The Material Parameter Identification for Functionally Graded Materials by the Isoparametric Graded Finite Element

2012 ◽  
Vol 446-449 ◽  
pp. 3609-3614 ◽  
Author(s):  
Li Xin Huang ◽  
Lin Wang ◽  
Yue Chen ◽  
Qi Yao ◽  
Xiao Jun Zhou
Keyword(s):  
Parameter Identification ◽  
Functionally Graded Materials ◽  
Material Parameter ◽  
Identification Problem ◽  
Optimization Method ◽  
Functionally Graded ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Material Parameter Identification ◽  
Graded Materials

A material parameter identification method is proposed for functionally graded materials (FGMs) which are modeled by the isoparametric graded finite elements (IGFE). The material parameter identification problem is formulated as the problem of minimizing the objective function defined as a square sum of differences between the measured displacement and the computed displacement by the IGFE. Levenberg-Marquardt optimization method, in which the sensitivity analysis of displacements with respect to the material parameters is based on the finite difference approximation method, is used to solve the minimization problem. Numerical example is given to illustrate the validity of the proposed method for parameter identification.

Material parameter identification in functionally graded structures using isoparametric graded finite element model

2016 ◽  
Vol 23 (6) ◽  
pp. 685-698 ◽  
Author(s):  
Lixin Huang ◽  
Ming Yang ◽  
Xiaojun Zhou ◽  
Qi Yao ◽  
Lin Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Parameter Identification ◽  
Material Parameter ◽  
Element Model ◽  
Functionally Graded ◽  
Identification Algorithm ◽  
Material Parameter Identification ◽  
Measured Displacement ◽  
Graded Structures

AbstractAn identification algorithm based on an isoparametric graded finite element model is developed to identify the material parameters of the plane structure of functionally graded materials (FGMs). The material parameter identification problem is formulated as the problem of minimizing the objective function, which is defined as a square sum of differences between measured displacement and calculated displacement by the isoparametric graded finite element approach. The minimization problem is solved by using the Levenberg-Marquardt method, in which the sensitivity calculation is based on the differentiation of the governing equations of the isoparametric graded finite element model. The validity of this algorithm is illustrated by some numerical experiments. The numerical results reveal that the proposed algorithm not only has high accuracy and stable convergence, but is also robust to the effects of measured displacement noise.

DETERMINATION OF PARAMETERS IN NONLINEAR HYPERBOLIC PDES VIA A MULTIHARMONIC FORMULATION, USED IN PIEZOELECTRIC MATERIAL CHARACTERIZATION

2006 ◽  
Vol 16 (06) ◽  
pp. 869-895 ◽  
Author(s):  
B. KALTENBACHER
Keyword(s):  
Parameter Identification ◽  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Material Parameter ◽  
Model Problem ◽  
Nonlinear Partial Differential Equations ◽  
Identification Problem ◽  
Field Quantity ◽  
Material Parameter Identification

In this paper we consider the problem of determining material parameter curves that appear as coefficients in nonlinear partial differential equations of hyperbolic type. In order to demonstrate our ideas of an identification method for this class of problems, we consider the model problem of identifying c in the nonlinear wave equation dtt - (c(dx)dx)x = 0 from boundary measurements. Motivated by the fact that in many applications, this inverse problem is naturally posed in frequency domain rather than in time domain, we work in the Fourier transformed setting. Here, nonlinearity can be accounted for by using a multiharmonic Ansatz for the measured field quantity. The searched for material parameter curves are approximated by polynomials of arbitrary order, which enables a reformulation of the parameter identification problem purely in frequency domain, although the parameter curve is a function of time domain values of the field quantity. Based on this formulation, we develop a reconstruction algorithm by means of the above-mentioned model problem. Regularization of the typically unstable identification problem is here achieved by bandlimiting the data and restricting the number of degrees of freedom in the solution. We outline the extension of the proposed method to more general material parameter identification problems, focusing especially on the piezoelectric PDEs, for which we also give numerical results.

Parameter Identification for Piezoelectric Material in a Piezoelectric Laminated Composite Beam Model

2012 ◽  
Vol 174-177 ◽  
pp. 448-454
Author(s):  
Shuang Bei Li ◽  
Lin Jie Jiang ◽  
Du Yi Mo ◽  
Li Xin Huang
Keyword(s):  
Parameter Identification ◽  
Analytical Solutions ◽  
Composite Beam ◽  
Laminated Composite ◽  
Identification Problem ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Beam Model ◽  
Parameter Identification Problem ◽  
Laminated Composite Beam

A fit-to-data technique was proposed to identify the mechanical and piezoelectric parameters of a model involving a piezoelectric laminated composite beam. Analytical solutions for displacement of the model were derived for parameter identification. The parameter identification problem was formulated as the problem of minimizing the objective function defined as a square sum of differences between the measured displacement and the computed displacement by the analytical solutions. Levenberg-Marquardt method was used to solve the minimization problem. The sensitivities of displacements with respect to the parameters were based on the finite difference approximation method. Numerical example shows that the proposed technique for parameter identification is effective.

scholarly journals Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects

2021 ◽  
Author(s):  
Paulina Stempin ◽  
Wojciech Sumelka
Keyword(s):  
Functionally Graded Materials ◽  
Timoshenko Beam ◽  
Functionally Graded ◽  
Beam Model ◽  
Material Parameter Identification ◽  
Graded Materials ◽  
Size Dependent ◽  
Non Local ◽  
Thick Beam ◽  
Euler Bernoulli Beam

AbstractIn this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the s-FTB model. The differences in results between s-FTB and s-FEBB models are shown as well to indicate when shear deformations need to be considered. Finally, material parameter identification and validation based on the bending of SU-8 polymer microbeams confirm the effectiveness of the presented model.

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials
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