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.

Material uncertainty effect on vibration control of smart composite plate using polynomial chaos expansion

Polynomial Chaos Expansion with Latin Hypercube sampling is used to study the effect of material uncertainty on vibration control of a smart composite plate with piezoelectric sensors/actuators. Composite material properties and piezoelectric coefficients are considered as independent and normally distributed random variables. Numerical results show substantial variation in structural dynamic response due to material uncertainty of active vibration control system. This change in response due to material uncertainty can be compensated by actively tuning the feedback control system. Numerical results also show variation in dispersion of dynamic characteristics and control parameters with respect to ply angle and stacking sequence.

Computationally efficient yet accurate analysis of composite plate

This article does not have an abstract.

Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

The way in which basal tractions, associated with mantle convection, couples with the lithosphere is a fundamental problem in geodynamics. A successful lithosphere-mantle coupling model for the Earth will satisfy observations of plate motions, intraplate stresses, and the plate boundary zone deformation. We solve the depth integrated three-dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection. The contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences. The basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations. We simultaneously fit stresses and plate motions in order to delineate a best-fit lithosphere-mantle coupling model. We use both the World Stress Map and the Global Strain Rate Model to constrain the models. We find that a strongly coupled model with a stiff lithosphere and 3-4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints. Our predicted deviatoric stresses, which are dominated by contribution from mantle tractions, range between 20-70 MPa. The best-fitting coupled models predict strain rates that are consistent with observations. That is, the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates. Comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving, although in a few regions, including western North America, tractions are resistive. Citation: Ghosh, A., W. E. Holt, and L. M. Wen (2013), Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics.

Guided Ultrasonic Wave Propagation through Inaccessible Damage in a Folded Plate using Sensor-Actuator Network

Rapid diagnostics and virtual imaging of damages in complex structures like folded plate can help reduce the inspection time for guided wave based NDE and integrated SHM. Folded plate or box structure is one of the major structural components for increasing the structural strength. Damage in the folded plate, mostly in the form of surface breaking cracks in the inaccessible zone is a usual problem in aerospace structures. One side of the folded plate is attached (either riveted or bonded) to adjacent structure which is not accessible for immediate inspection. The sensor-actuator network in the form of a circular array is placed on the accessible side of the folded plate. In the present work, a circular array is employed for scanning the entire folded plate type structure for damage diagnosis and wave field visualization of entire structural panel. The method employs guided wave with relatively low frequency bandwidth of 100-300 kHz. Change in the response signal with respect to a baseline signal is used to construct a quantitative relationship with damage size parameters. Detecting damage in the folded plate by using this technique has significant potential for off-line and on-line SHM technologies. By employing this technique, surface breaking cracks on inaccessible face of the folded plate are detected without disassembly of structure in a realistic environment.

Dynamics of a flexible splitter plate in the wake of a circular cylinder

Rigid splitter plates in the wake of bluff bodies are known to suppress the primary vortex shedding. In the present work, we experimentally study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate is free to continuously deform along its length due to the fluid forces acting on it; the flexural rigidity (EI) of the plate being an important parameter. Direct visualizations of the splitter plate motions, for very low values of flexural rigidity (EI), indicate periodic traveling wave type deformations of the splitter plate with maximum tip amplitudes of the order of I cylinder diameter. As the Reynolds number based on cylinder diameter is varied, two regimes of periodic splitter plate motions are found that are referred to as mode I and mode II, with a regime of aperiodic motions between them. The frequency of plate motions in both periodic modes is found to be close to the plane cylinder Strouhal number of about 0.2, while the average frequencies in the non-periodic regime are substantially lower. The measured normalized phase speed of the traveling wave for both periodic modes is also close to the convection speed of vortices in the plane cylinder wake. As the flexural rigidity of the plate (EI) is increased, the response of the plate was found to shift to the right when plotted with flow speed or Re. To better capture the effect of varying EI, we define and use a non-dimensional bending stiffness, K*, similar to the ones used in the flag flutter problem, K*=EI/(0.5 rho(UL3)-L-2), where U is the free-stream velocity and L is the splitter plate length. Amplitude data for different EI cases when plotted against this parameter appear to collapse on to a single curve for a given splitter plate length. Measurements of the splitter plate motions for varying splitter plate lengths indicate that plates that are substantially larger than the formation length of the plane cylinder wake have similar responses, while shorter plates show significant differences.

Horizontal pullout capacity of a group of two vertical plate anchors in clay

The horizontal pullout capacity of a group of two vertical strip plate anchors, placed along the same vertical plane, in a fully cohesive soil has been computed by using the lower bound finite element limit analysis. The effect of spacing between the plate anchors on the magnitude of total group failure load (P-uT) has been evaluated. An increase of soil cohesion with depth has also been incorporated in the analysis. For a weightless medium, the total pullout resistance of the group becomes maximum corresponding to a certain optimum spacing between the anchor plates which has been found to vary generally between 0.5B and B; where B is the width of the anchor plate. As compared to a single plate anchor, the increase in the pullout resistance for a group of two anchors becomes greater at a higher embedment ratio. The effect of soil unit weight has also been analyzed. It is noted that the interference effect on the pullout resistance increases further with an increase in the unit weight of soil mass.