Symmetric Shape Transformations of Folded Shell Roofs Determining Creative and Rational Shaping of Building Free Forms

Abstract

The paper presents an innovative approach to solving interdisciplinary problems emerging in the design process of building free forms roofed with elastically transformed corrugated shells. The effectiveness and rationality of shaping such free forms and the creativeness in searching for the parametric forms require the application of their regular and symmetric models which have to be derived from the geometric and mechanical properties of the rationally transformed subsequent folds of these shells. Simplified smooth models used for engineering developments and accurate folded models implemented for scientific research have to be created by means of unconventional methods different from those presented in classical courses. Owing to the variety of the forms of the proposed innovative reference tetrahedrons and their parametric description, the algorithms developed by the authors have to be implemented in computer programs. The rationality of the transformed roof shells, revealed in the limitation of the level of the fold's initial stresses resulting from the shape transformation, and the attractiveness of these forms are achieved by the axial symmetry and contraction of each shell fold at its half-length. The symmetries adopted in the process of modeling such roof shells are also exploited by the discussed new method to obtain coherent unconventional general forms of entire buildings.

Folded Sheets as a Universal Material for Shaping Transformed Shell Roofs

“…Abramczyk [19] invented a condition requiring the contraction of the entire corrugated shell sheeting to pass halfway along the length of each its fold (Figure 6a,b). He utilized the lines of striction of various warped surfaces (Figure 7a,b) to obtain smooth models of shell folds characterized by the effectiveness of their shape transformations [20]. The Abramczyk's method also relates to calculations of the respective surface areas modeling compressing and stretching zones on the transformed folds [21].…”

“…The above dependencies were obtained by means of the experimental tests on the experimental stand [14,20,42] (see Figure 6). They made it possible to configurate the elaborated thin-walled FEM computer models [23] (Figures 14 and 15) used in computer simulations whose results are presented in the next section.…”

“…On the basis of the analysis made to date, it should be stated that the folded sheets with (a) free longitudinal edges (Figure 12a), and (b) stiffened longitudinal edges (Figure 12b) are characterized by mutually different geometrical relationships [14]. Both types of the sheets can be modeled with the same type of ruled surface, but the sectors of this surface corresponding to the above sheets must be different [20]. In the first case, the free longitudinal arcuate edges are modeled with curved lines.…”

“…Figure20. Nonlinear relations between the relative p wr increments of the surface area and the unit twist angle α j of a shell fold supported by two straight directrices obtained for various profiles: Series1-TR50 × 0.75 mm × 8.0 m; Series2-T55 × 0.88 mm × 6.2 m; Series3-TR85 × 0.75 mm × 5.0 m; Series4-TR136 × 0.88 mm × 6.0 m; Series5-T160 × 0.75 mm × 6.6 m.…”