Optimal Shape Design Under Transient Dynamic Loading
This paper deals with the optimal design of structural shapes of member under the action of transient dynamic loads. A mathematical programming approach is proposed and the use of sequential linear programming is recommended for optimization. Transient dynamic analysis is carried out using finite element discretization and modal superposition approach. The paper mainly concentrates on the computation of design sensitivities for shape changes. First the design profile is modelled using a finite number of design ordinates using which the smooth shapes are generated by employing algebraic curves, cubic splines or B-splines. The FE mesh is automatically generated and the nodal coordinate derivatives with respect to design variables are computed and stored. By carrying out the numerical integration of the transformed equation of motion and the adjoint equations in terms of generalized coordinates, the design sensitivities for the time dependent constraints are computed.
KeywordsDesign Variable Design Sensitivity Shape Design Modal Superposition Mathematical Programming Approach
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- 1.RAMAKRISHNAN, C.V. and FRANCAVILLA, A.- Structural Shape Optimization using Penalty Functions, Int. Journal of Struct. Mechanics,vol.3, 403–422(1974).Google Scholar
- 2.FRANCAVILLA, A., RAMAKRISHNAN, C. V. and ZIENKIEWICZ O.C., Optimization of Shape to Minimize Stress Concentration, Journal of Strain Analysis(U.K), vol.10,No.2(1975).Google Scholar
- 3.BENNETT, J.A. and BOTKIN, M.E.- ‘The Optimum Shape’-Automated Structural Design, Plenum Press, 1986.Google Scholar
- 5.LEVY, H.J.-Minimum Weight Design Under Dynamic Loading,Ph.D Dissertation, New York Univ, 1972.Google Scholar
- 6.FENG, T.T. — Optimal Design of Elastic Structures Under Dynamic Loads, Ph.D Dissertation, Mechanics and Hydraulics Program, College of Engineering, Univ.of lowa,May 1975.Google Scholar
- 7.FENG, T.T., ARORA, J.S. and HANG Jr, E.J. — Optimal Structural Design Under Dynamic Loads, Int. Jour, of Num.Meth. Engg, vol. 11, 39–52(1977).Google Scholar
- 8.YANG, R.J. and BOTKIN, M.E. — The Relationship Between the Variational Approach and the Implicit Differentiation Approach to Shape Design Sensitivities — in ‘The Optimum Shape’ by Bennet, J.A. and Botkin, M.E., 1986.Google Scholar
- 9.RAMAKRISHNAN, C.V. — “Development of a Two/Three Dimentional Shape Optimization Program with Solid Modelling,Semi-Automatic Mesh Generation and Adaptive Mesh Refinement” in ‘Control of Boundaries and Stabilization’- J. Simon(Ed.),Springer-Verlag, 1989.Google Scholar