Analysis and control of geometrically nonlinear responses of piezoelectric FG porous plates with graphene platelets reinforcement using B\'ezier extraction

In this study, we propose an effective numerical approach to analyse and control geometrically nonlinear responses for the functionally graded (FG) porous plates reinforced by graphene platelets (GPLs) integrated with piezoelectric layers. The basis idea is to use isogeometric analysis (IGA) based on the B\'ezier extraction and the $C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying the B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control meshes can be transformed into the B\'ezier elements which allow us to inherit the standard numerical procedure like the finite element method (FEM). The mechanical displacement field is approximated based on the $C^0$-HSDT whilst the electric potential is assumed to be a linear function through the thickness of each piezoelectric sublayer. The FG plate contains the internal pores and GPLs dispersed in the metal matrix either uniformly or non-uniformly according to various different patterns along the thickness of plate. In addition, to control dynamic responses, two piezoelectric layers are perfectly bonded on the top and bottom surfaces of the FG plate. The geometrically nonlinear equations are solved by the Newton-Raphson iterative procedure and the Newmark's time integration scheme. The influences of the porosity coefficients, weight fractions of GPLs as well as the external electrical voltage on the geometrically nonlinear behaviours of the plates with different porosity distributions and GPL dispersion patterns are evidently investigated through numerical examples. Then, a constant displacement and velocity feedback control approaches are adopted to active control the geometrically nonlinear static as well as the dynamic responses of the FG porous plates, where the effect of the structural damping is considered, based on a closed-loop control with piezoelectric sensors and actuators.Comment: 39 pages, 20 figure

Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect

Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material (FGM) close to reality. Mathematical formulations concern the Timoshenko shear deformation theory. Small scale and atomic interactions are shaped as maintained by the nonlocal strain gradient elasticity approach. Since there is no bifurcation point for FGMs, whenever both boundary conditions are rotational and the neutral surface does not match the mid-plane, the clamp configuration is examined only. The fourth-order ordinary differential stability equations will be converted into the sets of algebraic ones utilizing the GWRM whose accuracy was proved before. After that, by simply solving the achieved polynomial constitutive relation, the parametric study can be started due to various predominant and overriding factors. It was found that the flexomagneticity is further visible if the ferric nanobeam is constructed by FGM technology. In addition to this, shear deformations are also efficacious to make the FM detectable

Geometric Nonlinear Finite Element and Genetic Algorithm Based Vibration Energy Harvesting from Functionally Graded Nonprismatic Piezolaminated Beams

Energy harvesting technology has the ability to create autonomous, self-powered systems which do not rely on the conventional battery for their operation. The term energy harvesting is the process of converting the ambient energy surrounding a system into some useful electrical energy using certain materials. Among several energy conversion techniques, the conversion of ambient vibration energy to electrical energy using piezoelectric materials has great deal of importance which encompasses electromechanical coupling between mechanical and electrical domains. The energy harvesting systems are designed by incorporating the piezoelectric materials in the host structure located in vibration rich environment. The work presented in this dissertation focuses on upgrading the concept of energy harvesting in order to engender more power than conventional energy harvesting designs. The present work deals with first the finite element (FE) formulation for coupled thermo-electro-mechanical analysis of vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated cantilever beam. A two noded beam element with two degrees of freedom (DOF) at each node has been used in the FE formulation. The FG material (i.e. non-homogeneity) in the axial direction has been considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) have been modelled using the Euler-Bernoulli beam theory and Hamilton‘s principle is used to solve the governing equation of motion. The simultaneous variation of tapers (both width and height in length directions) is incorporated in the mathematical formulation. The FE formulation developed in the present work has been compared with the analytical solutions subjected to mechanical, electrical, thermal and thermo-electro-mechanical loading. Results obtained from the present work shows that the axially FG nonprismatic beam generates more output power than the conventional energy harvesting systems. Further, the work has been focussed towards the nonlinear vibration energy harvesting from an axially FG non-prismatic piezolaminated cantilever beam. Geometric nonlinear based FE formulation using Newmark method in conjunction with Newton-Raphson method has been formulated to solve the obtained governing equation. Moreover, a real code GA based constrained optimization technique has also been proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of the beam and voltage of the PZT sensor. It is observed that more output power can be obtained based on the present optimization formulation within the allowable limits of stress and voltage than that of selection of design variables by trial and error in FE modelling

Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales

Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory.

This article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated. When the nanoplate is subjected to a transverse harmonic loading and all the edges are considered as simple boundaries, the governing equations can be solved with a closed-form solution, from which the maximum dynamic deflections are obtained. To validate the results of the new proposed plate theory, the comparisons between ours and the well-known papers in the literature are presented. The influences of different nonlocal parameters and material properties on the nanoplate's dynamic responses are also studied.N/

DETECTION OF NONLOCAL CALIBRATION PARAMETERS AND RANGE INTERACTION FOR DYNAMICS OF FGM POROUS NANOBEAMS UNDER ELECTRO-MECHANICAL LOADS

The present investigation examines the range of effect of nonlocal parameters on dynamic behavior of a smart beam-like nanostructure modeled as sandwich functionally graded porous nanobeam with piezoelectric layers. Therefore, the study is concentrated on determining length of the structure for which nonlocal effects are observed for vibration of nanobeam under in-plane electro-mechanical forces. The nanobeam-based NEMS device model is obtained based on assumptions of the nonlocal strain gradient theory in conjunction with Reddy higher-order shear deformation theory. The investigation present differences in obtained results for nanostructure’s free vibration based on classical and nonlocal assumptions. To study range of application of nonlocal parameters for different length of simply supported nanobeam, defined eigenvalue problem is solved in view of variation of length to thickness ratio, distribution of material properties, as well as electro-mechanical loads. What is more, the study attempts to determine and calibrate values of size-dependent coefficients based on expected natural frequencies, material properties, and applied loads. The results are completed with extensive discussion on the dependence of nonlocal parameters on nanobeam’s dynamic response, thus may be an important step forward to extend understanding of ultra-small structure’s behavior

Design and Analysis of Smart Building Envelope Materials and Systems

As the largest consumer of electricity, the buildings sector accounts for about 76% of electricity use and 40% of all U.S. primary energy use and associated greenhouse gas (GHG) emissions. Research shows that a potential energy saving of 34.78% could be achieved by the smart buildings comparing to conventional buildings. Therefore, a smart management of building sectors becomes significantly important to achieve the optimal interior comfort with minimal energy expenditure. The ability of adaptation to the dynamic environments is considered the central aspect in smart building systems, which can be segmented into the passive adaptation and the active adaptation. The passive adaptation refers to the designs that do not change with the dynamic environment but improve the building overall performance by the integration of originally separated components, or by the application of advanced engineering materials. The active adaptation refers to the building management system (BMS) that actively responds and evolves with the changing environment, through the continuous monitoring of the surroundings via the sensor network, and the smart response through the controlling algorithms in the central controlling unit. This Ph.D. dissertation focuses on developing materials and systems for the smart building envelope, including a photovoltaic integrated roof with passive adaptation, and self-powered window systems with active responses environment. As the skin of a building, the building envelope provides the first level resistance towards air, water, heat, light and noise, which makes it the ideal target for the passive adaptation to the environments, as well as the perfect sensing location in the building management system for the active adaptation. This dissertation starts with a discussion of the building integrated photovoltaic thermal (BIPVT) roofing panel, including the fabrication, performance demonstration, and micromechanics-based theoretical modeling. The panel is structurally supported by a functionally graded material (FGM) panel made with high-density polyethylene as the matrix and aluminum particles as reinforcement. It prevents the heat from entering the building and directs the heat to the water tubes embedded inside the panel for the thermal energy harvesting, such that the overall energy efficiency is significantly improved. The design, fabrication and performance of the system is discussed, and an innovative non-destructive analysis method is developed to captures the authentic particle distribution of the FGM. As the main structural component, functionally graded material is comprehensively tested and modeled in elastic, thermoelastic, elastoplastic, and thermo-elastoplastic performance, based on the equivalent inclusion based method. An ensemble average approach was used to convert the particles’ interaction in the microscope to the averaged relation in the macroscope, such that both particle to matrix influence and particle to particle pair-wise interactions are characterized. The idea of the equivalent inclusion method extends to the plastic modeling of the FGM, by formulating an ensemble average form of the matrix stress norm in the macroscale that incorporate the local disturbance of particle reinforcement in the microscale. The accuracy of the proposed algorithm is verified and validated by comparing with another theory in homogeneous composite and experiments, respectively. To the best of the author’s knowledge, no prior theoretical algorithm has been proposed for the elastoplastic modeling of functionally graded materials. Therefore, the proposed algorithm can be used as a foundation and reference for further investigation and industry prediction of graded composites. Based on the theoretical modeling of the mechanical properties, a high order plate theory is also proposed in this dissertation to study for the thermo-mechanical performance of the FGM panel, to provide structural design guideline for the BIPVT panels. The shearing and bending behaviors are decomposed, solved independently, and combined to formulate the final solution. The shear strain components are assumed to follow a parabolic variation across the thickness, while the bending components follow the solution from classical plate theory. Closed-form solutions for the circular panel under different loadings are provided, with verification by comparing to other models and validation to experiments. Two smart window systems are proposed and demonstrated in this dissertation to actively monitor the building environment with active responses, and energy harvesting techniques are investigated to harvest energy from ambient environment the eternal power supply to the system. The thermoelectric powered wireless sensor network (TPWSN) platform is first demonstrated and discussed, where the energy is harvested from the temperature difference across the window frame. The TPWSN sits completely inside the window/façade frame with no compromise of the outlook and continuously monitors the building environment for the optimal control of the building energy consumption and indoor comfort. The energy harvesting technique grants eternal battery lifetime and significantly simplifies the installation and maintenance of the system with considerable saving of time and cost. In addition, the platform provides energy to various types of sensors for different kinds of sensing needs and store the data to the Google cloud for permanent storage and advanced analytics. The thermoelectric powered system works well for the sensors and microcontrollers but fails to provide enough power to the actuators. A novel sun-powered smart window blinds (SPSWB) system is designed, prototyped, and tested in this dissertation with solar energy harvesting on window blinds which provides enough power for the actuators. The thin-film photovoltaic cells are attached on one side of slats for energy harvesting and a PVdF-HFP coating is attached on the other side for the passive cooling. The voltage regulation and battery management systems are designed and tested, where a stable 55% energy efficiency from the PV into the battery has been achieved. The automatic control of the window blinds is accomplished with the help of sensors and a microcontroller. The energy equilibrium analysis is proposed and demonstrated with the local solar data to incorporate the influence of local weather conditions and solar zenith angle, from which we demonstrated that much more power than needed can be harvested. The abundant energy harvested validates the feasibility and the robustness of the system and proves its wide application potentials to various sensors and applications. In conclusion, both passive and active adaptations to the environment are investigated to build up the next generation of smart building envelope systems. The building integrated photovoltaic thermal roof is designed, fabricated, tested, and modeled in detail, which provides structural support to the external loads and improves the energy efficiency of buildings. The smart window/façade systems serve as a platform for various sensors and actuators via the energy harvesting from the ambient environment, and could significantly improve the energy expenditure with minimal impact of internal comfort

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

The nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship" is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Karman type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams

Thermal buckling and elastic vibration analysis of functionally graded beams and plates using improved third-order shear deformation theory

Functionally graded materials (FGMs) have been developed for general purpose structural components such as rocket engine components or turbine blades where the components are exposed to extreme temperatures. The earliest FGMs were introduced by Japanese scientists in the mid-1980s as ultra-high temperature-resistant materials for aerospace applications. Recently, these materials have found other uses in electrical devices, energy transformation, biomedical engineering, optics, etc. FGMs are microscopically inhomogeneous spatial composite materials, typically composed of a ceramic-metal or ceramic-polymer pair of materials. Therefore, it is important to investigate the behaviors of engineering structures such as beams and plates made from FGMs when they are subjected to thermal and dynamic loads for appropriate design. The material property profiles of FGMs vary across the graded direction. Therefore, using an improved third order shear deformation theory (TSDT) based on more rigorous kinetics of displacements to predict the behaviors of functionally graded beams and plates is expected to be more suitable than using other theories. Thus, in this research, the improved TSDT is used to investigate thermal buckling and elastic vibration response of functionally graded beams and plates. For the first time in this research temperature dependent material property solutions, are adopted to investigate thermal buckling results of functionally graded beams and plates. Additionally, the research includes natural frequency and forced vibration analysis of functionally graded plates subjected to a uniformly distributed dynamic load acting over the plate domain. To obtain the solutions, the Ritz method using polynomial and trigonometric functions for defining admissible displacements and rotations is applied to solve the governing equations. The numerical results are validated by published and experimental results. To clearly understand functionally graded materials beam specimens were manufactured from alumina-epoxy using a multi-step sequential infiltration technique. These beams were then subject to microscopic analysis to determine the profiles of the constituents. Finally experiments were conducted to determine the vibration characteristics and the results were compared to analysis using the improved TSDT. To compute theoretical parts in this research, the material compositions of the functionally graded beams and plates are assumed to vary smoothly and continuously throughout the thickness according to the power law distribution. Several significant aspects such as thickness and aspect ratios, materials, temperature, added mass etc. which affect analytical results are taken into account and discussed in detail. The original work in this thesis includes the application of the improved TSDT to thermal buckling and elastic vibration problems of functionally graded beams and plates. New critical buckling temperature results for the case of temperature dependent material properties have been solved by an iterative calculation technique. The results reveal that the effect of temperature dependent material on reduced buckling temperatures is more profound for a thicker beam and plate than a thinner one. The relationship between the critical temperatures and natural frequencies of the beam and plate structures are also presented and discussed

Advanced Mechanical Modeling of Nanomaterials and Nanostructures

This reprint presents a collection of contributions on the application of high-performing computational strategies and enhanced theoretical formulations to solve a wide variety of linear or nonlinear problems in a multiphysical sense, together with different experimental studies