Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method

Abstract

Keywords:Finite element method Edge-based smoothed finite element method Thermoelastic crack Crack-tip element Stress intensity factor a b s t r a c t This paper presents a singular edge-based smoothed finite element method (ES-FEM) for solving twodimensional thermoelastic crack problems. The physical domain is first discretized using linear triangular elements which can be generated easily for complicated geometries, and then the smoothing domains are constructed based on edges of these elements. Each smoothing domain is bounded by a set of enclosed line segments. The finite element equations are obtained utilizing the smoothed Galerkin weak form with edge-based smoothing domains. One needs only values of assumed temperature/displacement on each segment of the smoothing domains to form thermal stiffness matrix/stiffness matrix of the system. To produce the proper stress singularity, a layer of five-node crack-tip elements is designed around a crack tip. The stress intensity factors are evaluated using interaction integral with the domain form. Several numerical examples with different boundary conditions are investigated and the numerical results are in excellent agreement with the reference solutions. The thermal and mechanical influence on the crack growth is explored with different thermal and mechanical conditions. It has been found that the present method is more accurate than standard finite element method (FEM) using the same mesh.

Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

“…Work [3] reports a solution to the problem of thermoelasticity. Thermal impact on crack growth under different thermal and mechanical conditions was investigated, based on the edge method (ES-FEM); this method is more accurate than a standard finite-element method (FEM).…”

Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux

“…The algorithm used for the solution of the analyzed problem can be described as follows: the system of integral equations 7, (8) of the problem of heat conduction is used to find the functions µ(t 1 ) and γ ′ (t 2 ). Substituting these functions in the system of equations (9), (12) of the problem of thermoelasticity allows us to find the unknown functions Q 1 (t 1 ) and Q 2 (t 2 ). Then the stress intensity factors (SIF) K I and K II , which are the real quantities that characterize the stress-deformed state in the vicinity of the crack tips, are found according to the formula [14]…”

“…The SIE of heat conduction and thermoelasticity with special Cauchy-type kernels for a plane with thermally insulated cracks or heat-conducting cuts located in a circular foreign inclusion [10], as well as for bodies with thermal cylindrical inclusions and crack [11] are deduced by the method of functions of a complex variable. The solutions of the thermoelasticity problem for a plane with a crack on the basis of the finite element method [12] and the Fourier integral transform method [13] were presented.…”

Thermoelastic fracture modelling in 2D by an adaptive cracking particle method without enrichment functions

“…In recent decades, cracking under steady thermal loading has been studied using conventional numerical methods, and much of the development is similar to the development of non-thermal computational fracture. Examples of early numerical analysis of thermoelastic fracture mechanics use the finite element method (FEM) as in [7,8], where discontinuities of both temperature and displacement at cracks are modelled by element interfaces, so the issue of remeshing during crack propagation remains [9].…”