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2003 Fiscal Year Final Research Report Summary

HIGHER NUMERICAL EFFICIENCY AND ACCURACY THROUGH MESHLESS EVALUATION OF DOMAIN INTEGRALS

Research Project

Project/Area Number 13650080
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Materials/Mechanics of materials
Research InstitutionSHINSHU UNIVERSITY

Principal Investigator

TANAKA Masataka  SHINSHU UNIVERSITY, FACULTYY OF ENGINEERING, PROFESSOR, 工学部, 教授 (40029319)

Co-Investigator(Kenkyū-buntansha) MATSUMOTO Toshiro  SHINSHU UNIVERSITY, FACULTY OF ENGINEERING, ASSOCIATE PROFESSOR, 工学部, 助教授 (10209645)
Project Period (FY) 2001 – 2003
KeywordsComputational Mechanics / Boundary Element Method / Integral Equation / Domain Integral / Dual Reciprocity Method / Meshless Evaluation / Fundamental Solution / Heat Conduction
Research Abstract

The main advantage of the boundary element methods is that in most linear problems accurate numerical analysis can be performed through mesh division of the boundary only. However, even for the linear problems of inhomogeneous materials where the property changes as a function of coordinates or of the inhomogeneous initial conditions, domain integrals inevitably arise in the boundary integral equation to be solved. In these cases, we have to evaluate the domain integrals using the cell or element division of the domain. This would lead to reducing attraction of the boundary element method. In other cases an "approximate" fundamental solution is employed for the formulation, we have to discretize the domain and include the nodal quantities in the domain as the final system of equations. Therefore, it has been one of the main subjects of the BEM how to effectively evaluate such domain integrals.
In boundary element research so far, there are several methods available in the literature : The boundary-domain element or Green element method, multi-reciprocity or dual reciprocity method, the analog equation method, and so on. Among them, the dual reciprocity method seems to be very attractive to evaluate approximately the domain integrals by using rather simple functions.
This paper is concerned with numerical investigations of the dual reciprocity method for some typical problems frequently encountered in practice. First, we had been collecting a wide range of approximate functions which can be used for the dual reciprocity method. Then, we had applied some selected functions to the problem solving and checked the numerical properties of solution procedure based on the dual reciprocity principle. Through these investigations we can develop very good computer codes for accurate, efficient analysis of the problems. A series of the academic papers on the topics have been submitted to international journals, and most of them have been already published.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 石黒周司: "境界要素法による異方性体の2次元非線形非定常熱伝導解析"日本機械学会論文集(A編). 69A-680. 707-710 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masataka Tanaka: "An inverse problem of coupled thermoelasticity in reconstructing heat fluxes and thermal stresses"Proc.11^<th> Annual ASCE Conf. 173-176 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 石黒周司: "ホモトピー論を用いた改良化された境界要素法による異方性体の2次元非線形非定常熱伝導解析"長野県工科短期大学校紀要. 6. 1-5 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Krishna M.Singh: "Dual reciprocity boundary element analysis of transient advection-diffusion"Int.J.Numerical Methods for Heat & Fluid Flow. 13. 663-646 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 田中 正隆: "温度依存性材料の非定常熱伝導問題に対する時間ステップDRBEM(2次元問題の検討)"境界要素法論文集. 20. 45-50 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 田中 正隆: "非定常熱伝導問題の時間ステップBEMへの二重相反法の適用(3次元問題での検討)"日本機械学会2003年度年次大会講演論文集. Vol.I. 77-78 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Ishiguro, M.Tanaka: "Boundary element analysis of transient nonlinear heat conduction problems"Trans.JSME. Vol.69A. 707-710 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, A.Guzik: "An inverse problem of coupled thermoelasticity in reconstructing heat fluxes and thermal stresses"Proc. 11^<th> Annual ASCE Conf.. 173-176 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Ishiguro, M.Tanaka: "Boundary element analysis of transient nonlinear heat conduction problem based on homotopy theory"Bull. Nagano Polytech.. Vol.6. 1-6 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.M.Singh, M.Tanaka: "Dual reciprocity boundary element analysis of transient advection-diffusion"Int. J. Numerical Methods for Heat & Fluid Flow. Vol.13. 663-646 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, S.TaKaKuwa: "Time-stepping BEM via DRM for transient heat conduction problems"Trans. JASCOME, J. of BEM. Vol.20. 45-50 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, S.Takakuwa: "A dual reciprocity time-stepping BEM for transient heat conduction problems of functionally graded materials"Trans. JSME, Ser.A. Vol.68A. 1702-1707 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, Y.Suda: "A dual reciprocity BEM applied to the thermoelastic problem of temperature-dependent materials"Trans. JSME, Ser.A. Vol.68A. 1285-1291 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, Y.Suda, S.Takakuwa: "Application of dual reciprocity method to time-stepping BEM applied to the transient heat conduction problem"Bulletin of JASCOME. Vol.2. 1-4 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, Y.Suda: "A dual receiprocity BEM applied to the steady-state heat conduction problem in temperature-dependent materials"Trans. JSME, Ser.A. Vol.68A. 717-722 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tanaka, T.Matsumoto, S.Takakuwa: "Dual reciprocity time-stepping BEM applied to the transient heat conduction problem of functionally graded materials (Study on 3D problems)"Trans. JASCOME, J of BEM. Vol.190. 21-26 (2002)

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Published: 2005-04-19  

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