Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method

Lotfi, Yasaman; Parand, Kourosh; Rashedi, Kamal; Rad, Jamal Amani

doi:10.1007/s00366-019-00835-9

Cited by 6 publications

(2 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Meng et al (2020) proposed a smooth FEM to analyze the displacement, potential, and temperature responses for FGPSs under multi physical coupling fields. Unfortunately, the FEM heavily depends on the mesh, and will cause extraordinary mesh distortion in handling the large deformation and crack propagation problems (Huang et al, 2023a; Lotfi et al, 2021; Meng et al, 2019; Shayegan, 2023). Furthermore, the FEM discretizes the problem domain into a lot of elements with homogeneous material properties, which is difficult to truly simulate the properties of the FGPSs (Dai et al, 2017; Liu et al, 2019b; Yang et al, 2022b).…”

Section: Introductionmentioning

confidence: 99%

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Ma,

Zhou,

et al. 2024

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

Functionally graded piezoelectric structures (FGPSs) have excellent electromechanical properties and are promising for engineering applications. However, the inhomogeneous material properties and piezoelectric effects create great difficulties in the mechanical analysis of the FGPSs. In this paper, a Hermite interpolation element-free Galerkin method (HIEFGM) is proposed for the numerical analysis of the FGPSs. The HIEFGM utilizes a set of nodes to represent the problem domain, which can ideally reflect the inhomogeneous material properties of the FGPSs. Firstly, the governing equations of the FGPSs are derived through the constitutive equation, equilibrium equation, and boundary conditions. Secondly, the approximating function of the field quantities is obtained by the improved moving least-square method and Hermite interpolation. The HIEFGM formulation of the FGPSs is obtained using the variational principle. Furtherly, the influence of weight function, scaling parameter, and node densities on the HIEFGM of the FGPSs is discussed in detail through a parameter study. Finally, the availability of present method is estimated by several examples with different configurations and boundary conditions. The influence of gradation exponent on the electromechanical responses of the FGPSs is analyzed. The results show that the present method has excellent accuracy and stability in analyzing the FGPSs. As the gradation exponent increases, the distribution of the field quantities of the FGPSs exhibits nonlinear characteristics. This work may provide an effective methodology for the analysis of the FGPSs, and contribute to the theoretical research and engineering application of the FGPSs.

show abstract

Section: Introductionmentioning

confidence: 99%

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Ma,

Zhou,

et al. 2024

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

show abstract

“…Determination of a time-dependent free boundary in a two-dimensional parabolic problem was studied in [28]. In [40] the inverse moving boundary problem was solved by applying the radial basis function (RBF) collocation method. The complex variable reproducing kernel particle method and finite point method are applied for inverse problem of heat conduction equations in one dimensional and two dimensional in [16,17,53].…”

Section: Introductionmentioning

confidence: 99%

INverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation

Karami

Abbasbandy

Shivanian

2020

Filomat

View full text Add to dashboard Cite

In this paper we investigated the inverse problem of identifying an unknown time-dependent coefficient and free boundary in heat conduction equation. By using the change of variable we reduced the free boundary problem into a fixed boundary problem. In direct solver problem we employed the meshless local Petrov-Galerkin (MLPG) method based on the moving least squares (MLS) approximation. Inverse reduced problem with fixed boundary is nonlinear and we formulated it as a nonlinear least-squares minimization of a scalar objective function. Minimization is performed by using of f mincon routine from MATLoptimization toolbox accomplished with the Interior - point algorithm. In order to deal with the time derivatives, a two-step time discretization method is used. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments.

show abstract

Numerical solution of singular boundary value problems using advanced Adomian decomposition method

Umesh

Kumar

2020

Engineering with Computers

View full text Add to dashboard Cite

Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method

Cited by 6 publications

References 54 publications

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

INverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation

Numerical solution of singular boundary value problems using advanced Adomian decomposition method

Contact Info

Product

Resources

About