Fluid mechanics of free subduction on a sphere. Part 1. The axisymmetric case

To understand how a spherical geometry influences the dynamics of gravity-driven subduction of the oceanic lithosphere on Earth, we study a simple model of a thin and dense axisymmetric shell of thickness $h$ and viscosity $\eta _1$ sinking in a spherical body of fluid with radius $R_0$ and a lower viscosity $\eta _0$ . Using scaling analysis based on thin viscous shell theory, we identify a fundamental length scale, the ‘bending length’ $l_b$ , and two key dimensionless parameters that control the dynamics: the ‘flexural stiffness’ $St = (\eta _1/\eta _0)(h/l_b)^3$ and the ‘sphericity number’ $\varSigma = (l_b/R_0)\cot \theta _t$ , where $\theta _t$ is the angular radius of the subduction trench. To validate the scaling analysis, we obtain a suite of instantaneous numerical solutions using a boundary-element method based on new analytical point-force Green functions that satisfy free-slip boundary conditions on the sphere's surface. To isolate the effect of sphericity, we calculate the radial sinking speed $V$ and the hoop stress resultant $T_2$ at the leading end of the subducted part of the shell, both normalised by their ‘flat-Earth’ values (i.e. for $\varSigma = 0$ ). For reasonable terrestrial values of $\eta _1/\eta _0$ ( $\approx$ several hundred), sphericity has a modest effect on $V$ , which is reduced by $< 7\,\%$ for large plates such as the Pacific plate and by up to 34 % for smaller plates such as the Cocos and Philippine Sea plates. However, sphericity has a much greater effect on $T_2$ , increasing it by up to 64 % for large plates and 240 % for small plates. This result has important implications for the growth of longitudinal buckling instabilities in subducting spherical shells.

Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

In this paper, mixed formulations are presented in the framework of isogeometric Reissner–Mindlin plates and shells with the aim of alleviating membrane and shear locking. The formulations are based on the Hellinger-Reissner functional and use the stress resultants as additional unknowns, which have to be interpolated in appropriate approximation spaces. The additional unknowns can be eliminated by static condensation. In the framework of isogeometric analysis static condensation is performed globally on the patch level, which leads to a high computational cost. Thus, two additional local approaches to the existing continuous method are presented, an approach with discontinuous stress resultant fields at the element boundaries and a reconstructed approach which is blending the local control variables by using weights in order to compute the global ones. Both approaches allow for a static condensation on the element level instead of the patch level. Various numerical examples are investigated in order to verify the accuracy and effectiveness of the different approaches and a comparison to existing elements that include mechanisms against locking is carried out.

Study of Structural Irregularities in different Seismic Zones using Response Spectrum Analysis

The Indian Standard code IS-1893: 2002 (Part-I) defines various types of structural irregularities. The code suggests a special approach of study for irregular structures. The earthquake effect leads to the damage the property and many people loss their life. So, we've to understand the structural performance under seismic load before construction. In this study varying plan irregularities which are often inevitable thanks to building requirements and architectural imperatives, and having a serious impact on building costs are investigated. The objective of the project is to carry out Response spectrum analysis of two RCC buildings is to be done in four different seismic zones of India (i.e., Zone-2, Zone-3, Zone-4, Zone-5). ETABS model of G+10 RCC with Varying Geometry plan is considered in this analysis. The analysis is done using Extended Three-Dimensional Analysis of Building System software. Various response parameters like lateral force, story drift, Displacement are often determined. The evaluation of response of structures subjected to lateral loading with the help of frequency and the magnitude of stress resultant, is also included in the scope of this paper. Keywords: Plan irregularity, Vertical geometric irregularities Response spectrum method, ETABS, Structural Irregularities, Lateral Loading, Non-Linear Analysis, Storey Drift, Storey Displacement.

Mixed finite element formulation for bending of laminated beams using the refined zigzag theory

This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

Climate-smart livestock production: options for Nigerian farmers

This paper is focused on reviewing the three key pillars of climate-smart agriculture (CSA) in relation to livestock production (i.e., increased productivity, mitigation of greenhouse gases emissions and adaptation to climate change) while exploring the development intervention options for Nigerian livestock farmers. The most serious impacts of climate change are anticipated in grazing systems because of their dependence on climatic conditions and the natural resource base, and their limited adaptation opportunities. Impacts are expected to be most severe in arid and semi-arid grazing systems at low latitudes, where higher temperatures and lower rainfall are expected to reduce yields on range lands and increase land degradation. The dual pathways of responses between climate change and livestock production activities were depicted in this review. It is of note that climate change as a natural phenomenon works on the principle of causes and effect. The actions and in-actions of man will dictate the type of results obtainable in his immediate environment. Means by which livestock farmers can mitigate the GHGs and adapt to the effect of climate changes were discussed in this paper. Concerted efforts at ameliorating the effect of climate change on livestock production are needed. The smart options for rearing livestock are capable of mitigating the attendant effect of production activities of the stocks, reducing the stress obtainable from altered environment and ensuring food security. Nigeria as a country will need to evolve policies that will ensure promotion and subsequent adoptions of technologies that are smart in terms of increasing productivity of farm animals, reducing emissions of GHG and positively altering the effect of climate change. Cet article se concentre sur l'examen des trois piliers clés de l'agriculture intelligente face au climat (ASC) en relation avec la production animale (c.-à-d. Augmentation de la productivité, atténuation des émissions de gaz à effet de serre et adaptation au changement climatique) tout en explorant les options d'intervention de développement pour les éleveurs nigérians. Les impacts les plus graves du changement climatique sont anticipés dans les systèmes de pâturage en raison de leur dépendance aux conditions climatiques et de la base de ressources naturelles, et de leurs possibilités d'adaptation limitées. Les impacts devraient être les plus graves dans les systèmes de pâturage arides et semi-arides à basses latitudes, où des températures plus élevées et des précipitations plus faibles devraient réduire les rendements sur les pâturages et augmenter la dégradation des terres. Les doubles voies de réponses entre le changement climatique et les activités de production animale ont été décrites dans cette revue. Il est à noter que le changement climatique en tant que phénomène naturel fonctionne sur le principe des causes et des effets. Les actions et les in-actions de l'homme dicteront le type de résultats pouvant être obtenus dans son environnement immédiat. Les moyens par lesquels les éleveurs peuvent atténuer les GES et s'adapter aux effets des changements climatiques ont été discutés dans ce document. Des efforts concertés pour atténuer les effets du changement climatique sur la production animale sont nécessaires. Les options intelligentes pour l'élevage du bétail sont capables d'atténuer l'effet connexe des activités de production des stocks, de réduire le stress résultant de l'altération de l'environnement et d'assurer la sécurité alimentaire. Le Nigéria, en tant que pays, devra élaborer des politiques qui assureront la promotion et l'adoption ultérieure de technologies intelligentes en termes d'augmentation de la productivité des animaux d'élevage, de réduction des émissions de GES et de modification positive des effets du changement climatique.

Simulation of Wrinkling during Bending of Composite Reinforcement Laminates

When a thick laminate is subjected to bending, under certain boundary conditions, wrinkles may appear and develop due to the inextensibility of the fibers. Wrinkling is one of the most critical defects in composite manufacturing. Numerical simulation of the onset and growth of such wrinkles is an important tool for defining optimal process parameters. Herein, several bending experiments of thick laminates are presented. They were found to lead to severe wrinkling and delamination of different kinds. It is shown that the history of loading changed the developed wrinkles. Stress resultant shell finite elements specific to textile reinforcement forming show their relevance to provide, for these wrinkles induced by bending, results in good agreement with the experiments, both with regard to the onset of the wrinkles and to their development. This numerical approach was used to improve the understanding of the phenomena involved in wrinkling and to define the conditions required to avoid it in a given process.