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In this paper, we formulate the problem of elastodynamic transformation cloaking for Kirchoff-Love plates and elastic plates with both in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value prob...
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In this paper, we formulate the problem of elastodynamic transformation cloaking for Kirchoff-Love plates and elastic plates with both in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic plate (virtual problem) to that of an anisotropic and inhomogeneous elastic plate with a hole surrounded by a cloak that is to be designed (physical problem). For Kirchoff-Love plates, the governing equation of the virtual plate is transformed to that of the physical plate up to an unknown scalar field. In doing so, one finds the initial stress and the initial tangential body force for the physical plate, along with a set of constraints that we call the cloaking compatibility equations. It is noted that the cloaking map needs to satisfy certain boundary and continuity conditions on the outer boundary of the cloak and the surface of the hole. In particular, the cloaking map needs to fix the outer boundary of the cloak up to the third order. Assuming a generic radial cloaking map, we show that cloaking a circular hole in Kirchoff-Love plates is not possible; the cloaking compatibility equations and the boundary conditions are the obstruction to cloaking. Next, relaxing the pure bending assumption, the transformation cloaking problem of an elastic plate in the presence of in-plane and out-of-plane displacements is formulated. In this case, there are two sets of governing equations that need to be simultaneously transformed under a cloaking map. We show that cloaking a circular hole is not possible for a general radial cloaking map; similar to Kirchoff-Love plates, the cloaking compatibility equations and the boundary conditions obstruct transformation cloaking. Our analysis suggests that the path forward for cloaking flexural waves in plates is approximate cloaking formulated as an optimal design problem.
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Using large scale molecular dynamics simulations we investigate the properties of the nonaffine displacement field induced by macroscopic uniaxial deformation of amorphous silica, a strong glass according to Angell's classificatio...
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Using large scale molecular dynamics simulations we investigate the properties of the nonaffine displacement field induced by macroscopic uniaxial deformation of amorphous silica, a strong glass according to Angell's classification. We demonstrate the existence of a length scale ξ characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "boson-peak" anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than ξ where classical continuum elasticity becomes simply unapplicable.
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Born stability criteria were employed in the framework of extended generalised exponential potential to calculate the theoretical strength and range of stability of a perfect uniaxially stressed crystal lattice of group IV bcc met...
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Born stability criteria were employed in the framework of extended generalised exponential potential to calculate the theoretical strength and range of stability of a perfect uniaxially stressed crystal lattice of group IV bcc metals: titanium, zirconium, and hafnium. The analysis depicts two ranges of stability, a bcc phase and a body centered tetragonal phase. The computed value of theoretical strength and strain of bcc Ti, Zr and Hf agree satisfactorily with the experimentol limits. The second-order elastic constants C_(11) and C_(12) were also computed.
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Molecular simulations, when they are used to understand properties characterizing the mechanical strength of solid materials, such as stress-strain relation or Born stability criterion, by using elastic constants, are sometimes se...
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Molecular simulations, when they are used to understand properties characterizing the mechanical strength of solid materials, such as stress-strain relation or Born stability criterion, by using elastic constants, are sometimes seriously time consuming. In order to resolve this problem, we propose an efficient simulation approach under constant external stress and temperature, modifying Parrinello-Rahman (PR) method using useful sampling techniques developed recently—massive Nose-Hoover chain method and hybrid -Monte Carlo method. Test calculations on the Ni crystal employing the embedded atom method have shown that our method greatly improved the efficiency in sampling the elastic properties compared with the conventional PR method.
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In this paper, we present simple empirical relations for the calculation of mechanical properties such as bulk modulus (B) and microhardness (H) of a~I b~(III) C_2~(VI) and a~(II) b~(IV) C_2~V chalcopyrite semiconductors. Therefor...
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In this paper, we present simple empirical relations for the calculation of mechanical properties such as bulk modulus (B) and microhardness (H) of a~I b~(III) C_2~(VI) and a~(II) b~(IV) C_2~V chalcopyrite semiconductors. Therefore, it has been shown that bulk modulus of these compounds can be evaluated by using two parameters i.e. average inter-atomic distance and melting temperature rather than a number of parameters and constants as used by previous workers so far. On the basis of this result a simple bulk modulus-microhardness relationship is proposed and used to estimate the microhardness of these semiconductors. The results obtained by the proposed approach are in close agreement with the experimental data and shows a systematic trend.
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The paper examines econometric relationship between electricty consumption and variables like, income, price of electricity and diesel (used in for captive power generation to meet the shortages), and reliability of power supply f...
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The paper examines econometric relationship between electricty consumption and variables like, income, price of electricity and diesel (used in for captive power generation to meet the shortages), and reliability of power supply from utilities in five major consumer categories in India. These categories are, residential, commercial, agriculture, small and medium industries, and large industries. Income and price elasticities of electricty consumption are estimated at the natioanl level for these consumers by pooling data across 19 states spread over 9 years (1985/86-1993/94). The results show that electricity consumption in commercial and large industrial sectors are income elastic (>1), while residential, agricultural and small and medium industries are income inelastic (<1). The short-run price elasticities vary from -1.35 in agriculture, -0.65 in residential, -0.45 in large industry, -0.26 in commercial and insignficant in small and medium industry. Total power shortages from utilities affect most the commercial sector foolowed by the residential sector.
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The elastic constants c_(11) and c_(44) of single-crystal NaCl-structure δ-TiN_x(001) layers, with x ranging from 0.67 to 1.0, were determined using sound velocity measurements. Picosecond ultrasonic optical pump/probe techniques...
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The elastic constants c_(11) and c_(44) of single-crystal NaCl-structure δ-TiN_x(001) layers, with x ranging from 0.67 to 1.0, were determined using sound velocity measurements. Picosecond ultrasonic optical pump/probe techniques were employed to generate and detect longitudinal sound waves and surface acoustic waves (SAW) in order to obtain c_(11)(x) and c_(44)(x), respectively. SAW generation was achieved by depositing a periodic series of Al bars on the TiN_x(001) layers to spatially modulate the surface reflectivity. c_(11) and c_(44) were found to decrease continuously from 626 and 156 GPa with x=1 to 439 and 92 GPa with x=0.67. The Voit-Reuss-Hill average aggregate elastic moduli E_(VRH)(x) obtained from our measured c_(11)(x) and c_(44)(x) values are in good agreement with previous TiN_x(001) nanoindentation results.
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In this paper we present a theoretical analysis of the effect of magnetostriction on quantum oscillations of elastic constants in metals under strong magnetic fields. It is shown that at low temperatures a significant softening of...
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In this paper we present a theoretical analysis of the effect of magnetostriction on quantum oscillations of elastic constants in metals under strong magnetic fields. It is shown that at low temperatures a significant softening of some acoustic modes could occur near peaks of quantum oscillations of the electron density of states at the Fermi surface. This effect is caused by the Condon magnetic instability, and it can give rise to a lattice instability. We show that the most favorable conditions for this instability to be revealed occur in metals whose Fermi surfaces include nearly cylindrical segments.
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We measured zirconium tungstate's elastic constants C_(ij). This compound shows relatively soft, nearly isotropic elastic constants with normal Poisson ratios and no approach to Born instability. ZrW_2O_8 shows normal ambient-temp...
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We measured zirconium tungstate's elastic constants C_(ij). This compound shows relatively soft, nearly isotropic elastic constants with normal Poisson ratios and no approach to Born instability. ZrW_2O_8 shows normal ambient-temperature elastic constants C_(ij), but remarkable dC_(ij) / dT that show dominant low-frequency acoustic-vibration modes. From the bulk modulus, we estimated the total ambient-temperature thermodynamic Grueneisen parameter as γ = -1.2. The dB/dT slope gives a Grueneisen parameter γ = - 7. The 300-0 K bulk-modulus increase (40%) seems unprecedented and breaks Birch's law of corresponding states.
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Sectoral heterogeneity has been shown to affect country-level welfare gains from trade (measured by costs of autarky) that can be calculated by sector-specific trade elasticities and home expenditure shares. However, empirical ana...
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Sectoral heterogeneity has been shown to affect country-level welfare gains from trade (measured by costs of autarky) that can be calculated by sector-specific trade elasticities and home expenditure shares. However, empirical analyses of multi-sector models are restricted to a limited number of countries and sectors, mostly due to the lack of data on sector-specific home expenditure shares. This paper first proposes a solution to this limitation by changing the way that foreign products are aggregated at the destination country, where 'unbiased' multi-sector welfare gains can be captured by using country-specific trade elasticity measures. Second, the restrictive assumption of unitary importer-income elasticity is relaxed, and it is shown that the trade elasticity in the calculation of welfare gains is replaced by the newly-introduced welfare elasticity, a function of trade and income elasticities. Empirical evidence suggests that equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.
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