An improved plate theory of order (1,2) for thick composite laminates

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains

Closed extended r-spin theory and the Gelfand–Dickey wave function

We study a generalization of genus-zero r-spin theory in which exactly one insertion has a negative-one twist, which we refer to as the “closed extended” theory, and which is closely related to the open r-spin theory of Riemann surfaces with boundary. We prove that the generating function of genus-zero closed extended intersection numbers coincides with the genus-zero part of a special solution to the system of differential equations for the wave function of the rth Gelfand–Dickey hierarchy. This parallels an analogous result for the open r-spin generating function in the companion paper Buryak et al. (2018) to this work

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory

A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous, laminated composite, and sandwich plates

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear-deformation theory, whereas the fine displacement field has a piecewise-linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best-performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous-plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient, C0 a continuous function of (x1,x2) coordinates whose first-order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures

Full-field strain reconstruction using uniaxial strain measurements: Application to damage detection

This work investigates the inverse problem of reconstructing the continuous displacement field of a structure using a spatially distributed set of discrete uniaxial strain data. The proposed technique is based on the inverse Finite Element Method (iFEM), which has been demonstrated to be suitable for full-field displacement, and subsequently strain, reconstruction in beam and plate structures using discrete or continuous surface strain measurements. The iFEM uses a variationally based approach to displacement reconstruction, where an error functional is discretized using a set of finite elements. The effects of position and orientation of uniaxial strain measurements on the iFEM results are investigated, and the use of certain strain smoothing strategies for improving reconstruction accuracy is discussed. Reconstruction performance using uniaxial strain data is examined numerically using the problem of a thin plate with an internal crack. The results obtained highlight that strain field reconstruction using the proposed strategy can provide useful information regarding the presence, position, and orientation of damage on the plate

C0 triangular elements based on the Refined Zigzag Theory for multilayered composite and sandwich plates

The Refined Zigzag Theory (RZT) has been recently developed for the analysis of homogeneous, multilayer composite and sandwich plates. The theory has a number of practical and theoretical advantages over the widely used First-order Shear Deformation Theory (FSDT) and other types of higher-order and zigzag theories. Using FSDT as a baseline, RZT takes into account the stretching, bending, and transverse shear deformations. Unlike FSDT, this novel theory does not require shear correction factors to yield accurate results for a wide range of material systems including homogeneous, laminated composite, and sandwich laminates. The inplane zigzag kinematic assumptions, which compared to FSDT add two additional rotation-type kinematic variables, give rise to two types of transverse shear strain measures - the classical average shear strain (as in FSDT) and another one related to the cross-sectional distortions enabled by the zigzag kinematic terms. Consequently, with a fixed number of kinematic variables, the theory enables a highly accurate modeling of multilayer composite and sandwich plates even when the laminate stacking sequence exhibits a high degree of transverse heterogeneity. Unlike most zigzag formulations, this theory is not affected by such theoretical anomalies as the vanishing of transverse shear stresses and forces along clamped boundaries. In this paper, six- and three-node, C0-continuous, RZT-based triangular plate finite elements are developed; they provide the best compromise between computational efficiency and accuracy. The element shape functions are based on anisoparametric (aka interdependent) interpolations that ensure proper element behavior even when very thin plates are modeled. Continuous edge constraints are imposed on the transverse shear strain measures to derive coupled-field deflection shape functions, resulting in a simple and efficient three-node element. The elements are implemented in ABAQUS - a widely used commercial finite element code - by way of a user-element subroutine. The predictive capabilities of the new elements are assessed on several elasto-static problems, which include simply supported and cantilevered laminated composite and sandwich plates. The numerical results demonstrate that the new RZT-based elements provide superior predictions for modeling a wide range of laminates including highly heterogeneous sandwich laminations. They also offer substantial improvements over the existing plate elements based on FSDT as well as other higher-order and zigzag-type element

Nanoparticulate Metal Oxide Top Electrode Interface Modification Improves the Thermal Stability of Inverted Perovskite Photovoltaics

Solution processed {\gamma}-Fe2O3 nanoparticles via the solvothermal colloidal synthesis in conjunction with ligand-exchange method are used for interface modification of the top electrode in inverted perovskite solar cells. In comparison to more conventional top electrodes such as PC(70)BM/Al and PC(70)BM/AZO/Al, we show that incorporation of a {\gamma}-Fe2O3 provides an alternative solution processed top electrode (PC(70)BM/{\gamma}-Fe2O3/Al) that not only results in comparable power conversion efficiencies but also improved thermal stability of inverted perovskite photovoltaics. The origin of improved stability of inverted perovskite solar cells incorporating PC(70)BM/ {\gamma}-Fe2O3/Al under accelerated heat lifetime conditions is attributed to the acidic surface nature of {\gamma}-Fe2O3 and reduced charge trapped density within PC(70)BM/ {\gamma}-Fe2O3/Al top electrode interfaces.Comment: 24 pages, 11 figure

Population dynamics, delta vulnerability and environmental change: comparison of the Mekong, Ganges–Brahmaputra and Amazon delta regions

Tropical delta regions are at risk of multiple threats including relative sea level rise and human alterations, making them more and more vulnerable to extreme floods, storms, surges, salinity intrusion, and other hazards which could also increase in magnitude and frequency with a changing climate. Given the environmental vulnerability of tropical deltas, understanding the interlinkages between population dynamics and environmental change in these regions is crucial for ensuring efficient policy planning and progress toward social and ecological sustainability. Here, we provide an overview of population trends and dynamics in the Ganges–Brahmaputra, Mekong and Amazon deltas. Using multiple data sources, including census data and Demographic and Health Surveys, a discussion regarding the components of population change is undertaken in the context of environmental factors affecting the demographic landscape of the three delta regions. We find that the demographic trends in all cases are broadly reflective of national trends, although important differences exist within and across the study areas. Moreover, all three delta regions have been experiencing shifts in population structures resulting in aging populations, the latter being most rapid in the Mekong delta. The environmental impacts on the different components of population change are important, and more extensive research is required to effectively quantify the underlying relationships. The paper concludes by discussing selected policy implications in the context of sustainable development of delta regions and beyond