ROTATED MUTUALLY SUPPORTED ELEMENTS IN TRUNCATED ICOSAHEDRIC DOMES

摘要

Various studies have shown that the conversion of many 3D elementary configurations composed of basic polyhedral shapes to equivalent mutually supported element (MSE) configurations may not always be viable. This is particularly evident when, for reasons of economy, elements with identical cross-sections wish to be used. Without mathematical validation, the sole use of small-scale models as a means of verifying MSE geometry has, in many instances, been found not to be reliable. Modelling elements with relatively low stiffness may be easily forced into position. This can result in incorrectly aligned elements and therefore configured layouts whose behaviour is difficult to predict. Additional stresses potentially caused by element misalignment may further result in undesirable early yielding or buckling. A geometric indicator is considered that enables the appraisal of the feasibility of MSE configuration conversion at the conceptual stage resulting in economy of design effort. To illustrate the procedure, the construction of a truncated icosahedric dome is used although the principle may be applied to any elementary configuration and its MSE conversion. The effects on the eccentricities between MSEs as a result of varying the elements orientation via imposed rotation angles are considered. The advantages and disadvantages of the technique using elements of circular and rectangular cross-section MSEs for construction are discussed.