Shape design sensitivity analysis and optimization of general plane arch structures

The problem of shape design sensitivity analysis over a plane arch structure is studied based on a variational formulation of a curved beam in linear elasticity. A general formula is derived using the material derivative concept for the shape design sensitivity of the stress defined at a local segment. The obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation and provides accurate values. Since a complete description is given to the shape and its variation of the arch, the formulation can manage more complex design problems with ease and also gives better optimum design information than previously available. Several examples are used to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems so as to illustrate its excellent applicability. (C) 2002 Elsevier Science B.V. All rights reserved.