Abstract
A numerical method of structural dynamic shape optimization is presented by using reproducing kernel particle method (RKPM), by which the mesh distortion that exists in shape optimal method based on finite element can be eliminated completely and the optimal model for structural dynamic optimization design is built. The discreteness-based design sensitivity analysis in both natural frequency and dynamic response is proposed by using direct differentiation method and discrete derivatives on the basis of structural dynamic analysis, in which the penalty method is employed into imposing the essential boundary conditions, and the derivatives of shape functions with respect to design variables are derived. The algorithm of dynamic sensitivity analysis is testified by numerical example, and the numerical results obtained are in good agreement with those obtained using semi-analytical method and global finite differences method. Finally, by integrating the algorithm mentioned based on RKPM with parameterized descriptive method of boundary shape, two examples for structural dynamic shape optimization are performed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bakshi P, Pandey PC (2000) Semi-analytical sensitivity using hybrid finite elements. Comput Struct 77(2):201–213
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
Bogomolni M, Kirsch U, Sheinman I (2006) Efficient design sensitivities of structures subjected to dynamic loading. Int J Solids Struct 43(18–19):5485–5500
Falco SA, Afonso SMB, Vaz LE (2004a) Analysis and optimal design of plates and shells under dynamic loads-I: finite element and sensitivity analysis. Struct Multidiscipl Optim 27(3):189–196
Falco SA, Afonso SMB, Vaz LE (2004b) Analysis and optimal design of plates and shells under dynamic loads-II: optimization. Struct Multidiscipl Optim 27(3):197–209
Francavilla A, Ramakrishnan CV, Zienkiewicz OC (1975) Optimization of shape to minimize stress concentration. J Strain Anal 10(2):63–70
Gong SG, Chen YP, Huang YQ (2006a) Application research of meshless method in shape optimization. China Mech Eng 17(12):1290–1294 (In Chinese)
Gong SG, Chen YP, Huang YQ et al (2006b) Shape optimization and sensitivity analysis based on element-free galerkin methods. Chin J Mech Eng 42(6):199–204 (In Chinese)
Grandhi R (1993) Structural optimization with frequency constraints-a review. AIAA J 31(12):2296–2303
Grindeanu I, Choi KK, Chen JS et al (1999) Shape design optimization of hyperelastic structures using a meshless method. AIAA J 37(8):990–997
Gu SN, Xu B, Rong JH et al (2005) Recent progresses on structural dynamic design methods. J Mech Strength 27(2):156–162 (In Chinese)
Keulen FV, Haftka RT, Kim NH (2005) Review of option for structural design sensitivity analysis part I: linear system. Comput Methods Appl Mech Eng 194:3213–3243
Kim NH, Choi KK (2001) Design sensitivity analysis and optimization of nonlinear transient dynamics. Mechan Struct Mach 29(3):351–371
Kim NH, Choi KK, Chen JS et al (2000) Meshless shape design sensitivity analysis and optimization for contact problem with friction. Comput Mech 25:157–168
Kim NH, Choi KK, Botkin ME (2003) Numerical method for shape optimization using meshfree method. Struct Multidiscipl Optim 24:418–429
Liao BY, Zhou XM, Yin ZH (2003) Modern mechanical dynamics and its engineering application-modeling, analysis, simulation, control, modification and optimization. China Machine Press, Beijing (Chinese version)
Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Eng 20:1081–1106
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
Pourazady M, Fu Z (1996) An integrated approach to structural shape optimization. Comput Struct 60(2):279–289
Rong JH, Zheng JL, Xu FH (2002) Structural dynamic modification and optimization design. China Communications Press, Beijing (Chinese version)
Yoo HH, Cho JE, Chung JT (2006) Modal analysis and shape optimization of rotating cantilever beams. J Sound Vib 290:223–241
Zhang ZQ, Zhou JX, Zhou N et al (2005) Shape optimization using reproducing kernel particle method and an enriched genetic algorithm. Comput Methods Appl Mech Eng 194:4048–4070
Zhou JX, Wang XM, Zhang ZQ et al (2005a) On the enhancement of computation and exploration of discretization approaches for meshless shape design sensitivity analysis. Struct Multidiscipl Optim 31:96–104
Zhou JX, Zhang HY, Zhang L (2005b) Reproducing kernel particle method for free and forced vibration analysis. J Sound Vib 279:389–402
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, J., Gong, S., Huang, Y. et al. Structural dynamic shape optimization and sensitivity analysis based on RKPM. Struct Multidisc Optim 36, 307–317 (2008). https://doi.org/10.1007/s00158-007-0166-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-007-0166-7