Browsing by Author "Mota Soares, C.M."
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- 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.
- Higher-order finite element models for the static linear and nonlinear behaviour of functionally graded material plate-shell structuresPublication . Moita, J.S.; M. Franco Correia, V.; Mota Soares, C.M.; Herskovits, J.In this work, finite element formulations based on higher order shear deformation theories are used for the nonlinear static analysis of Functionally Graded Material plate-shell type structures. Linear and geometric nonlinear behaviour of the plate-shell type structures are considered. For the nonlinear analysis, the incremental equilibrium path is obtained using the updated Lagrangian procedure and Newton-Raphson incremental-iterative method, incorporating the automatic arc-length method for the cases of snap-through occurrence. The finite element models are based on a non-conforming triangular flat plate/shell element with 3 nodes and 8 or 11 degrees of freedom per node. The solutions of some illustrative plate-shell examples are performed, and the results are presented and discussed with numerical alternative models.
- 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.
- Multiobjective optimization of ceramic-metal functionally graded plates using higher order modelsPublication . M. Franco Correia, Victor; Aguilar Madeira, J.F; Araújo, A.L; Mota Soares, C.M.; ElsivierA methodology of multiobjective design optimization of ceramic–metal composite plates with functionally graded materials, with properties varying through the thickness direction, obtained by an adequate variation of volume fractions of the constituent materials, is presented in this paper. Constrained optimization is conducted for different behavior objectives like the maximization of buckling load or fundamental natural frequency. Mass minimization and material cost minimization are also considered. The optimization problems are constrained by stress based failure criteria and other structural response constraints or manufacturing limitations. The design variables are the index of the power-law distribution in the metal-ceramic graded material and the thicknesses of the graded material and/or the metal and ceramic faces. An equivalent single layer finite element plate model having a displacement field based on a higher order shear deformation theory, accounting for the temperature dependency of the material properties, was developed and validated for the analysis of through-the-thickness ceramic-metal functionally graded plates. The optimization problems are solved with two direct search derivative-free algorithms: GLODS (Global and Local Optimization using Direct Search) and DMS (Direct MultiSearch). DMS, the multiobjective optimization solver, is started from a set of local minimizers which are initially determined by the global optimizer algorithm GLODS for each one of the objective functions.
- Multiobjective optimization of functionally graded material plates with thermo- mechanical loadingPublication . M.Franco Correia, V.; Aguilar Madeira, J.F.; Araújo, A.L.; Mota Soares, C.M.This work addresses the design optimization of ceramic–metal composite plates with functionally graded material properties, varying through the thickness direction, subjected to thermo-mechanical loadings. Constrained multiobjective optimization is performed for mass minimization and material cost minimization as well as the minimization of stress failure criteria or maximization of natural frequency. The optimization problems are constrained by stress based failure criteria among other structural response constraints and manufacturing limitations. The design variables are the index of the power-law distribution in the metal-ceramic graded material and the thicknesses of the graded material and, eventually, also the metal and ceramic faces. A finite element plate model based on a higher order shear deformation theory, accounting for the transverse shear and transverse normal deformations and considering the temperature dependency of the material properties, is applied for the optimal design of ceramic-metal functionally graded plates. The optimization problems are solved with two direct search derivative-free algorithms: GLODS (Global and Local Optimization using Direct Search) and DMS (Direct MultiSearch). A few multiobjective optimization problems are studied and the results are presented for benchmarking purposes.