Browsing by Author "Reddy, J.N."
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- Benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates using PVDFPublication . Moleiro, F; Soares, C.M. Mota; Soares, C.A. Mota; Reddy, J.N.The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.
- Deformations and stresses of multilayered plates with embedded functionally graded material layers using a layerwise mixed modelPublication . Moleiro, F.; M. Franco Correia, V.; Araújo, A.L.; Mota Soares, C.M.; Ferreira, A.J.M.; Reddy, J.N.This work presents a new layerwise mixed model for the static analysis of multilayered plates with embedded functionally graded material (FGM) layers subjected to transverse mechanical loads. This model is capable to fully describe a two-constituent metal-ceramic FGM layer continuous variation of material properties in the thickness direction, using any given homogenization method to estimate its effective properties. The present model is based on a mixed least-squares formulation with a layerwise variable description for displacements, transverse stresses and in-plane strains, chosen as independent variables. This mixed formulation ensures that the interlaminar continuity requirements at the layers interfaces, where the material properties actually change, are fully fulfilled a priori for all independent variables. The order of the in-plane two-dimensional finite element approximations and the order of the z-expansion through each layer thickness, as well as the number of layers, whether FGM layers or not, are considered free parameters. The full description of the FGM effective properties is achieved by applying to the z-continuous elastic coefficients a z-expansion through the layer thickness of a given order, set as an added free parameter, in a similar approach to finite element approximations. The numerical results consider both single-layer and multilayered functionally graded plates with different side-to-thickness ratios, using either Mori-Tanaka or the rule of mixtures estimates for the FGM effective properties with different material gradation profiles. The present model results are assessed by comparison with three-dimensional (3D) exact solutions and closed form solutions, which demonstrate its capability to predict a highly accurate quasi-3D description of the displacements and stresses distributions altogether.
- Fully coupled thermomechanical analysis of multilayered plates with embedded FGM skins or core layers using a layerwise mixed modelPublication . Moleiro, F.; M.Franco Correia, V.; Ferreira, A.J.M.; Reddy, J.N.This work presents a new layerwise mixed model for the fully coupled thermo-mechanical static analysis of multilayered plates with embedded functionally graded material (FGM) layers, either skins or core layers, under thermal and/or mechanical loads. This model is able to fully describe a two-constituent metal-ceramic FGM layer z-continuous effective properties through-thickness, using any given homogenization method, and is here extended to the fully coupled thermo-mechanical analysis. It is based on a mixed least-squares formulation with a layerwise variable description for displacements, transverse stresses and in-plane strains, along with temperature, transverse heat flux and in-plane components of the thermal gradient, taken as independent variables. This mixed formulation ensures that the interlaminar continuity requirements, where the material properties may actually change, are fully fulfilled a priori by all chosen independent variables. The numerical results consider single-layer and multilayered plates with different side-to-thickness ratios, under thermal or mechanical loads, using mainly Mori-Tanaka estimate for the FGM effective properties with different material gradation profiles. The results are assessed by comparison with three-dimensional (3D) exact solutions, and demonstrate the model capability to predict a highly accurate quasi-3D thermo-mechanical description of the through-thickness distributions of displacements and stresses, as well as temperature and heat flux.
- Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulationPublication . Moleiro, F.; Mota Soares, C.M.; Mota Soares, C.A.; Reddy, J.N.This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interlaminar C0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.