Addendum to: An energy model for the optimal design of linear continuum structures
The original paper of the above title presents an analytical model for problems in the optimal design of linearly elastic continuum structures, where the material modulus tensor has the role of design variable. Both internal (strain) energy and the expression of generalized cost are represented conveniently there, in a form where the modulus tensor is transformed into vector coordinates. The general design of linear continuum structures is stated as a max-min problem. Optimality conditions for the transformed design problem have particularly simple form. Both local properties, represented by the relative values of components of the modulus tensor, and the global distribution of structural resource (material) are variable in the design. With some modification to the original formulation, these separate aspects of design can be represented explicitly in the model. This modified form, which directly facilitates study of the role of local properties in the prediction of optimal design, and which ultimately serves as the basis for schemes to perform computational solution, is described and substantiated here.
energy model continuum structures material design variational formulation minimum compliance