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An optimization method is presented for design of tree-type frames as supporting structures of free-form shells. A unified algorithm for modeling complex external boundary as well as the internal boundary is presented utilizing the B-spline curves of orders with odd numbers. An algorithm for generating tree-type frame is presented based on iterative function system (IFS) of fractal geometry. The type of branching of the tree is selected from the list of preassigned types. Formulations of sensitivity analysis are presented for total strain energy with respect to the nodal coordinates including those constrained on the shell surface. It is demonstrated in the numerical examples that the nodal locations of the tree-type support structure can be optimized to minimize the total strain energy of the structure including the roof and support frame. It is shown that the strain energy due to bending deformation is mainly reduced through optimization; thus, an ideal load path utilizing axial forces to the ground is achieved.

SHAPE GENERATION OF TREE-TYPE SUPPORT STRUCTURE OF FREE-FORM SHELL USING FRACTAL GEOMETRY