An Inverse Analysis Algorithm of Material Parameters for Functional Graded Materials

2011 ◽  
Vol 243-249 ◽  
pp. 6011-6017
Author(s):  
Li Xin Huang ◽  
Qi Yao ◽  
Lin Wang ◽  
Xiao Jun Zhou
Keyword(s):  
Inverse Analysis ◽  
Element Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Graded Materials ◽  
Analysis Algorithm ◽  
Material Parameters ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Measured Displacement

An inverse analysis algorithm is proposed to identify the material parameters of functional graded materials (FGMs). The inverse analysis of the material parameters 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 a finite element model. Levenberg-Marquardt method is used to solve the minimization problem. The sensitivities of displacements with respect to the material parameters are based on the finite difference approximation method. A numerical example is given to demonstrate the effectiveness of the proposed algorithm.

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.

Numerical modeling of inverse problem of parameter identification for viscoelastic functionally graded materials/structures

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Linlin Zhang ◽  
Haitian Yang
Keyword(s):  
Inverse Problem ◽  
Recursive Algorithm ◽  
Functionally Graded ◽  
High Fidelity ◽  
Graded Materials ◽  
Content Type ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Constitutive Parameters ◽  
Derivatives Of

PurposeThis paper attempts to develop an efficient algorithm to solve the inverse problem of identifying constitutive parameters in VFG (viscoelastic functionally graded) materials/structures.Design/methodology/approachAn adaptive recursive algorithm with high fidelity is developed to acquire the derivatives of displacements with respect to constitutive parameters, which are required for the accurate and stable gradient based inverse analysis. A two-step strategy is presented in the process of identification, by which the unknown parameters can be separately identified and the scale and complexity of the inverse VFG problem are reduced. At each step, the process of identification is treated as an optimization problem that is solved by the Levenberg–Marquardt method.FindingsThe solution accuracy of forward problems and derivatives of displacements can be stably achieved with different step sizes, and constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures can be effectively and accurately identified. By examining the reliability, resolution, impacts of reference information and noisy data, the effectiveness of the proposed approach is numerically verified via three numerical examples.Originality/valueAn adaptive recursive algorithm is developed for derivatives computing with high fidelity, providing a solid platform for the sensitivity analysis and thereby a two-step strategy in conjunction with Levenberg–Marquardt method is presented in the process of identification. Consequently, an effective algorithm is developed to identify constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures.

Experimental Acoustic Field Characterization of Enclosures by Impedance Estimates and Modal Analysis

1987 ◽  
Vol 109 (4) ◽  
pp. 388-396 ◽  
Author(s):  
M. W. Trethewey ◽  
J. A. Cafeo
Keyword(s):  
Particle Acceleration ◽  
Experimental Method ◽  
Acoustic Field ◽  
Sound Pressure ◽  
Normal Modes ◽  
Element Model ◽  
Acoustic Mode ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Cavity Characteristics

An experimental method to characterize the acoustic field inside an enclosure in terms of the active and reactive components is presented. The method uses a finite difference approximation of the sound pressure from two closely spaced microphones to estimate the specific acoustic impedance and particle acceleration throughout a cavity. The impedance is then used to decompose the sound pressure at a point into components caused by the progressive and standing waves. The reactive or standing wave components within the cavity are further characterized in a normal modes fashion by extracting the modal parameters from the acoustic particle acceleration frequency response functions. The underlying theory of the technique is discussed. An experimental evaluation consisting of an analysis of the cavity characteristics of a tube with several end terminations is presented. For a reflective termination the experimental natural frequencies differed by less than 7 Hz between the analytical solution and a finite element model. For a semiabsorptive termination the experimental method shows the degradation of the high frequency reactive field due to the increased absorption and also the minimal effect on the low order acoustic mode characteristics.

A New Approach to the Solution of Elastohydrodynamic Lubrication of Crankshaft Bearings

1990 ◽  
Vol 204 (3) ◽  
pp. 187-197 ◽  
Author(s):  
H Xu ◽  
E H Smith
Keyword(s):  
Internal Combustion Engines ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Element Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Finite Width ◽  
Time Step ◽  
Non Linear System ◽  
Solution Accuracy

A study of the elastohydrodynamic lubrication of crankshaft bearings in internal combustion engines is presented in this paper. A new method for simulating the performance of a finite width bearing and two-dimensional flexible structure is developed and introduced. The method is based on a finite element model of the structure and finite difference approximation of the Reynolds equation. In order to reduce the number of unknowns in the derived simultaneous equations, a modified form of the Reynolds equation is employed. The non-linear system of integro-differential equations is solved by a Newton—Raphson method. Analysis of a dynamically loaded Ruston—Hornsby bearing is performed and the method is found to be both rapid and robust. The influence of mesh and time step sizes upon the solution accuracy is studied.

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