Fast and efficient analysis of transient nonlinear heat conduction problems using combined approximations (CA) method

Abstract The combined approximations (CA) method is very efficient and can provide high quality results, when dealing with structural optimization problems. In this study, the CA method is utilized to reduce the computational effort in transient nonlinear heat transfer analysis. In the CA approach, binomial series are used as high quality basis vectors for reduced basis expression. Transient nonlinear temperature fields are then calculated without solving complete set of nonlinear system equations. Both two-dimensional and three-dimensional numerical problems are studied to verify the accuracy and efficiency of CA method, when solving transient nonlinear heat conduction problems.

[1]  U. Kirsch.  Reduced basis approximations of structural displacements for optimaldesign , 1991 .

[2]  Y. Jarny,et al.  Transient heat conduction within periodic heterogeneous media: A space-time homogenization approach , 2015 .

[3]  P. K. Banerjee,et al.  2D and 3D transient heat conduction analysis by BEM via particular integrals , 2002 .

[4]  Guiyong Zhang,et al.  A node-based smoothed point interpolation method (NS-PIM) for thermoelastic problems with solution bounds , 2009 .

[5]  M. Hematiyan,et al.  Boundary element analysis of nonlinear transient heat conduction problems involving non-homogenous and nonlinear heat sources using time-dependent fundamental solutions , 2010 .

[6]  Xiaolin Huang,et al.  Nonlinear transient response of functionally graded plates with general imperfections in thermal environments , 2007 .

[7]  U. Kirsch,et al.  Efficient reanalysis for topological optimization , 1993 .

[8]  Su-huan Chen,et al.  Structural modal reanalysis for topological modifications with extended Kirsch method , 2003 .

[9]  Eric Li,et al.  Smoothed finite element method with exact solutions in heat transfer problems , 2014 .

[10]  Uri Kirsch,et al.  Procedures for approximate eigenproblem reanalysis of structures , 2004 .

[11]  U. Kirsch.  Combined approximations – a general reanalysis approach for structural optimization , 2000 .

[12]  Satya N. Atluri,et al.  The meshless local Petrov-Galerkin method for the analysis of heat conduction due to a moving heat source, in welding , 2011 .

[13]  Guangyao Li,et al.  A reanalysis method for local modification and the application in large-scale problems , 2014 .

[14]  Guangyao Li,et al.  THERMO-MECHANICAL ANALYSIS OF COMPOSITE PRESSURE VESSELS USING EDGE-BASED SMOOTHED FINITE ELEMENT METHOD , 2014 .

[15]  Oded Amir,et al.  Efficient non‐linear reanalysis of skeletal structures using combined approximations , 2008 .

[16]  G. Y. Li,et al.  A cell-based smoothed radial point interpolation method (CS-RPIM) for heat transfer analysis , 2014 .

[17]  Uri Kirsch,et al.  Nonlinear and dynamic structural analysis using combined approximations , 2007 .

[18]  I. Singh,et al.  Meshless element free Galerkin method for unsteady nonlinear heat transfer problems , 2007 .

[19]  Indra Vir Singh,et al.  A numerical solution of composite heat transfer problems using meshless method , 2004 .

[20]  Uri Kirsch,et al.  Efficient design sensitivities of structures subjected to dynamic loading , 2006 .

[21]  Dawid Taler,et al.  Modeling of transient response of a plate fin and tube heat exchanger , 2015 .

[22]  Uri Kirsch,et al.  Efficient, Accurate Reanalysis for Structural Optimization , 1999 .

[23]  Hu Wang,et al.  A Parallel Reanalysis Method Based on Approximate Inverse Matrix for Complex Engineering Problems , 2013 .

[24]  Uri Kirsch.  Efficient sensitivity analysis for structural optimization , 1994 .

[25]  A. Khosravifard,et al.  Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method , 2011 .

[26]  Hu Wang,et al.  “Seen Is Solution” a CAD/CAE integrated parallel reanalysis design system , 2016 .

[27]  Shengchuan Wu,et al.  An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system , 2010 .

[28]  Uri Kirsch,et al.  Error evaluation in approximate reanalysis of structures , 2004 .

[29]  Toshiro Matsumoto,et al.  Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials , 2006 .

[30]  Uri Kirsch,et al.  Nonlinear dynamic reanalysis of structures by combined approximations , 2006 .

[31]  Uri Kirsch,et al.  A unified reanalysis approach for structural analysis, design, and optimization , 2003 .