This article presents a design methodology based on a stiffness and volume optimization algorithm for three-dimensional nonlinear hyperstatic and pre-stressed structures composed of elements only subjected to axial forces, with a special emphasis on tensegrity structures. The algorithm is based on dimensionless numbers called morphological indicators that allow finding, within a given family of structures, the geometry related to a maximum stiffness or a minimum volume of materials or the best ratio between stiffness and volume. The algorithm takes into account the buckling of the struts and different materials for cables and struts. This article first demonstrates the optimization algorithm and then gives numerical confirmations and examples.
Within the framework of sustainable development we strive for structures with a minimum volume of material. When we only consider criteria on resistance and buckling, Samyn and Latteur prove that even at the stage of conceptual design a clear hierarchy among the different truss typologies can be established. Up to now, stiffness constraints -such as the upper limit on static displacements -were not considered. However, an optimum obtained by minimising the volume, only considering the strength criterion, often results in solutions which violate the stiffness constraint(s). To avoid large displacements a stress level reduction can be imposed. However, this comes at the cost of a significant volume increase. With an optimisation process that involves the stiffness constraints at the stage of conceptual design, an optimum can be obtained without the necessity to alter the structure drastically afterwards, which partly annihilates the main objective of minimal use of material. This approach compares the different truss types on a new priority scale, generating new optima. This implicates a non-negligible change in the truss choice at conceptual design stage. The solutions are logically depended on the displacement criterions. This approach forms a first step to a new design philosophy that considers all the stiffness constraints (static displacements, resonance, local and global buckling) at conceptual design stage and is called design for stiffness.
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