Finite block method for transient heat conduction analysis in functionally graded media

A peridynamic (PD) model of functionally graded materials (FGMs) is presented to simulate transient heat conduction in the FGM plate with insulated cracks. The surface correction is considered in the model to reduce the surface effect near the domain boundary and insulated cracks. In order to verify the proposed model, a numerical example for the FGM plate is carried out. The results show good agreement with the analytical solution. The convergence of the model with the surface correction for FGMs without cracks is then investigated. The results reveal that our model converges to the classical solutions in the limit of the horizon going to zero. The effects of two material points discretization schemes on the accuracy of numerical results are investigated. For transient heat conduction of FGMs with a static crack, the results obtained from the proposed PD model agree well with that from the finite element method. Finally, transient heat conduction of the FGM plate with a dynamic horizontal crack and intersecting cracks is simulated and discussed.

Download Full-text

A New and Efficient Meshless Computational Approach for Transient Heat Conduction in Anisotropic Nonhomogeneous Media: Fragile Points Method and Local Variational Iteration Scheme

Volume 11: Heat Transfer and Thermal Engineering ◽

10.1115/imece2020-24516 ◽

2020 ◽

Author(s):

Yue Guan ◽

Rade Grujicic ◽

Xuechuan Wang ◽

Leiting Dong ◽

Satya N. Atluri

Keyword(s):

Heat Conduction ◽

Computing Time ◽

Nonlinear Problems ◽

Transient Heat Conduction ◽

Current Approach ◽

Computational Approach ◽

Functionally Graded ◽

Efficient Technology ◽

Variational Iteration ◽

Backward Euler

Abstract A new and efficient computational approach is presented for analyzing transient heat conduction problems. The Fragile Points Method (FPM) utilized for spatial discretization can, on one hand, like many other meshless methods, be free of the requirement of high-quality meshing, and on the other hand, bypass the difficulty of domain integration problem which is commonly seen in Galerkin meshfree methods. With local, polynomial and discontinuous trial and test functions, the method has a great potential in solving problems with rupture and fragmentation without remeshing. Anisotropy and nonhomogeneity which is challengeable for many spatial numerical methods do not give rise to any difficulties in the present implementation. The Local Variational Iteration Method (LVIM) in the time domain is a highly efficient technology in solving nonlinear problems, in which the time steps can be an order of magnitude larger than the traditional backward Euler scheme and the computing time can be cut by a half. The FPM+LVIM solver is also connected to the prepossessing module of ABAQUS which helps generating the domain partition. It shows the compatibility of the current approach with various partitions and makes it more friendly for engineer users. Several 2D and 3D numerical examples with functionally graded and composite materials are then provided as validations.

Download Full-text