One of the defining properties of thin shell problems is that the solution can be viewed as a linear combination of local features, each with its own characteristic thickness-dependent length scale. ...For perforated shells it is thus possible that for the given dimensionless thickness, the local features dominate, and the problem of deriving effective material parameters becomes ill-posed. In the general case, one has to account for many different aspects of the problem that directly affect the effective material parameters. Through a computational study we derive a conjecture for the admissible thickness-ranges. The effective material parameters are derived with a minimisation process over a set of feasible instances. The efficacy of the conjecture and the minimisation process is demonstrated with an extensive set of numerical experiments.
•Perforated shells have a characteristic critical thickness.•Homogenisation fails if the dimensionless thickness is below the critical value.•Shell geometry has an effect on homogenisation even if all other features remain constant.
A top–down strategy based on the second-order asymptotic method is proposed for solving the Steklov eigenvalue problems on composite perforated materials with three-scale and two-periodic structures. ...Three different kinds of configurations are considered where the cavities are distributed only in the meso-scale, micro-scale, and both-scale representative cells respectively. Firstly, the second-order two-scale asymptotic expansion is performed between the macroscopic and the mesoscopic scale. Then, the second-order two-scale analysis is further developed on the mesoscopic cell functions at the microscopic level. While the asymptotic expansions of the first-order mesoscopic cell functions are similar for the three cases, the expansions of the second-order mesoscopic cell functions are distinguished from each other. It is interesting that when the holes with different scales are considered for the third case, the cell functions defined on the mesoscopic scale are dependent explicitly on the ratio between the mesoscopic and microscopic periods after homogenization. The three-scale asymptotic expansions of the eigenvalues are derived based on the "corrector equations" in a uniform manner and calculated in the integration form. The multi-scale finite element procedures are established based on these proposed asymptotic models and both the two- and three-dimensional asymptotic computations are carried out. By comparing the asymptotic computations with the classic finite element algorithm, it is demonstrated that this second-order three-scale asymptotic algorithm is effective in approximating the Steklov eigenvalues and reproducing the local oscillations of the eigenfunctions with less computational cost and the convergence of the second-order solutions are also confirmed. It is also instructive that when the parameters existing on the cavity boundaries are considered in the perforated materials, the second-order expansion terms should be included in the multi-scale analysis to reflect the asymptotic behavior of the structures correctly.
This work presents an approach to evaluate axially compressed metallic foams with the presence of holes on the structure further than foam voids. Adding holes, the total material weight is decreased ...but the stiffness is not linearly reduced. The stress-strain characterization is investigated and presented considering the number, size, and thickness of rectangular holes. The characterization uses representative volume elements to decompose the foam into fundamental portions. Symmetries, boundary conditions and homogenization principles are combined in a formulation in terms of parameters describing the holes, resulting in a parametric characterization. Examples are presented where the influence of holes is analyzed.
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Dostopno za:
BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
High performance is reported for a symmetric ultracapacitor (UC) cell made up of hierarchically perforated graphene nanosheets (HPGN) as an electrode material with excellent values of energy density ...(68.43 Wh kg−1) and power density (36.31 kW kg−1). Perforations are incorporated in the graphite oxide (GO) and graphene system at room temperature by using silica nanoparticles as template. The symmetric HPGN‐based UC cell exhibits excellent specific capacitance (Cs) of 492 F g−1 at 0.1 A g−1 and 200 F g−1 at 20 A g−1 in 1M H2SO4 electrolyte. This performance is further highlighted by galvanostatic charge–discharge study at 2 A g−1 over a large number (1000) of cycles exhibiting 93% retention of the initial Cs. These property features are far superior as compared to those of symmetric UC cells made up of only graphene nanosheets (GNs), i.e. graphene sheets without perforations. The latter exhibit Cs of only 158 F g−1 at 0.1 A g−1 and the cells is not stable at high current density.
A high specific capacitance (Cs) value is obtained for a symmetric ultracapacitor (UC) cell in 1 M H2SO4 electrolyte by using hierarchically nanoperforated graphene nanosheets (HPGN) as an electrode material. Nanoperforations are introduced in graphene by simple stirring in silica nanoparticle dispersion followed by HF treatment. The HPGN is shown to deliver a remarkably high energy density (68.43 Wh kg−1) as compared to earlier reports for graphene‐based materials.
This paper presents a numerical method for modeling the micromechanical behavior and macroscopic properties of fiber-reinforced composites and perforated materials. The material is modeled by a ...finite rectangular domain containing multiple circular holes and elastic inclusions. The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series. The analytical solution for the complementary problem of a circular domain containing holes and inclusions is obtained by using a combination of the series expansion technique with a direct boundary integral method. The boundary conditions on the physical external boundary are satisfied by adopting an overspecification technique based on a least squares approximation. All of the integrals arising in the method can be evaluated analytically. As a result, the elastic fields and effective properties can be expressed explicitly in terms of the coefficients in the series expansions. Several numerical experiments are conducted to verify the accuracy and efficiency of the numerical method and to demonstrate its application in determination of the macroscopic properties of composite materials.
We consider a fracture mechanics problem for heat-releasing isotropic material weakened by a doubly periodic system of identical cylindrical channels of circular cross section. It is considered that ...as the intensity of heat release increases in the material, its elastic properties become temperature dependent and failure of the material occurs. It is accepted that rectilinear cracks with bonds between the faces at the end zones originate from the surface of holes. The condition of limit equilibrium of a crack with end zone is formulated with regard to criterion of ultimate stretching of material’s bonds.
The problem of modeling of the mechanism of a warmth transfer through sites which are located around a seam in clothes of a special purpose are considered and formalized. The mathematical dependence, ...reflecting temperature and heat flux density changes in an internal surface of the integrity of the sites which are located round a seam in protective clothes in the conditions of non-stationary heat conductivity is presented. The generalized model is received which allows to simulate, and consistently reproduce process of heating and to determine temperature and a heat flux density on an internal surface of the multilayered metallized material at any moment of time. Adequacy to the received mathematical model is confirmed experimentally.
The work devoted to improvement of manufacturing techniques of special protective clothes from the metallized materials on the basis of fiber glass. On the basis of mathematical modeling of a heat ...transfer through the punched top material sites in the conditions of non-stationary heat conductivity technological support of process of production of heat-shielding suits of firefighters which allows to form qualitative, reliable knots and connections of details of clothes is developed. Pilot studies of the thermotight and strengthened connections of details of clothes proved efficiency of application of new technology and the equipment.
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