Study on steady-state thermal conduction with singularities in multi-material composites

Increasing demand in material and mechanical properties has led to production of complex composite structures. The composite structures, made of different materials, possess a variety of properties derived from each material. This has brought challenges in both analytical and numerical studies in thermal conduction which is of significant importance for thermoelastic problems. Therefore, a unified and effective approach would be desirable. The present study makes a first attempt to determining the analytical symplectic eigen solution for steady-state thermal conduction problem of multi-material crack. Based on the obtained symplectic eigen solution (including higher order expanding eigen solution terms), a new symplectic analytical singular element (SASE) for numerical modeling is constructed. It is concluded that composite structures composed of multi-material with complex geometric shapes can be modeled by the developed method, and the generalized flux intensity factors (GFIFs) can be solved accurately and efficiently.

[1]  T. Q. Bui,et al.  Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method , 2013 .

[2]  T. Chiu,et al.  Heat conduction in a functionally graded medium with an arbitrarily oriented crack , 2013 .

[3]  Xiaofei Hu,et al.  A novel singular finite element on mixed-mode bimaterial interfacial cracks with arbitrary crack surface tractions , 2011 .

[4]  T. Q. Bui,et al.  Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading , 2012 .

[5]  C. Chao,et al.  Thermal problem of curvilinear cracks in bonded dissimilar materials , 1993 .

[6]  Xiaofei Hu,et al.  A Novel Singular Finite Element on Mixed-Mode Dugdale Model Based Crack , 2012 .

[8]  Chuanzeng Zhang,et al.  Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM , 2013 .

[9]  Tinh Quoc Bui,et al.  Analysis of cracked shear deformable plates by an effective meshfree plate formulation , 2015 .

[10]  Sohichi Hirose,et al.  An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics , 2015 .

[11]  A. Leung,et al.  Hamiltonian Approach to Analytical Thermal Stress Intensity Factors—Part 1: Thermal Intensity Factor , 2010 .

[12]  Sohichi Hirose,et al.  Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element , 2015 .

[13]  L. Marin.  A meshless method for the stable solution of singular inverse problems for two-dimensional Helmholtz-type equations , 2010 .

[14]  M. Denda,et al.  A formalism for anisotropic heat transfer phenomena: Foundations and Green’s functions , 2014 .

[15]  V. Mantič,et al.  Treatment of singularities in Helmholtz-type equations using the boundary element method , 2004 .

[16]  Bhushan Lal Karihaloo,et al.  Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery , 2006 .

[17]  Martin Costabel,et al.  Edge Stress Intensity Functions in Polyhedral Domains and their Extraction by a Quasidual Function Method , 2004 .

[18]  Chuanzeng Zhang,et al.  Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method , 2014 .

[19]  A. Leung,et al.  Finite-Element Discretized Symplectic Method for Steady-State Heat Conduction with Singularities in Composite Structures , 2015 .

[20]  Xiaofei Hu,et al.  A new enriched finite element for fatigue crack growth , 2013 .

[21]  Chuanzeng Zhang,et al.  Interfacial dynamic impermeable cracks analysis in dissimilar piezoelectric materials under coupled electromechanical loading with the extended finite element method , 2015 .

[22]  Bhushan Lal Karihaloo,et al.  XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi‐materials , 2004 .

[23]  W. Zhong,et al.  Hamiltonian principle based stress singularity analysis near crack corners of multi-material junctions , 2003 .

[24]  S. W. Tsai,et al.  Temperature distribution and heat flow around a crack of arbitrary orientation in a functionally graded medium , 2014 .

[25]  Zohar Yosibash,et al.  Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation , 2011 .

[26]  Bin Chen,et al.  Singular boundary method for heat conduction problems with certain spatially varying conductivity , 2015, Comput. Math. Appl..

[27]  T. Q. Bui,et al.  Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method , 2014 .

[28]  Zhaojun Zhang,et al.  A singular element for reissner plate bending problem with V-shaped notches , 2014 .

[29]  Soheil Mohammadi,et al.  Thermo-mechanical XFEM crack propagation analysis of functionally graded materials , 2013 .

[30]  L. Marin.  An invariant method of fundamental solutions for two-dimensional steady-state anisotropic heat conduction problems , 2016 .

[31]  Q. Qin,et al.  Symplectic model for piezoelectric wedges and its application in analysis of electroelastic singularities , 2007 .

[32]  N. S. Mera,et al.  An iterative algorithm for singular Cauchy problems for the steady state anisotropic heat conduction equation , 2002 .

[33]  Liviu Marin,et al.  Treatment of singularities in the method of fundamental solutions for two-dimensional Helmholtz-type equations , 2010 .

[34]  Tinh Quoc Bui,et al.  A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures , 2015 .

[35]  Barna A. Szabó,et al.  Numerical analysis of singularities in two-dimensions part 1: Computation of eigenpairs , 1995 .

[36]  Xiaofei Hu,et al.  A novel singular finite element of mixed-mode crack problems with arbitrary crack tractions , 2011 .

[37]  T. Q. Bui.  Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS , 2015 .

[38]  Julien Yvonnet,et al.  A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM , 2011 .

[39]  Wen Chen,et al.  The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity , 2015 .

[40]  Tinh Quoc Bui,et al.  On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis , 2016 .

[41]  N. S. Mera,et al.  Singularities in anisotropic steady‐state heat conduction using a boundary element method , 2002 .

[42]  Chuanzeng Zhang,et al.  Transient dynamic interface crack analysis in magnetoelectroelastic bi-materials by a time-domain BEM , 2015 .

[43]  C. Chao,et al.  Thermal problem of curvilinear cracks in bonded dissimilar materials with a point heat source , 1993 .

[44]  Yan Gu,et al.  Singular boundary method for inverse heat conduction problems in general anisotropic media , 2014 .

[45]  T. Rabczuk,et al.  Extended isogeometric analysis for dynamic fracture in multiphase piezoelectric/piezomagnetic composites , 2016 .

[46]  G. C. Sih,et al.  Heat Conduction in the Infinite Medium With Lines of Discontinuities , 1965 .

[47]  A. Leung,et al.  Electroelastic singularities and intensity factors for an interface crack in piezoelectric–elastic bimaterials , 2015 .

[48]  L. Marin.  Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data , 2008 .

[49]  G. Tupholme,et al.  Steady-state heat transfer through extended plane surfaces , 1995 .