Design optimization of nonlinear structures with rate-dependent and rate- independent constitutive models. (English) Zbl 0780.73050
Summary: A design optimization process for nonlinear structures with history- dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material nonlinear effects is used. Shape, non-shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non- shape design parameters are treated in the example problems.
MSC:
| 74P99 | Optimization problems in solid mechanics |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74Hxx | Dynamical problems in solid mechanics |
Keywords:
history-dependent materials; endochronic constitutive theory; yield surface; total Lagrangian formulation; control volume concept; static and impact loading conditionsReferences:
| [1] | and , ’Design sensitivity analysis of nonlinear structures-III: shape variation of viscoplastic structures’, in (ed.), Structural Optimization: Status and Review Chap. 17, AIAA Series: Progress in Astronautics and Aeronautics. American Institute of Aeronautics and Astronautics, Washington, DC, 1993. |
| [2] | Arora, Comput. Struct. 32 pp 691– (1989) |
| [3] | Choi, Int. j. numer. methods eng. 24 pp 2039– (1987) |
| [4] | Haftka, AIAA J. 24 pp 1187– (1986) |
| [5] | Haririan, Comput. Struct. 26 pp 123– (1987) |
| [6] | Ryu, Comput. Struct. 21 pp 245– (1985) |
| [7] | Szefer, Arch. Mech. 39 pp 247– (1987) |
| [8] | Tsay, Struct. Opt. 1 pp 203– (1989) |
| [9] | Tsay, Comp. Methods Appl. Mech. Eng. ASCE 81 pp 183– (1990) |
| [10] | Wu, AIAA J. 25 pp 1118– (1987) |
| [11] | Wu, Eng. with Comput. 2 pp 53– (1987) |
| [12] | Wu, Comput. Mech. 3 pp 129– (1988) |
| [13] | (ed.), Structural Optimization: Status and Promise, AIAA Series: Progress in Aeronautics and Astronautics. American Institute of Aeronautics and Astronautics, Washington, DC, 1993. · doi:10.2514/4.866234 |
| [14] | Jao, Comput. Mech. 8 pp 25– (1991) |
| [15] | Jao, Comput. Mech. 10 pp 39– (1992) |
| [16] | Arora, Eng. Opt. 13 pp 173– (1988) |
| [17] | Introduction to Optimum Design, McGraw-Hill, New York, 1989. |
| [18] | Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1982. |
| [19] | and , Applied Optimal Design, Wiley Interscience, New York, 1979. |
| [20] | Hsieh, Comp. Methods Appl. Mech. Eng. ASCI 43 pp 195– (1984) |
| [21] | The Finite Element Method, McGraw-Hill, New York, 1977. |
| [22] | Arora, Adv. Eng. Software 8 pp 194– (1986) |
| [23] | ’Unified formulation for response analysis and design sensitivity analysis of nonlinear structures using endochronic constitutive theory’, Ph.D Thesis, Graduate College, The University of Iowa, Iowa City, Iowa, 1990. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
