Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier's method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

Fracture analysis of cracked plate panels using NI-MVCCI technique

The objective of this paper is to propose a numerically integrated modified virtual crack closure integral (NI-MVCCI) technique for fracture analysis of cracked plate panels. NI-MVCCI technique is generalized one and the expressions for computing the strain energy release rate (SERR) are independent of the finite element employed. NI-MVCCI technique has been demonstrated for 4-noded, 8-noded (regular and quarter-point) and 9-noded isoparametric finite elements. Numerical studies on fracture analysis of 2-D crack (mode-I and mode-II) problems have been conducted employing these elements. SERR and stress intensity factors (SIF) have been computed for these problems and found to be in good agreement with the respective analytical solutions available in the literature. The appropriate Gauss numerical integration order to be employed for each of these elements for accurate computation of SERR and SIF has been recommended based on the studies.

Characteristics of Arabian Sea mini warm pool and Indian summer monsoon

Arabian Sea Mini Warm Pool (ASMWP) is a part of the Indian Ocean Warm Pool and formed in the eastern Arabian Sea prior to the onset of the summer monsoon season. This warm pool attained its maximum intensity during the pre-monsoon season and dissipated with the commencement of summer monsoon. The main focus of the present work was on the triggering of the dissipation of this warm pool and its relation to the onset of summer monsoon over Kerala. This phenomenon was studied utilizing NCEP/NCAR (National Center for Environmental Prediction/National Center for Atmospheric and Research) re-analysis data, TRMM Micro wave Imager (TMI) and observational data. To define the ASMWP, sea surface temperature exceeding 30.25A degrees C was taken as the criteria. The warm pool attained its maximum dimension and intensity nearly 2 weeks prior to the onset of summer monsoon over Kerala. Interestingly, the warm pool started its dissipation immediately after attaining its maximum core temperature. This information can be included in the present numerical models to enhance the prediction capability. It was also found that the extent and intensity of the ASMWP varied depending on the type of monsoon i.e., excess, normal, and deficient monsoon. Maximum core temperature and wide coverage of the warm pool observed during the excess monsoon years compared to normal and deficient monsoon years. The study also revealed a strong relationship between the salinity in the eastern Arabian Sea and the nature of the monsoon.

The hazard potential of the western segment of the Makran subduction zone, northern Arabian Sea

Evaluating the hazard potential of the Makran subduction zone requires understanding the previous records of the large earthquakes and tsunamis. We address this problem by searching for earthquake and tectonic proxies along the Makran Coast and linking those observations with the available constraints on historical seismicity and the tell-tale characteristics of sea floor morphology. The earthquake of Mw 8.1 of 1945 and the consequent tsunami that originated on the eastern part of the Makran are the only historically known hazardous events in this region. The seismic status of the western part of the subduction zone outside the rupture area of the 1945 earthquake remains an enigma. The near-shore shallow stratigraphy of the central part of Makran near Chabahar shows evidence of seismically induced liquefaction that we attribute to the distant effects of the 1945 earthquake. The coastal sites further westward around Jask are remarkable for the absence of liquefaction features, at least at the shallow level. Although a negative evidence, this possibly implies that the western part of Makran Coast region may not have been impacted by near-field large earthquakes in the recent past-a fact also supported by the analysis of historical data. On the other hand, the elevated marine terraces on the western Makran and their uplift rates are indicative of comparable degree of long-term tectonic activity, at least around Chabahar. The offshore data suggest occurrences of recently active submarine slumps on the eastern part of the Makran, reflective of shaking events, owing to the great 1945 earthquake. The ocean floor morphologic features on the western segment, on the contrary, are much subdued and the prograding delta lobes on the shelf edge also remain intact. The coast on the western Makran, in general, shows indications of progradation and uplift. The various lines of evidence thus suggest that although the western segment is potentially seismogenic, large earthquakes have not occurred there in the recent past, at least during the last 600 years. The recurrence period of earthquakes may range up to 1,000 years or more, an assessment based on the age of the youngest dated coastal ridge. The long elapsed time points to the fact that the western segment may have accumulated sufficient slip to produce a major earthquake.

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.