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ADVANCES IN OPTIMIZATION FOR STRUCTURAL ENGINEERING
Edited by: B.H.V. Topping
Lagrangian Model for Shape Optimal Design of Thin Shells of Revolution
J.I. Barbosa*, C.M. Mota Soares#, C.A. Mota Soares# and R.P. Leal**
*Escola Nautica Infante D. Henrique, Oeiras, Portugal
J.I. Barbosa, C.M. Mota Soares, C.A. Mota Soares, R.P. Leal, "Lagrangian Model for Shape Optimal Design of Thin Shells of Revolution", in B.H.V. Topping, (Editor), "Advances in Optimization for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 199-204, 1996. doi:10.4203/ccp.40.8.2
In this paper the theory of shape and sizing sensitivity analysis is presented for static global and local objective functions and/or constraints for thin axisymmetric shells, using the Lagrangian approach. The design variables considered are thicknesses, nodal radial coordinates and the angle defined by the axis of the revolution and a normal to the frustum generating line.
A model with two node frustum element with eight degrees of freedom is used for the analysis of the real and adjoint structure.
The objective of the design can be the minimization of the volume of the shell material, the minimization of the maximum stresses or the minimization of the maximum displacement. The constraint functions are the displacements, stresses, enclosed volume of the structure and the volume of shell material.
Two test examples are here presented which show that the Lagrangian formulation and an alternative discrete approach using the same element give the same expected results, although the discrete formulation proved to be more efficient with regard to CPU time.
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