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Sensitivity analysis and shape optimization based on FE–EFG coupled method

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Abstract

By use of 4-node isoparametric quadrangle interface element between finite element (FE) and meshless regions, a collocation approach is introduced to couple firstly FE and element-free Galerkin (EFG) method in this paper. By taking derivative of discreteness equilibrium equation at interface element with respect to design variable, a numerical method for discreteness-based shape design sensitivity analysis in interface element is obtained. The design sensitivity analysis (DSA) of coupled FE–EFG method is achieved by employing the DSA of nodal displacement at the interface element. The numerical method presented is testified by examples. It can be observed excellent agreement between the numerical results and the analytical solution. Finally the shape optimization of fillet is achieved by using coupled FE–EFG method. The result obtained show that imposing of the essential boundary condition is easy to implement, the computational time is reduced and the distortion of mesh is avoided.

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References

  • Arora JS (1993) An exposition of the material derivative approach for structural shape sensitivity analysis. Comput Methods Appl Mech Eng 105:41–62

    Article  MATH  MathSciNet  Google Scholar 

  • Attaway SW, Heinstein MW, Swegle JW (1994) Coupling of smooth particle hydrodynamics with the finite element method. Nuclear Eng Des 150(3):199–205

    Article  Google Scholar 

  • Belegundu AD, Rajan SD (1988) A shape optimization approach based on natural design variable and shape function. Comput Methods Appl Mech Eng 66:87–106

    Article  MATH  Google Scholar 

  • Belytschko T, Lu YY, Gu L (1994) Element free Galerkin method. Int J Numer Methods Eng 37:229–256

    Article  MATH  MathSciNet  Google Scholar 

  • Belytschko T, Organ D, Krongauz Y (1995) A coupled finite element-element free Galerkin method. Comput Mech 17:186–195

    MATH  MathSciNet  Google Scholar 

  • Belytschko T, Krongauz Y, Organ D et al (1996) Meshless method: an overview and recent developments. Comput Methods Appl Mech Eng 139:3–47

    Article  MATH  Google Scholar 

  • Bobaru F, Mukherjee S (2001) Shape sensitivity analysis and shape optimization in planar elasticity using the element-free Galerkin method. Comput Methods Appl Mech Eng 190:4319–4337

    Article  MATH  Google Scholar 

  • Botkin ME (1982) Shape optimization of plate and shell structures. AIAA J 20(2):268–273

    Article  Google Scholar 

  • Bokin ME, Bennett JA (1985) Shape optimization of three-dimension folded plate structures. AIAA J 23(11):1804–1810

    Article  Google Scholar 

  • Braibant V, Morelle P (1990) Shape optimization design and free mesh generation. Struct Optim 2:223–231

    Article  Google Scholar 

  • Bugeda G, Oliver J (1993) A general methodology for structural shape optimization problems using automatic adaptive remeshing. Int J Numer Method Eng 36:3161–3185

    Article  MATH  Google Scholar 

  • Chen T, Raju IS (2003) A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems. Comput Methods Appl Mech Eng 192:4533–4550

    Article  MATH  Google Scholar 

  • De Vuyst T, Vignjevic R, Campbell JC (2005) Coupling between meshless and finite element method. Int J Impact Eng 31:1054–1064

    Article  Google Scholar 

  • Ding YL (1986) Shape optimization of structures: a literature survey. Comp Struct 24(6):985–1004

    Article  MATH  Google Scholar 

  • Gong SG, Chen YP, Huang YQ (2005a) Study on design sensitivity analysis based on EFG method in mechanical shape optimization. In: International conference on mechanical engineering and mechanics, proceedings of ICMEM2005, October 26–28, 2005, Nanjing, China, pp 876–881

  • Gong SG, Huang YQ, Xie GL et al (2005b) The shape optimization and sensitivity analysis based on fictitious load variable (in Chinese). Chin J Comput Mech 22(2):183–188

    Google Scholar 

  • Gong SG, Chen YP, Huang YQ et al (2006) Shape optimization and design sensitivity analysis based on element-free Galerkin method (in Chinese). Chin J Mech Eng 42(6):199–204

    Article  Google Scholar 

  • Grindeanu I, Kim NH, Choi KK, Chen JS (2002) CAD-based shape optimization using a meshfree method. Concurr Eng Res Appl 10(1):55–66

    Article  Google Scholar 

  • Gu YX, Cheng GD (1993) Research and application of numerical methods of structural shape optimization (in Chinese). Comp Struct Mech Appl 10(3):321–335

    Google Scholar 

  • Haftka RT, Grandhi RV (1986) Structure shape optimization: a survey. Comput Methods Appl Mech Eng 57:91–106

    Article  MATH  MathSciNet  Google Scholar 

  • Hegen D (1996) Element-free Galerkin methods in combination with finite element approaches. Comput Methods Appl Mech Eng 135:143–166

    Article  MATH  Google Scholar 

  • Howard MA, Raphael TH (1986) Sensitivity analysis of discrete structural system. AAIA J 24(5):823–832

    Article  Google Scholar 

  • Huerta A, Fernández-Méndez S, Liu W (2004) A comparison of two formulations to blend finite elements and mesh-free methods. Comp Methods Appl Mech Eng 193:1105–1117

    Article  MATH  Google Scholar 

  • Karutz H, Kräetzig WB (2002) A quadtree data structure for the coupled finite-element/element-free Galerkin method. Int J Numer Methods Eng 53:375–391

    Article  MATH  Google Scholar 

  • Karutz H, Chudoba R, Krätzig WB (2002) Automatic adaptive generation of a coupled finite element/element-free Galerkin discretization. Finite Element Anal Des 38:1075–1091

    Article  MATH  Google Scholar 

  • Kim NH, Choi KK, Chen JS et al (2000) Meshless shape design sensitivity and optimization for contact problem with friction. Comput Mech 25:157–168

    Article  MATH  Google Scholar 

  • Kim NH, Choi KK, Botkin ME (2003) Numerical method for shape optimization using meshfree method. Struct Multidiscipline Optim 24:418–429

    Article  Google Scholar 

  • Krongauz Y, Belytschko T (1996) Enforcement of essential boundary conditions in meshless approximation using finite element. Comput Methods Appl Mech Eng 131:133–145

    Article  MATH  MathSciNet  Google Scholar 

  • Lacroxi D, Bouillard Ph (2003) Improved sensitivity analysis by a coupled FE–EFG method. Comp Struct 81:2431–2439

    Article  Google Scholar 

  • Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares method. Math Comput 37:141–158

    Article  MATH  MathSciNet  Google Scholar 

  • Liu GR, Gu YT (2001) A point interpolation method for two-dimension solids. Int J Numer Methods Eng 50:937–951

    Article  MATH  Google Scholar 

  • Liu TX, Liu G (2003) On applying EFG–FE coupling method to solving 2-D contact problems (in Chinese). J Northwestern Polytech Univ 21(4):499–503

    Google Scholar 

  • Pandey PC, Bakshi P (1999) Analytical response sensitivity computation using hybrid finite elements. Comput Struct 71:525–534

    Article  Google Scholar 

  • Phan AV, Mukherjee S, Mayer JR (1998) Stress, stress sensitivity and shape optimization in two-dimensional linear elasticity by the boundary contour method. Int J Numer Methods Eng 42:1391–1407

    Article  MATH  MathSciNet  Google Scholar 

  • Rabczuk T, Eibl J (2004) Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element approach. Int J Solids Struct 41:1061–1080

    Article  MATH  Google Scholar 

  • Rao BN, Rahman S (2001) A coupled meshless-finite element method for fracture analysis of cracks. Int J Pressure Vessels Piping 78:647–657

    Article  Google Scholar 

  • Sauer M (2000) Adaptive Kopplung des Netzfreien SPH-Verfahrensmit Finiten Elementen zur Berechnung von Impaktvorgängen, PhD thesis, Universität der Bundeswehr München (Deutschland)

  • Timoshenko SP, Goodier JN (1970) Theory of elasticity. McGraw-Hill, New York

    MATH  Google Scholar 

  • Van Keulen F, Haftka RT, Kim NH (2005) Review of options for structural design sensitivity analysis. Part I: linear systems. Comput Methods Appl Mech Eng 194:3213–3243

    Article  MATH  Google Scholar 

  • Wang XM, Zhou JX, Zhang ZQ et al (2005) Improved reproducing kernel particle method for shape design sensitivity analysis (in Chinese). Chin J Comput Mech 22(4):420–424

    Google Scholar 

  • Xiao QZ, Dhanasekar M (2002) Coupling of FE and EFG using collocation approach. Adv Eng Softw 33:507–515

    Article  MATH  Google Scholar 

  • Yang R, Chol KK (1985) Accuracy of finite element shape design sensitivity analysis. J Struct Mech 13(2):223–239

    Google Scholar 

  • Yang HT, Liu Y (2003) A coupled FEM–EFGM technique and its application (in Chinese). Chin J Comput Mech 20(5):511–517

    Google Scholar 

  • Zhang YJ, Wang SJ, Wang EZ (2003) Analysis of two-phase continuous porous media with FEM-EFGM coupled method (in Chinese). Chin J Comput Phys 20(2):142–146

    Google Scholar 

  • Zhang JP, Gong SG, Li YM, Chen RK (2008) Structural dynamic shape optimization and sensitivity analysis based on RKPM. Struct Multidisciplinary Optim 36(3):307–317

    Article  Google Scholar 

Download references

Acknowledgments

This research is funded by National Natural Science Foundation of China [50875223,50475143], Supported by Scientific Research Fund of Hunan Provincial Education Department [06B096,08A079] and Doctoral Research Fund of Xiangtan University [06QDZ16]. The financial support to the first author is gratefully acknowledged.

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Authors and Affiliations

  1. School of Mechanical Engineering, Xiangtan University, Xiangtan, Hunan, 411105, China

    S. G. Gong, G. L. Xie, J. P. Zhang, S. H. Nie & Y. M. Li

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  1. S. G. Gong
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  2. G. L. Xie
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  3. J. P. Zhang
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  4. S. H. Nie
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  5. Y. M. Li
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Correspondence to S. G. Gong.

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Gong, S.G., Xie, G.L., Zhang, J.P. et al. Sensitivity analysis and shape optimization based on FE–EFG coupled method. Res Eng Design 20, 117–128 (2009). https://doi.org/10.1007/s00163-008-0057-y

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  • DOI: https://doi.org/10.1007/s00163-008-0057-y

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