Computing the kern of a general cross-section

The ‘kern’ of a cross-section is the convex region within which any point load applied will produce stresses of the same sign as that of the load throughout the entire cross-section. Based on theorems of Mofid and Yavari [Int. J. Solids Struct. 31 (1998) 2377], an algorithm is presented that can compute the kern of any cross-section numerically. We have developed a program based on this algorithm. A few examples are solved using this program. The results are compared with those of Wilson and Turcotte [Adv. Engng Software 17 (1993) 113] and Mofid and Yavari and excellent agreement is observed.     

A study of the edge-zone equation of Mindlin-Reissner plate theory in bending of laminated rectangular plates

Summary The bending equations of the Mindlin-Reissner theory of plates laminated of transversely isotropic layers are reformulated in terms of the boundary-layer and transverse displacement functions. Analytical expressions are obtained for the primary response quantities of rectangular laminates with various boundary conditions. It is found that various edge conditions have boundary-layer effects on the primary and secondary response quantities that can be characterized as nonexistent, weak, or strong.     

A correspondence principle for fractal and classical cracks

In this paper we introduce a correspondence principle between fractal cracks and notches. This correspondence principle defines an equivalent smooth blunt crack for a fractal crack. Once this transformation is accomplished, the laws of linear elastic fracture mechanics apply. Since the root radius of the equivalent crack is finite, the crack may be further reduced to a notch visualized as an elongated elliptical void. Therefore, the laws of the LEFM and those of Neuber’s ‘notch mechanics’ coincide, and they can be used interchangeably. In other words, we have shown that the three mathematical representations of discontinuities in the displacement field, a notch, a classic Griffith crack and a fractal crack, are related, and the pertinent relationships are determined by the proposed correspondence principle. We also give an estimation of the size of the plastic region ahead of a self-similar (or self-affine) fractal crack tip.     

A hybrid CT/DT double-sampled SMASH Σ? modulator for broadband applications in 90?nm CMOS technology

In this paper, a hybrid continuous-time (CT)/discrete-time (DT) multi-stage noise shaping (MASH) sigma?Cdelta (????) modulator architecture for broadband applications is presented. The double-sampling technique is employed in the DT second-stage modulator in order to reduce the power consumption of the overall modulator. Flat and unity signal transfer functions are used in the first- and second-stage modulators, respectively, to relax the output swing of the analog building blocks without influencing the inherent anti-aliasing behavior of the first-stage CT modulator. The proposed structure is insensitive to the amplifier limited dc gain of CT stage and avoids the need of compensation for finite gain-bandwidth induced error in CT loop filter. As a design example, the proposed MASH 2-2 modulator is designed in a 90?nm CMOS technology with 1?V power supply. Circuit level simulation results with HSPICE achieve the maximum SNDR of 74.8?dB and dynamic range of 76.5?dB in 12.5?MHz bandwidth with 17?mW power consumption while operating at 200?MHz sampling rate.     

Synergy derived by combining graphene and carbon nanotubes as nanofillers in composites

Both one-dimensional carbon nanotubes as well as two-dimensional graphene sheets have been extensively investigated as nanofillers in composites. However there are very few reports on their combined use in composite materials. Here we report the mechanical properties including Young's modulus, tensile strength and fatigue properties of an epoxy polymer reinforced with various combinations of graphene and carbon nanotube fillers- i.e., nanotubes alone, graphene alone and a mixture of graphene and nanotubes. We find that at low nanofillers loadings (< 0.1% weight), the graphene fillers performed better than both singlewalled as well as multiwalled carbon nanotubes. However, interestingly it was the combination of carbon nanotubes with graphene that yielded the greatest improvement in mechanical properties. Optical microscopy of thin micro-tomed slices of the composites indicated that in the presence of the nanotubes the graphene sheets appear to have aggregated into chains forming a network structure. Such long range ordering of the nanofillers is very unusual in a nanocomposite system and is likely responsible for the enhanced mechanical properties.     

Sn<Superscript>4+</Superscript> and La<Superscript>3+</Superscript> co doped TiO<Subscript>2</Subscript> nanoparticles and their optical,photocatalytic and antibacterial properties under visible light

Sn⁴⁺ and La³⁺ co-doped TiO₂ photocatalytic material with nanoparticle structure have been successfully prepared using SnCl₂·2H₂O and La(NO₃)₃·6H₂O as precursors. Scanning electron microscopy, X-ray diffraction, transmission electron microscopy and UV–visible spectroscopy have been used to for the characterization of the morphology, crystal structure, particle size and optical properties of the samples. The photocatalytic properties of sample with various amount of La doped TiO₂ have been studied by photo degradation of methyl orange (MO) in water under visible light. XRD patterns showed both rutile and anatase phases for 5 mol% of Sn and 5–10 mol% of La. But anatase phase with a little rutile phase was formed for 5 mol%Sn and 10 mol%La. The prepared Sn and La co doped TiO₂ photo-catalyst showed optical absorption edge in the visible light area and exhibited excellent photo-catalytic ability for degradation of MO solution under visible irradiation. Antibacterial behavior towards E. coli was then studied under visible irradiation. The synthesized T-5%Sn-10%La powder exhibited superior antibacterial activity under visible irradiation compared to the pure TiO₂.     

On applications of generalized functions to the analysis of Euler–Bernoulli beam–columns with jump discontinuities

In this article some applications of the distribution theory of Schwarz to the analysis of beam–columns with various jump discontinuities are offered. The governing differential equation of an Euler–Bernoulli beam–column with jump discontinuities in flexural stiffness, displacement, and rotation, and under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam–column method is introduced. Using this method, instead of solving the differential equation of the beam–column in the space of generalized functions, another differential equation can be solved in the space of classical functions. Some examples of beam–columns and columns with various jump discontinuities are solved. Deflections of beam–columns and buckling loads for columns with jump discontinuities are calculated using the Laplace transform method in the space of generalized functions.     

Efficiency of carbon sorbents in mitigating polar herbicides leaching from tropical soil

Clean Technologies and Environmental Policy - Imidazolinones are a group of herbicides with high potential of leaching and long half-lives that are posing a threat to water resources’ quality...