, we assessed its deformation mechanisms under hypervelocity impact (from 2 to 6 km/s), based on a serial of in silico studies. It is found that the cracks are formed preferentially in the zigzag directions which are consistent with that observed from tensile deformation. Specifically, the boundary condition is found to exert an obvious influence on the stress distribution and transmission during the impact process, which eventually influences the penetration energy and crack growth. For similar sample size, the circular shape graphene possesses the best impact resistance, followed by hexagonal graphene membrane. Moreover, it is found the failure shape of graphene membrane has a strong relationship with the initial kinetic energy of the projectile. The higher kinetic energy, the more number the cracks. This study provides a fundamental understanding of the deformation mechanisms of monolayer graphene under impact, which is crucial in order to facilitate their emerging future applications for impact protection, such as protective shield from orbital debris for spacecraft.
Balaenid whales, as continuous ram filter feeders, can efficiently separate prey from water by baleen. The feeding process of balaenid whales is extremely complex, in which the flow distribution and pressure drop in the oral cavity play a significant role. In this paper, a theoretical model coupled with oral cavity velocity and pressure in balaenid whales is established based on mass conservation, momentum conservation and pressure drop equations, considering both the inertial and the friction terms. A discrete method with section-by-section calculation is adopted to solve the theoretical model. The effects of four crucial parameters, i.e. the ratio of filtration area to inlet area (S), the Reynolds number of entrance (Re in ), the ratio of thickness to permeability of the porous media formed by the fringe layer (φ) and the width ratio of the anteroposterior canal within the mouth along the tongue (APT channel) to that along the lip (APL channel) (H) are discussed. The results show that, for a given case, the flow distribution and the pressure drop both show increasing trends with the flow direction. For different cases, when S is small, Re in is small and φ is large, a good flow pattern emerges with a smoother flow speed near the oropharynx, better drainage, better shunting and filtration, and higher energy efficiency. However, for smaller values of H, some energy efficiency is sacrificed to achieve additional average transverse flow in order to produce better shunting and filtration. The research in this paper provides a reference for the design of high-efficiency bionic filters.
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