Folded Sheets as a Universal Material for Shaping Transformed Shell Roofs

This article provides a novel insight into specific properties of flat folded sheets transformed elastically into building roof shells. Elastic twist transformations of the sheets resulting from the arrangement of the sheets on two skew roof directrices cause changes in the geometric and mechanical sheet properties of the roof shell sheeting composed of these sheets. Regular smooth-ruled surfaces and their characteristic lines are used in the analysis of changes in the geometric properties. In the analysis of the mechanical changes, the constitutive relations and complex state of stresses are considered. The analysis is carried out on the basis of the results of the experimental tests and FEM computer simulations. They have led to the development of such a method of shaping of the effectively transformed folded covers that ensures the initial effort of each shell fold to be the smallest possible.

Innovative Building Forms Determined by Orthotropic Properties of Folded Sheets Transformed Into Roof Shells

Qualitative and quantitative characteristics of geometrical and mechanical changes of nominally plane steel sheets folded in one direction, caused by big elastic shape transformations were invented on the basis of the authors' tests, analyzes and computational models of thin-walled folded sheets transformed into shell shapes. Both geometrical and mechanical changes produce significant restrictions in using sheets for shell forms. The deliberate transformations and sheets' characteristics are required to obtain attractive and innovative forms of roof shells and their consistent structures as well as entire buildings. The search for effective solutions related to free forms of buildings and shape transformations of sheets especially in the fields of: shape transformation, effort and stabilization of their walls is necessary due to the high sensitivity of thin-walled open profiles to boundary conditions and loads. A method for shaping such free form buildings that effectively exploit specific orthotropic properties of the transformed sheeting is presented.

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

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.

Effect of the number of design variables in thickness optimization of concrete barrel roof shells using evolutionary algorithms

This study looks into some practical implications of using evolutionary algorithms for optimization of free-form concrete shells in search of methods for automating design representation and determining the number of design variables. This study reports the insights and learnings from a set of numerical experiments, by changing the number of parameters, on thickness optimization of a barrel roof shell subjected to self-weight, an additional snow load, and an earthquake response spectrum. The practical advantages and challenges of two methods, parametric and direct representations, are analysed, and a spectrum of methods between these two extremes are investigated through experiments. The results demonstrate how changing the number of variables affects the quality of the design and the performance of the algorithm and why a systematic problem-dependent method for finding the best design representation and number of variables outside this spectrum can be beneficial.

Bifurcation Buckling Analysis of Conical Roof Shell Subjected to Dynamic Internal Pressure by the Finite Element Method

Cylindrical tanks with conical roof shells are utilized as oil storage tanks and for some containment vessels. It is known that conical roof shells and torispherical shells subjected to static internal pressure buckle into a displaced shape with circumferential waves caused by an instability condition commonly called bifurcation buckling. It can be important to obtain the dynamic bifurcation buckling load in designing conical roof shells. In this paper, the bifurcation buckling pressure is calculated for dynamic pressure during accident conditions as characterized by step pressure loading, ramp pressure loading and pulse pressure loading. The minimum bifurcation buckling pressure is shown to be a linear function of radius-to-thickness ratio R/h of the shell in a linear fashion on a logarithmic scale. The minimum bifurcation buckling pressure is minimum for conical roof shells subjected to the step loading. The minimum dynamic bifurcation buckling pressure for step loading is about half of the static bifurcation buckling pressure.