# 탄성 구조물의 안정성을 고려한 형상설계민감도해석

• 최주호 (한국항공대학교 항공우주 및 기계공학부)
• Published : 2006.01.01
• 69 6

#### Abstract

This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section and bottle shaped column are chosen to illustrate the efficiency of the presented method.

#### Keywords

Shape Design Sensitivity Analysis;Buckling Load;Stability Problem

#### References

1. Haftka, R.T. and Gurdal, Z., 1992, Elements of Structual Optimization, Kluwer Academic publishers; 3rd Revised and Expanded Edition, USA
2. Choi, K.K. and Kim, N.H., 2005, Structual Sensitivity Analysis and Optimization, Springer Science+Business Media Inc, USA
3. Gu, Y.X., Zhao, G.Z., Zhang, H.W., Kang, Z. and Grandhi, R.V., 2000, 'Buckling Design Optimization of Complex Built-up Structures with Shape and Size Variables,' Structural Multidisciplinary Optimization, Vol. 19, No. 3, pp. 183-191 https://doi.org/10.1007/s001580050101
4. de Boar, H., van Keulen, F., 2000, 'Refined Semi-Analytical Design Sensitvities,' International Journal of Solids and Structures, Vol. 37, No. 46/47, pp. 6961-6980 https://doi.org/10.1016/S0020-7683(99)00322-4
5. Ozakca, M., Taysi, N., Kolcu, F., 2003, 'Buckling Analysis and Shape Optimization of Elastic Variable Thickness Circular and Annular Plates-II. Shape Optimization,' Engineering Structures, Vol. 25, No. 2, pp. 193-199 https://doi.org/10.1016/S0141-0296(02)00134-7
6. Washizu, K., 1974, Variational Methods in Elasticity and Plasticity, (International Series of Monographs in Aeronautics and Astronautics. Division I: Solid and Structural Mechanics, v. 9), Pergamon Press; 2nd editon, UK
7. Zolesio, J.P., 1981, 'The Material Derivative (or Speed) Method for Shape Optimization,' in Optimization of Distributed Parameters Structures, Haug, E.J. and Cea, J., Sijthoff-Noordhoff, Alphen aan den Rijn, pp. 1152-1194
8. Choi, J.H. and Won, J.H., 2005, 'Boundary Method in FEM-Based Shape Design Sensitivity Analysis of Elastostatics Problems,' submitted to Finite Elements in Analysis and Design