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Glaucio H Paulino - One of the best experts on this subject based on the ideXlab platform.
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geometric nonlinear analyses of functionally graded beams using a tailored lagrangian formulation
Mechanics Research Communications, 2011Co-Authors: Carlos A. Almeida, Juan Carlos Torrico Albino, Ivan F M Menezes, Glaucio H PaulinoAbstract:Abstract This paper presents a geometric nonlinear analysis formulation for beams of functionally graded cross-sections by means of a Total Lagrangian formulation. The influence of Material Gradation on the numerical response is investigated in detail. Two examples are given that illustrate the main features of the formulation, in which the behavior of beams of graded cross-sections is compared with homogeneous Material beams. A motivation for this work is the potential development of functionally graded risers for the offshore oil exploration industry.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global–local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global---local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.
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Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems
Journal of Intelligent Material Systems and Structures, 2009Co-Authors: Wilfredo Montealegre Rubio, Emilio C. N. Silva, Glaucio H PaulinoAbstract:This work explores the design of piezoelectric transducers based on functional Material Gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; how- ever, this work focuses on finding the optimal Material Gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT opti- mal Material Gradation for maximizing specified resonance frequencies; (ii) to design piezo- electric resonators, thus, the optimal Material Gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal Material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the 'modal assurance criterion' is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear pro- gramming, and the concept of continuum approximation of Material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.
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Optimal design of periodic functionally graded composites with prescribed properties
Structural and Multidisciplinary Optimization, 2009Co-Authors: Glaucio H Paulino, Emilio C. N. Silva, Chau H. LeAbstract:The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a Material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite Material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of Materials in the last few years. In this work, the objective is to extend the Material design method to obtain functionally graded Material architectures, i.e. Materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous Material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded Material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional Material Gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric Material Gradation, and a Material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded Material cell design. Finally the influence of Material Gradation on extreme Materials is investigated, which includes Materials with near-zero shear modulus, and Materials with negative Poisson’s ratio.
Mohammad Reza Barati - One of the best experts on this subject based on the ideXlab platform.
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Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory
Microsystem Technologies, 2018Co-Authors: Mohammad Reza Barati, Hossein ShahverdiAbstract:A new modeling of nano-mechanical mass sensors constructed from porous nanoMaterials is presented based on generalized nonlocal strain gradient theory (NSGT). In this model, true small size effects including softening and hardening mechanisms are considered for more reliable analysis of mass nanosensors. The present biomass nanosensor is based on an oscillating higher order nanoscale plate in contact with an elastic substrate. Nano-pores or nano-voids are incorporated to the model based on a modified rule of mixture. According to the Hamilton’s principle, the formulation of nano-mass sensor is derived. Applying Galerkin’s method, the frequency shift due to the mass sensing is obtained. It is indicated that the mass detection of nano-mechanical sensors is significantly influenced by the porosities, nanoparticle mass, nanoparticle numbers, nonlocal parameter, strain gradient parameter, Material Gradation, elastic foundation and geometrical parameters.
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Magneto-hygro-thermal vibration behavior of elastically coupled nanoplate systems incorporating nonlocal and strain gradient effects
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017Co-Authors: Mohammad Reza BaratiAbstract:Magneto-hygro-thermal vibration analysis of double-layered nanoplates made of functionally graded Materials is presented based on higher order refined plate theory. For the first time, a double-layered nanoplate is modeled via nonlocal strain gradient theory in which both stiffness-softening and stiffness-hardening effects are incorporated. Another novelty of this paper is that the effects of magnetic and hygro-thermal fields on inhomogeneous double-layered nanoplates are considered to study their behavior under different physical fields. The Gradation of Material properties is considered using power-law model. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton’s principle. These equations are solved for hinged nanoplates via Galerkin’s method. It is indicated that type of vibration, moisture rise, temperature rise, nonlocal parameter, strain gradient parameter, Material Gradation, elastic foundation and side-to-thickness have a remarkable influence on vibration behavior of double-layered nanoscale plates.
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A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate
Composite Structures, 2017Co-Authors: Mohammad Reza Barati, Ashraf M. ZenkourAbstract:Abstract In this paper, a general bi-Helmholtz nonlocal strain-gradient elasticity model is developed for wave dispersion analysis of porous double-nanobeam systems on elastic substrate. The present model incorporates three scale coefficients to examine wave dispersion relations much accurately. Porosity-dependent Material properties of inhomogeneous nanobeams are defined via a modified power-law function. Based on Hamilton’s principle, the governing equations of double-nanobeam system on elastic substrate are obtained. Solving analytically these equation gives wave frequencies and phase velocities as a function of wave number. It is demonstrated that phase velocities of a nanoporous double-nanobeam system rely on the porosities, Material Gradation, nonlocal parameters, strain gradient parameter, interlayer springs, elastic substrate and wave number.
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Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams
Mechanical Systems and Signal Processing, 2017Co-Authors: Farzad Ebrahimi, Mohammad Reza BaratiAbstract:Abstract In this article, the size-dependent and porosity-dependent vibrational behavior of magneto-electro-elastic functionally graded (MEE-FG) nanoscale beams on two-parameter elastic substrate is presented via a third-order shear deformation beam model. Porosity-dependent Material coefficients of the nanobeam are compositionally graded throughout the thickness according to a modified power-law model. Incorporation of small size effect is carried out based on Eringen’s nonlocal elasticity theory. Through Hamilton’s principle, derivation of nonlocal governing equations is performed. After analytically solving these equations, the influences of porosity, elastic foundation, magnetic potential, applied voltage, scale coefficient, Material Gradation and slenderness ratio on the frequencies of the porous MEE-FG nanobeams are examined.
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On wave propagation in nanoporous Materials
International Journal of Engineering Science, 2017Co-Authors: Mohammad Reza BaratiAbstract:Abstract In this paper, a general bi-Helmholtz nonlocal strain-gradient elasticity model is developed for wave dispersion analysis of porous double-nanobeam systems in thermal environments. The present model incorporates three scale coefficients to examine wave dispersion relations much accurately. Porosity-dependent Material properties of inhomogeneous nanobeams are defined via a modified power-law function. Based on Hamilton's principle, the governing equations of double-nanobeam system on elastic substrate are obtained. Solving analytically these equations gives wave frequencies and phase velocities as a function of wave number. It is demonstrated that phase velocities of a nanoporous double-nanobeam system rely on the porosities, thermal loading, Material Gradation, nonlocal parameters, strain gradient parameter, interlayer springs, elastic substrate and wave number.
Emilio C. N. Silva - One of the best experts on this subject based on the ideXlab platform.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global–local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global---local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.
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toward design of functionally graded piezoelectric ultrasonic motors using topology optimization
Internaltional Ultrasonics Symposium, 2009Co-Authors: Wilfredo Montealegre Rubio, Emilio C. N. SilvaAbstract:In this work, piezoelectric ultrasonic motors are designed based on the Functionally Graded Material (FGM) concept by using topology optimization. FGMs are composite advanced Materials, which are made by changing gradually the properties with position inside Material domain. The FGM concept applied to piezoelectric structures allows modifying their dynamic characteristics. In this work, Functionally Graded Piezoelectric Ultrasonic Motors (FGPUMs) are designed, aiming to find the optimal topology and Gradation of the Material properties along a specific direction to target desired eigenmode shapes. The design of FGPUMs is not an easy task to be accomplished by using trial and error methods; thus, the Topology Optimization Method (TOM) is applied to reach this goal. Here, FGPUMs are designed as standing-wave motors, by combining different vibration modes (different eigenmodes). The eigenmode control is achieved by maximizing the amplitude of vibration at certain user-defined points. The Modal Assurance Criterion is applied as mode shape-tracking method. To treat the Material Gradation, the Graded Finite Element is implemented. The optimization algorithm is implemented based on Sequential Linear Programming. To show the improvement and the advantage of using FGM and TOM for designing FGPUMs, a graded ultrasonic piezomotor, with Material Gradation along thickness direction, is considered.
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Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems
Journal of Intelligent Material Systems and Structures, 2009Co-Authors: Wilfredo Montealegre Rubio, Emilio C. N. Silva, Glaucio H PaulinoAbstract:This work explores the design of piezoelectric transducers based on functional Material Gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; how- ever, this work focuses on finding the optimal Material Gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT opti- mal Material Gradation for maximizing specified resonance frequencies; (ii) to design piezo- electric resonators, thus, the optimal Material Gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal Material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the 'modal assurance criterion' is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear pro- gramming, and the concept of continuum approximation of Material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.
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Optimal design of periodic functionally graded composites with prescribed properties
Structural and Multidisciplinary Optimization, 2009Co-Authors: Glaucio H Paulino, Emilio C. N. Silva, Chau H. LeAbstract:The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a Material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite Material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of Materials in the last few years. In this work, the objective is to extend the Material design method to obtain functionally graded Material architectures, i.e. Materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous Material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded Material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional Material Gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric Material Gradation, and a Material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded Material cell design. Finally the influence of Material Gradation on extreme Materials is investigated, which includes Materials with near-zero shear modulus, and Materials with negative Poisson’s ratio.
Zhengyu (jenny) Zhang - One of the best experts on this subject based on the ideXlab platform.
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Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements
International Journal of Solids and Structures, 2007Co-Authors: Zhengyu (jenny) Zhang, Glaucio H PaulinoAbstract:AbstractThe dynamic behavior of smoothly graded heterogeneous Materials is investigated using the finite element method. The global variation of Material properties (e.g., Young’s modulus, Poisson’s ratio and mass density) is treated at the element level using a generalized isoparametric formulation. Three classes of examples are presented to illustrate this approach and to investigate the influence of Material inhomogeneity on the characteristics of wave propagation pattern and stress redistribution. First, a cantilever beam example is presented for verification purposes. Emphasis is placed on the comparison of numerical results with analytical ones, as well as modal analysis for beams with different Material Gradation profiles. Second, wave propagation patterns are explored for a fixed-free slender bar considering homogeneous, bi-Material, tri-layered and smoothly graded Materials (steel/alumina), which also provide further verification of the numerical procedures. Comparison of stress histories in these samples indicates that the smooth transition of Material Gradation considerably alleviates the stress discontinuity in the bi-Material system (with sharp interface). Third, a three-point-bending epoxy/glass graded beam specimen is investigated for validation purposes. The beam is graded along the height direction. Stress evolution history at a location of interest is analyzed in detail, which not only reveals the dependence of stress evolution on Material Gradation direction, but also provides information predictive of potential Material failure time for graded beams with different Material Gradation profiles. Jointly, these three classes of examples provide proper verification and validation for the present numerical techniques
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Cohesive zone modeling of dynamic failure in homogeneous and functionally graded Materials
International Journal of Plasticity, 2005Co-Authors: Zhengyu (jenny) Zhang, Zhengyu Zhang, Glaucio H PaulinoAbstract:This work investigates dynamic failure processes in homogeneous and functionally graded Materials (FGMs). The failure criterion is incorporated in the cohesive zone model (CZM) using both a finite cohesive strength and work to fracture in the Material description. A novel CZM for FGMs is explored and incorporated into a finite element framework. The Material Gradation is approximated at the element level using a graded element formulation. Examples are provided to verify the numerical approach, and to investigate the influence of Material Gradation on crack initiation and propagation in Mode-I as well as in mixed-mode fracture problems. The examples include spontaneous rapid crack growth in homogeneous and FGM strips, dynamic crack propagation in actual monolithic and epoxy/glass FGM beams (three-point bending) under impact loading, and mixed-mode crack propagation in pre-cracked steel and graded plates.
Sylvia R. M. Almeida - One of the best experts on this subject based on the ideXlab platform.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global–local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.
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Layout and Material Gradation in topology optimization of functionally graded structures: a global---local approach
Structural and Multidisciplinary Optimization, 2010Co-Authors: Sylvia R. M. Almeida, Glaucio H Paulino, Emilio C. N. SilvaAbstract:By means of continuous topology optimization, this paper discusses the influence of Material Gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including Material Gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering Material Gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular Materials.