Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Fourth-derivative spectrophotometric determination of fungicide ferbam (iron(III) dimethyldithiocarbamate) in a commercial sample and wheat grains using 2,2′-bipyridyl

A procedure has been developed for the direct fourth-derivative spectrophotometric determination of iron(III) dimethyldithiocarbamate by converting it into an iron(II) 2,2'-bipyridyl complex, which is then dissolved in Triton X-100. Beer's law is obeyed over the concentration range 0.5-20 microg mL(-1 )in the final solution. Various parameters such as the effect of pH and interference of large number of ions on the determination of ferbam have been studied in detail. The method is sensitive, highly selective and can be used for the determination of ferbam in a commercial sample and in mixtures with various dithiocarbamates (ziram, zineb, maneb, etc.) and from wheat grains.     

Biofortification—A Frontier Novel Approach to Enrich Micronutrients in Field Crops to Encounter the Nutritional Security

Globally, many developing countries are facing silent epidemics of nutritional deficiencies in human beings and animals. The lack of diversity in diet, i.e., cereal-based crops deficient in mineral nutrients is an additional threat to nutritional quality. The present review accounts for the significance of biofortification as a process to enhance the productivity of crops and also an agricultural solution to address the issues of nutritional security. In this endeavor, different innovative and specific biofortification approaches have been discussed for nutrient enrichment of field crops including cereals, pulses, oilseeds and fodder crops. The agronomic approach increases the micronutrient density in crops with soil and foliar application of fertilizers including amendments. The biofortification through conventional breeding approach includes the selection of efficient genotypes, practicing crossing of plants with desirable nutritional traits without sacrificing agricultural and economic productivity. However, the transgenic/biotechnological approach involves the synthesis of transgenes for micronutrient re-translocation between tissues to enhance their bioavailability. Soil microorganisms enhance nutrient content in the rhizosphere through diverse mechanisms such as synthesis, mobilization, transformations and siderophore production which accumulate more minerals in plants. Different sources of micronutrients viz. mineral solutions, chelates and nanoparticles play a pivotal role in the process of biofortification as it regulates the absorption rates and mechanisms in plants. Apart from the quality parameters, biofortification also improved the crop yield to alleviate hidden hunger thus proving to be a sustainable and cost-effective approach. Thus, this review article conveys a message for researchers about the adequate potential of biofortification to increase crop productivity and nourish the crop with additional nutrient content to provide food security and nutritional quality to humans and livestock.     

Anion sensing 'venus flytrap' hosts: a modular approach

A series of podands based on three hydrogen bonding 'arms' have been prepared and their affinities for simple inorganic anions measured.     

Mixed boundary value problem of heat conduction for infinite slab

Summary An axisymmetric steady state heat conduction boundary value problem having mixed boundary conditions on both faces of an infinite slab, is reduced to a pair of Fredholm integral equations of the second kind. For large values of h, the slab thickness, a solution correct to O(h ^–6) is obtained by expanding the kernels in power series.Presently at Imperial College, London.     

Effects due to body-forces and body-couples in the interior of a micropolar elastic half-space—I

A general solution of the equilibrium equations is obtained for a half-space with a fixed boundary and arbitrary but axisymmetric distribution of body forces and body couples in the interior of the half-space. Few particular cases have been investigated in detail. The stresses have been obtained at the boundary and the displacements have been obtained in the interior of the half-space. Numerical results have been displayed graphically.

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Zusammenfassung Eine allgemeine lösung für Gleichgewicht eines Halbraums mit festem Rand und einer beliebigen, aber antisymmetrischen Verteilung von Körperkräften und Körpermomenten im Inneren wird gefunden. Einige Spezialfälle wurden ansführlich erforscht. Die Spannungen am Rand und die Verschiebungen im Inneren des Halbraums wurden erhalten. Numerische Resultate wurden graphisch dargestellt.

     

The Elementary Solution of Triple Integral Equations and The Solution of Triple Series Equations Involving Associated Legendre Polynomials and their Application

A method is developed for the formal solution of an important class of triple integral equations involving Bessel functions. The solution of the triple integral equations is reduced to two simultaneous Fredholm integral equations and the results obtained are simpler than those of other authors and also superior for the purposes of solution by iteration. In the same manner the formal solution of triple series equations involving associated Legendre polynomials is presented. The solution of the problem is reduced to that of solving a Fredholm integral equation of the first kind. Finally to illustrate the application of the results an electrostatic problem is discussed.     

Bending of a rectilinear regular polygonal plate with a circular hole by concentrated edge couples

Summary This paper presents a solution for the deflection, moments and shearing forces in a rectilinear regular polygonal plate, with even number of sides having a central circular hole, subjected to concentrated edge couples at two opposite points of the outer boundary. Complex variable technique has been employed to find the solution of the problem. The solution involves an infinite system of linear algebraic equations and a method of solving them is provided. The solution for a corresponding plane stress (strain) problem has been derived. Numerical results are presented in the form of tables and graphs.