Abstract
An answer to the question how random variations of design parameters affect the static structural response is presented in the paper. A variational approach for structural statics is formulated in the context of the finite element method, and stochastic sensitivity of static response is described in terms of the adjoint system technique. When compared with the conventional perturbations, the suggested technique seems to be original, as being completely second-order accurate. Illustrative examples are dealt with beam and shell elements. Numerical results are given for the first two probabilistic moments of displacement sensitivity gradients with respect to random design parameters. Concluding remarks point out to the need for stochastic sensitivity analysis for a better description of real objects, indicating that dynamic stochastic sensitivity analysis as worthy forthcoming work.
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References
Zienkiewicz, O.C., Taylor, R.L.: The finite element method, vol. 1. McGrew-Hill, London (1989)
Zienkiewicz, O.C., Taylor, R.L.: The finite element method, vol. 2. McGrew-Hill, London (1993)
Bathe K.-J.: Finite Element Procedures. Prentice-Hall, New Jersey (1996)
Haugh E.J., Choi K.K., Komkov V.: Design Sensitivity Analysis of Structural Systems. Academic Press, Orlando (1986)
Mroz Z., Haftka R.T.: First- and second-order sensitivity analysis of linear and nonlinear systems. AIAA J. 24, 1187–1192 (1986)
Choi K.K., Kim N.-H.: Structural Sensitivity Analysis and Optimization. Springer, New York (2010)
Drewko J., Hien T.D.: First- and second-order sensitivities of beams with respect to cross-sectional cracks. Arch. Appl. Mech. 74, 309–324 (2005)
Ding J., Pan Z., Chen L.: Parameter identification of multibody systems based on second order sensitivity analysis. Int. J. Non-Linear Mech. 47, 1105–1110 (2012)
Mroz Z., Bojczuk D.: Shape and topology sensitivity analysis and its application to structural design. Arch. Appl. Mech. 82, 1541–1555 (2012)
Bojczuk D., Mroz Z.: Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate. Struct. Multidisc. Optim. 45, 153–169 (2012)
Ghanem R.G., Spanos P.D.: Stochastic Finite Elements: A Spectral Approach. Springer, New York (1991)
Hisada, T., Nakagiri, S.: Stochastic finite element method for structural safety and reliability. Proc. 3rd Int. Conf. Struct. Safety Reliab., 395–402 (1981)
Liu W.K., Belytschko T., Mani A.: Random field finite elements. Int. J. Numer. Methods Eng. 23, 1831–1845 (1986)
Li J., Chen J.: Stochastic Dynamics of Structures. Wiley, Singapore (2009)
Greene M.S., Liu Y., Chen W., Liu W.K.: Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory. Comput. Methods Appl. Mech. Eng. 200, 309–325 (2011)
Kleiber M., Hien T.D.: The Stochastic Finite Element Method. Wiley, New Jersey (1992)
Kleiber, M., Hien, T.D.: Stochastic structural design sensitivity of static response. Int. J. Comput. Struct. 38, 659–667, (1991) Pergamon Press
Sluzalec A.: Stochastic shape sensitivity in powder metallurgy processing. Appl. Math. Model. 36, 3743–3752 (2012)
Rahman S.: Stochastic sensitivity analysis by dimensional decomposition and score functions. Probabilistic Engineering Mechanics 24, 278–287 (2009)
Liu W.K., Belytschko T., Mani A.: Probabilistic finite elements for nonlinear structural dynamics. Comput. Methods Appl. Mech. Engrg. 56, 64–81 (1986)
Jablonka A., Hien T.D.: Damping and dynamic sensitivity (in Polish: Tlumienie a wrazliwosc dynamiczna). Pomiary Automatyka Kontrola 57, 1040–1043 (2011)
Jablonka, A.: Numerical dynamic analysis of complex structures (in Polish: Numeryczna analiza dynamiczna konstrukcji zlozonych). Wybrane zagadnienia z dziedziny budownictwa, 535–543, Wyd. Pol. Sl. (2011)
Hien T.D., Kleiber M.: POLSAP—A Finite Element Code for Deterministic and Stochastic Analyses of Large 3D Structures. IPPT PAN, Warszawa (1990)
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Jablonka, A., Hien, T.D. A modified perturbation scheme for structural statics systems with random parameters. Arch Appl Mech 84, 821–831 (2014). https://doi.org/10.1007/s00419-014-0835-0
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DOI: https://doi.org/10.1007/s00419-014-0835-0