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<jats:title>Abstract</jats:title> <jats:p>The effectiveness of the coupling of the perturbation techniques and the finite element method has been demonstrated using a method called Asymptotic-Numerical Method (ANM). This... more
<jats:title>Abstract</jats:title> <jats:p>The effectiveness of the coupling of the perturbation techniques and the finite element method has been demonstrated using a method called Asymptotic-Numerical Method (ANM). This concept eliminates the major difficulties of the classical perturbation methods namely the complexity of the right hand sides and the limitation of the validity of the solution obtained. In this paper we present the development of this method and its applicability for large amplitudes free vibrations of plates. The displacement and the frequency are expanded into power series with respect to a control parameter. The nonlinear governing equation is transformed into a sequence of linear problems having the same stiffness matrix. Needing one matrix inversion, a large number of terms can be computed with a small computation time. Taking the starting point in the zone of validity, the method is reapplied in order to determine a further part of the nonlinear solution. In order to increase the zone of validity, the Pade approximants are incorporated. Iterations of this method lead to a powerful incremental method. Numerical tests for large amplitudes free vibrations of plates with various shapes and boundary conditions are reported. Recent improvements in the basic ANM algorithm as well as applications to various structural problems are added in order to exhibit the effectiveness and the applicability of this method.</jats:p>
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The aim of this paper is to elaborate a mathematical modeling and a numerical methodological approach based on radial basis functions and integral equation formulation for numerical solution of the non self adjoint partial differential... more
The aim of this paper is to elaborate a mathematical modeling and a numerical methodological approach based on radial basis functions and integral equation formulation for numerical solution of the non self adjoint partial differential system governing the dynamic behavior of Timoshenko beams. The fundamental solution of the basic operator is explicitly given and used to transform the PDE to an integral equation. Using the radial basis functions for the resulting body integral, the governing equation is reduced to an algebro-differential system. Based on the harmonic assumption and internal concatenation points an eigenvalue problem is obtained and numerically solved for various follower loads.
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The paper presents an optimization technique for the identification of dielectric and elastic properties of simply supported rectangular functionally graded piezoelectric plates (FGPM) using the exact three dimensional solution for the... more
The paper presents an optimization technique for the identification of dielectric and elastic properties of simply supported rectangular functionally graded piezoelectric plates (FGPM) using the exact three dimensional solution for the static deformations under mechanical load of FGPM rectangular plates. The procedure uses the Stroh-like formalism to obtain the exact solution for FGPM plates which can be expressed in more concise and easier handling forms comparing to other more complicated semi-analytical or numerical approaches used in the literature. Particle Swarm Optimizer (PSO) is then used to solve the optimization problem in order to identify the piezoelectric material properties in the z-direction. In order to validate the given exact solution, a numerical example for a single-layer FGPM plate is presented and compared to the previous findings in the literature. Several numerical examples are presented using PSO algorithm to solve the identification problem of piezoelectric material constants and good results are obtaind. The obtained results confirm the efficiency of the proposed coupled procedure and demonstrate that the PSO algorithm is an effective technique for solving optimal design problems to improve the performance of the piezoelectric materials for more energy storage.
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A generalized approach for the electromechanical analysis of laminated piezoelectric structures is obtained by Stroh formalism. The laminate consists of an homogeneous elastic or piezoelectric laminate of arbitrary thickness. The three... more
A generalized approach for the electromechanical analysis of laminated piezoelectric structures is obtained by Stroh formalism. The laminate consists of an homogeneous elastic or piezoelectric laminate of arbitrary thickness. The three dimensional differential equations of equilibrium of the multilayered are exactly satisfied at every point in the body. The continuity conditions at the interfaces between adjoining laminate are satisfied by the propagator matrix methodology. Various types of electrical and mechanical loading may be considered. Numerical results of stresses, electric potential and electric and elastic displacement for some multifunctional multilayered plates are presented.
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The differential scheme is extended to predict the effective properties of multiphase magnetoelectroelastic composite materials. The prediction of effective properties is done gradually by adding a series of incremental additions of a... more
The differential scheme is extended to predict the effective properties of multiphase magnetoelectroelastic composite materials. The prediction of effective properties is done gradually by adding a series of incremental additions of a small volume of particulate phase materials to an initial material (matrix phase). The construction process is compatible with high volume concentration of inclusion. A system of coupled differential equations is formulated and its numerical solution leads to effective properties of reinforced magnetoelectroelastic composites. For the numerical results, two-phase and three-phase magnetoelectroelastic composites are considered. The effective properties are presented as function of volume fractions and shapes of inclusions and compared with predictions based on the Mori–Tanaka and incremental self-consistent models.
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In this paper an N-phase Incremental Self Consistent model is developed for magnetoelectroelastic composites as well as the N-phase Mori-Tanaka and classical Self Consistent. Our aim here is to circumvent the limitation of the Self... more
In this paper an N-phase Incremental Self Consistent model is developed for magnetoelectroelastic composites as well as the N-phase Mori-Tanaka and classical Self Consistent. Our aim here is to circumvent the limitation of the Self Consistent predictions for some coupling effective properties at certain inclusion volume fractions. The anomalies of the SC estimates are more drastic when the void inclusions are considered. The mathematical modeling is based on the heterogeneous inclusion problem of Eshelby which leads to an expression for the strain-electric-magnetic field related by integral equations. The effective N-phase magnetoelectroelastic moduli are expressed as a function of magnetoelectroelastic concentration tensors based on the considered micromechanical models. The effective properties are obtained for various types, shapes and volume fractions of inclusions and compared with the existing results.
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Abstract The dynamic and parametric instabilities of single-walled carbon nanotubes (CNTs) conveying pulsating and viscous fluid embedded in an elastic medium are modeled and numerically investigated. The partial differential equation of... more
Abstract The dynamic and parametric instabilities of single-walled carbon nanotubes (CNTs) conveying pulsating and viscous fluid embedded in an elastic medium are modeled and numerically investigated. The partial differential equation of motion based on the nonlocal elasticity theory, Euler Bernoulli beam’s model and fluid–tube interaction is given. Based on the differential quadrature method, complex eigenmodes and associated eigenfrequencies are investigated with respect to the flow velocity as well as to the other considered physical parameters. Multimodal formulation based on real and complex eigenmodes are presented in the frequency and time domains. Models are elaborated for dynamic instabilities such as divergence and flutter as well as for parametric instability behaviors. The influences of the nonlocal parameter, the fluid pulsation and viscosity, the viscoelastic CNT parameter and the thermal effects on the dynamic behaviors of the CNT-fluid system are analyzed. Instability boundaries and interaction between the dynamic and parametric instabilities are investigated.
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In recent years, energy generation and harvesting took the attention of many researchers, especially the piezoelectric materials for their unique characteristics. One of the promising techniques for energy harvesting is the ocean wave... more
In recent years, energy generation and harvesting took the attention of many researchers, especially the piezoelectric materials for their unique characteristics. One of the promising techniques for energy harvesting is the ocean wave energy harvester resulting from the pressure coming from the ocean movement waves on a vertical cantilever with piezoelectric patches, this results in a fluid-structure interaction. A mathematical model is presented based on the Stokes equation for the flow and the Euler-Bernoulli beam theory for the structure motion. The finite element method (FEM) coupled with the quadratic differential method (QDM) are used to numerically solve the resulting partial differential equations with an implicit time scheme. The obtained numerical simulations are validated and discussed. Results show clear effect of the water pressure on the cantilever, as well as the pulsatile behavior of the water motion. This paper gives an adaptive numerical scheme to solve the FSI model for energy harvesting of ocean wave motion and the study gives more insights on the understanding of such problems.
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The problem of transverse impact velocity by spherical impactors on beam is, in this paper, approached by numerical modeling as a reference. A three-dimensional finite element model is modeled using the Abaqus Software, the hardening and... more
The problem of transverse impact velocity by spherical impactors on beam is, in this paper, approached by numerical modeling as a reference. A three-dimensional finite element model is modeled using the Abaqus Software, the hardening and strain rate effects of the material are taken into account. The aim of the study is to investigate the impact velocity, from which, the transient response results of the semi-analytical contact model are credible, by comparing its predictions to the numerical solution. The semi-analytical model was modeled at one of our research works using the finite difference method and the Hertz contact theory, coupled with the Stronge contact model.
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Abstract This paper presents an efficient hybrid optimization approach using a new coupling technique for solving the constrained optimization problems. This methodology is based on genetic algorithm, sequential quadratic programming and... more
Abstract This paper presents an efficient hybrid optimization approach using a new coupling technique for solving the constrained optimization problems. This methodology is based on genetic algorithm, sequential quadratic programming and particle swarm optimization combined with a projected gradient techniques in order to correct the solutions out of domain and send them to the domain’s border. The established procedures have been successfully tested with some well known mathematical and engineering optimization problems, also the obtained results are compared with the existing approaches. It is clearly demonstrated that the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature. The main application of this procedure is the location optimization of piezoelectric sensors and actuators for active control, the vibration of plates with some piezoelectric patches is considered. Optimization criteria ensuring good observability and controllability based on some main eigenmodes and residual ones are considered. Various rectangular piezoelectric actuators and sensors are used and two optimization variables are considered for each piezoelectric device: the location of its center and shape orientation. The applicability and effectiveness of the present methodological approach are demonstrated and the location optimization of multiple sensors and actuators are successfully obtained with some main modes and residual ones. The shape orientation optimization of sensors observing various modes as well as the local optimization of multiple sensors and actuators are numerically investigated. The effect of residual modes and the spillover reduction can be easily analyzed for a large number of modes and multiple actuators and sensors.
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In this work the Fokker-Planck-Kolmogorov equation associated to nonlinear stochastic differential equations with uncertain parameters is used to obtain the associated distribution functions. The exponential closure method is extended to... more
In this work the Fokker-Planck-Kolmogorov equation associated to nonlinear stochastic differential equations with uncertain parameters is used to obtain the associated distribution functions. The exponential closure method is extended to the considered random systems with uncertain parameters. Methodological approaches and numerical procedures based on meshfree method with radial basis function (RBF) and exponential closure are elaborated for the considered random equations. The obtained approximate solutions are well compared with the exact solution and Monte Carlo based results. For physical application, the dynamic behavior of beams with uncertain parameters excited by uniformly distributed Gaussian white noise is considered. The accuracy, effectiveness and advantages of the developed procedures in analyzing the probabilistic solutions of nonlinear stochastic systems with uncertain parameters excited by Gaussian white noise are demonstrated.
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Ultra-low carbon (ULC) steels, which are lightweight, are used in fabricating steel sheets for many applications, particularly the automobile sector where good formability and surface quality are required. For mechanical properties... more
Ultra-low carbon (ULC) steels, which are lightweight, are used in fabricating steel sheets for many applications, particularly the automobile sector where good formability and surface quality are required. For mechanical properties development reasons, the bake hardening technique of ultra-low carbon (ULC) steels is adopted during the automotive paint baking process at elevated temperature. Automotive outer body with bake-hardenable steel ensure good indentation strength and resistance to fatigue. Usually, the mechanical properties of automotive steels depend both on the chemical composition and thermal treatment. Consequently, the present paper aimed to design a car roof panel using elastic-plastic ULC steel sheet with and without bake hardening. Finite element (FE) analysis was used to predict the static indentation response of automotive roof panels. First of all, the roof panel was modelled via CATIA V5 and evaluated by FE analysis using ABAQUS Software. The results showed that ...
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This paper presents a methodological approach based on the homotopy and perturbation methods for thermal buckling and post-buckling analyses of the anisotropic laminated plates with temperature dependent properties. A power law... more
This paper presents a methodological approach based on the homotopy and perturbation methods for thermal buckling and post-buckling analyses of the anisotropic laminated plates with temperature dependent properties. A power law distribution in terms of temperature is used and the structure is subjected to a uniform temperature variation. A mathematical formulation that may account for various temperature dependent models is elaborated. Power series expansions of the displacement and the temperature are developed and the finite element method is used for numerical solutions. The critical buckling load and the post-buckling equilibrium path of plates under thermal loading are investigated. The effects of temperature dependent properties, structure geometry and boundary conditions on the thermal buckling and post-buckling behaviours are evaluated through parametric studies.
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In this article, the effective properties of new active–passive multifunctional viscomagnetoelectroelastic composite materials are modeled and numerically predicted. The correspondence principle, extended to linear... more
In this article, the effective properties of new active–passive multifunctional viscomagnetoelectroelastic composite materials are modeled and numerically predicted. The correspondence principle, extended to linear viscomagnetoelectroelasticity, and the Carson transform are coupled to the Mori–Tanaka micromechanical mean field approach. Based on the viscomagnetoelectroelastic convolution integral equations and the interfacial operators, the concentration tensors are derived for multi-phase and multi-coated viscomagnetoelectroelastic composites. The effective properties are derived in the frequency domain and then inverted numerically to the time domain using the inverse transform. The effective properties are thus obtained in both frequency and time domains. The obtained hybrid multifunctional coefficients can be used for their active and passive properties. The resulting visco-magneto-electro-elastic effects can be enhanced by a proper choice of the shape and volume fraction of rei...
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In this article, analytical and semi-analytical models of upper and lower bounds for the effective moduli of transversely isotropic piezoelectric heterogeneous materials based on the generalized Hashin–Shtrikman variational principle are... more
In this article, analytical and semi-analytical models of upper and lower bounds for the effective moduli of transversely isotropic piezoelectric heterogeneous materials based on the generalized Hashin–Shtrikman variational principle are presented. Compact matrix formulations are used to derive closed-form bound expressions for coupled and uncoupled effective moduli. Analytical models are given for some uncoupled coefficients and simplified formulations for the others. For more narrow bounds, downstream and upstream bounds are developed based on an incremental procedure. Numerical predictions are performed based on the developed methodological approaches, and the obtained results showed the applicability and effectiveness of the proposed models for transversely isotropic elastic and piezoelectric composite materials with ellipsoidal reinforcements of different types and shapes.
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In this paper, the effective properties of magnetoelectroelastic heterogeneous materials with ellipsoidal multi-inclusions are modeled and numerically investigated. The modeling is based on the integral equation that takes into account... more
In this paper, the effective properties of magnetoelectroelastic heterogeneous materials with ellipsoidal multi-inclusions are modeled and numerically investigated. The modeling is based on the integral equation that takes into account the multi-coated effect as well as the magnetoelectroelastic interfacial operators and global and local concentration tensors. Various types and kinds of coatings can be considered. The effective properties are predicted based on various micromechanical models such as Mori-Tanaka, Self-Consistent and Incremental Self-Consistent. These properties are presented in terms of the volume fractions of the multi-coated inclusions, thicknesses of the coatings, type and kind of inclusions.
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In this article, micromechanical modeling of magnetoelectroelastic composites with multicoated inclusions and functionally graded interphases are elaborated. The integral equation taking into account the continuously varying interphase... more
In this article, micromechanical modeling of magnetoelectroelastic composites with multicoated inclusions and functionally graded interphases are elaborated. The integral equation taking into account the continuously varying interphase properties as well as the multifunctional coating effects is introduced based on Green’s tensors and interfacial operators. Magnetoelectroelastic composites with functionally graded interphases are analyzed, and the effective properties are derived. Based on the Mori–Tanaka, Self-Consistent, and Incremental Self-Consistent models, the numerically predicted effective properties of magnetoelectroelastic composites are presented with respect to the volume fractions, shapes of the multicoated inclusions, and the thickness of the coatings. The multicoating and functionally graded interphase concepts can be used to optimize the effective properties of multifunctional composites. This can be used to design new multifunctional composite materials with higher coupling coefficients.
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The study of fluid-structure interaction (FSI) energy harvesting using piezoelectric patch integrated on beam structures has received significant attention over the past decades. In this work a mathematical model based on the Stokes... more
The study of fluid-structure interaction (FSI) energy harvesting using piezoelectric patch integrated on beam structures has received significant attention over the past decades. In this work a mathematical model based on the Stokes equation for the flow and the Euler-Bernoulli beam theory for the structure motion is presented. Hybrid optimization procedure is elaborated to find the optimal locations of the piezoelectric patches to calculate the maximum generated electric power. The finite element method (FEM) coupled with the quadratic differential method (QDM) is used to numerically solve the resulting partial differential equations with an implicit time scheme. The obtained numerical simulations are used to calculate the generated electric power. Hybrid optimization algorithm namely GA-PSO-SQP is applied to find the optimal locations of the piezoelectric patches to give maximum generated electric power. An adaptive numerical scheme is elaborated herein to solve the FSI model for energy harvesting from ocean wave motion. This algorithm is combined with optimization procedures and the study gives more insights on the understanding of such problems.
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This paper introduces a new hybrid optimization procedure named GA-PSO-SQP for resolution constrained engineering design problems. Certifiable issues in the engineering field are typically expansive scale or nonlinear or constrained... more
This paper introduces a new hybrid optimization procedure named GA-PSO-SQP for resolution constrained engineering design problems. Certifiable issues in the engineering field are typically expansive scale or nonlinear or constrained optimization problems, very well-designed numerical procedure is this way needed. This coupling is based on the genetic algorithm, the sequential quadratic programming and on the particle swarm optimization united with a projected gradient algorithm to deal constrained optimization problems. Numerical results based on well-known held back engineering design problems are reported and compared. The solutions acquired by the proposed technique are generally improved than those results given by other known methodologies in the open literature.
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In this paper, the non-ageing effective behavior of fractional viscoelastic reinforced composites is predicted based on the Mori-Tanaka approach. The mathematical modeling is based on the Carson-Laplace transform, the dynamic Greens... more
In this paper, the non-ageing effective behavior of fractional viscoelastic reinforced composites is predicted based on the Mori-Tanaka approach. The mathematical modeling is based on the Carson-Laplace transform, the dynamic Greens function and the integral equations. Various fractional viscoelastic models can be easily considered. The localization tensors relating local fields and macroscopic ones are derived based on the equivalence inclusion of Eshelby. The Homogenization of the effective behavior is obtained as a function of volume fractions of the constituents and their properties as well as of the volume fraction of reinforcements in the Carson domain.
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In this work the Meshfree with radial basis functions is elaborated to solve Kolmogorov-Feller (KF) equation associated to stochastic differential equations excited by a Poissonian white noise with uncertain parameters. The general... more
In this work the Meshfree with radial basis functions is elaborated to solve Kolmogorov-Feller (KF) equation associated to stochastic differential equations excited by a Poissonian white noise with uncertain parameters. The general polynomial chaos method is also elaborated to compare the results obtained when the exact solution not available. The accuracy and the effective of these methods are demonstrated.
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The aim of this paper is the elaboration of a new hybrid optimization procedure based on a coupling methodological approach for solving global optimization problem and active vibration control. This coupling is based on the genetic... more
The aim of this paper is the elaboration of a new hybrid optimization procedure based on a coupling methodological approach for solving global optimization problem and active vibration control. This coupling is based on the genetic algorithm, the sequential quadratic programming and on the particle swarm optimization combined with a projected gradient algorithm. The proposed methodological approach and its convergence to the global solution are proved through the tested solutions. The proposed methodological approach is applied to constrained optimal piezoelectric actuators location. The test results indicate that the proposed algorithm is extremely robust and can be successfully used to solve global optimization problems. Based on the obtained optimal location, active vibration control of beams with multi-piezoelectric patches is elaborated.
The Oldroyd-B constitutive model is widely used for describing the viscoelastic behavior of the blood. However, there is sill a lack of blood flow simulations using non-Newtonian models, hence, a poor understanding of many cardiovascular... more
The Oldroyd-B constitutive model is widely used for describing the viscoelastic behavior of the blood. However, there is sill a lack of blood flow simulations using non-Newtonian models, hence, a poor understanding of many cardiovascular diseases, mainly, atherosclerosis. In this paper, we intent to realize numerical computations of blood flow through arteries with the presence of a stenosis. We used the Newton iterations to deal with the nonlinear and coupled system of equations that includes the steady Navier-Stokes equations and the Oldroyd-B constitutive equations for viscolelastic fluids. The velocity and pressure field are calculated using the mixed finite elements discretization of the two dimensional spacial parameters. The numerical simulations are realized for a complex geometry of the flow domain with the existence of an arterial stenosis with fixed form. We demonstrated from the obtained results that the fluid behavior differs the Newtonian fluids and gives more realisti...
The aim of this work is to estimate the non-linear stochastic dynamic response for a reasonable calculation cost. For that, we propose an original approach based on the coupling of the Polynomial Chaos Expansion PCE with Component Mode... more
The aim of this work is to estimate the non-linear stochastic dynamic response for a reasonable calculation cost. For that, we propose an original approach based on the coupling of the Polynomial Chaos Expansion PCE with Component Mode Synthesis CMS condensation method. CMS method proved to be effective in reducing the size of the problem, while the PCE method allows taking problems with uncertain parameters. This approach allows a minimal computational cost. Otherwise, we present some numerical simulations demonstrate the effectiveness and applicability of the proposed approach.
In this paper, Fractional-time model for simply supported beams subjected to moving harmonic loads has been developed and studied numerically. Numerical fractional-time scheme coupled with the Galerkin method is elaborated to study the... more
In this paper, Fractional-time model for simply supported beams subjected to moving harmonic loads has been developed and studied numerically. Numerical fractional-time scheme coupled with the Galerkin method is elaborated to study the dynamical behavior of beams with fractional viscoelastic foundation, subjected to multiple harmonic moving loads and with a constant speed. Numerical results are obtained using the proposed methodological approach to study the effects of different system parameters, including, the load magnitude frequency, the order of the fractional derivative and the number of moving loads. The presented numerical technique is validated and compared with the Finite Element Method and the obtained results show a perfect agreement between the two methods.
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In this paper, mathematical modeling for the identification of effective electro-mechanical properties of homogeneous piezoelectric plate composites is proposed. The effective properties are investigated using micromechanical models based... more
In this paper, mathematical modeling for the identification of effective electro-mechanical properties of homogeneous piezoelectric plate composites is proposed. The effective properties are investigated using micromechanical models based on the heterogeneous inclusion problem of Eshelby. The concentration and localization tensors are used attributed to the Mori-Tanaka micromechanical approach. The homogenized coefficients for both electro-elastic and piezoelectric plates are then used to analyze the response of the polarized piezoelectric plate in z-direction. The influence of the direction of polarization in addition to the concentration of the fiber inclusion is analysed using the exact solution from the Stroh-like formalism. The Stroh-like formalism solution demonstrate the effect of the polarization direction of Epoxy/PZT-5 and PZT-C91/PZT-5 on the eletromechanical response of piezoelectric composite.
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This paper presents a numerical procedure to compute the stochastic dynamic response of large finite element models with uncertain parameters based on polynomial chaos and component mode synthesis methods. Polynomial chaos expansions at... more
This paper presents a numerical procedure to compute the stochastic dynamic response of large finite element models with uncertain parameters based on polynomial chaos and component mode synthesis methods. Polynomial chaos expansions at higher orders are used to derive the statistical solution of the dynamic response as well as the Monte Carlo simulation procedure. Based on various Component Mode Synthesis Methods (CMS), the size of the model is reduced. These methods are coupled with polynomial chaos expansion and the explicit mathematical formulations are given. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures are presented.
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In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent... more
In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent properties. Nonlinear thermal dependence distribution following a power law is adapted. Various types of multilayered composite plates with position and temperature-dependent material properties are considered. Mathematical formulations and explicit relationships are presented in the frame of finite element methods. The structure is subjected to linear and uniform temperature variations. The temperature and the displacement are expanded in power series with unknown terms, and the numerical solution is obtained by the finite element method. The homotopy method is used for nonlinear thermal buckling, and a continuation procedure is elaborated for nonlinear thermal–displacement responses. The nonlinear thermal critical buckling load is first computed and the postbuckling equilibrium path of FGM and laminated plates under thermal loading is investigated. Temperature-dependent properties and geometry effects as well as boundary conditions on the nonlinear thermal buckling and postbuckling behaviors are analyzed.
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In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of... more
In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of each layer of the composite plates have been assumed varying throughout the thickness direction. The imperfect interfaces between the layers are assumed to be mechanically compliant, dielectrically and magnetically weakly or highly conducting. In each layer, the state-space approach is firstly applied leading to space variable. Cauchy’s problem and adapted Runge-Kutta numerical procedure is used to solve the established state-space equation. The elaborated semi-analytical solution has been propagated throughout the multilayered multiferroic composites plates using the propagator matrix method and accounting the transfers matrices at each imperfect interface. The developed formulas have been programmed and the numerical obtained results have been wel...
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In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of... more
In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of each layer of the composite plates have been assumed varying throughout the thickness direction. The imperfect interfaces between the layers are assumed to be mechanically compliant, dielectrically and magnetically weakly or highly conducting. In each layer, the state-space approach is firstly applied leading to space variable. Cauchy’s problem and adapted Runge-Kutta numerical procedure is used to solve the established state-space equation. The elaborated semi-analytical solution has been propagated throughout the multilayered multiferroic composites plates using the propagator matrix method and accounting the transfers matrices at each imperfect interface. The developed formulas have been programmed and the numerical obtained results have been wel...