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Personne# Yafeng Wang

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Structure

A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buil

Design

vignette|Chaise de Charles Rennie Mackintosh, 1897.
Le design, le stylisme ou la stylique est une activité de création souvent à vocation industrielle ou commerciale, pouvant s’orient

Tensile structure

In structural engineering, a tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with tensegrity, which is a

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This paper presents a unifying framework for the form-finding and topology-finding of tensegrity structures. The novel computational framework is based on rank-constrained linear matrix inequalities. For form-finding, given the topology (i.e., member connectivities), the determination of the member force densities is formulated into a linear matrix inequality (LMI) problem with a constraint on the rank of the force density matrix. The positive semi-definiteness and rank deficiency condition of the force density matrix are well managed by the rank-constrained LMI-based formulation. A Newton-like algorithm is employed to solve the rank-constrained LMI problem. Two methods, named direct method and indirect method, are proposed to determine the nodal coordinates once the force densities have been obtained. For topology-finding, given the geometry (i.e., nodal coordinates), the determination of the topology is also formulated into an LMI problem with a constraint on the rank of the tangent stiffness matrix. Numerical examples demonstrate that different types of form-finding problems (such as tensegrity structures with single and with multiple self-stress states, symmetric and irregular tensegrity structures) can be uniformly and efficiently solved by the proposed approach. Furthermore, three well-known tensegrity structures are reproduced to verify the effectiveness of the proposed formulation on the topology-finding of tensegrity structures. (C) 2021 Elsevier Ltd. All rights reserved.

This study proposes a general computational framework for the form-finding of tensegrity structures. The procedure is divided into two stages in which the member force densities and nodal coordinates are obtained respectively. In the first stage, the determination of force densities is transformed into a rank minimization problem regarding the force density matrix and then formulated into a semi-definite programming. The unilaterality condition of member forces and the positive semi-definiteness condition of force density matrix are incorporated as constraints. In the second stage, the determination of nodal coordinates is formulated into a constrained nonlinear programming model. The nodal positions and member lengths are assigned as constraints and auxiliary variables are introduced to homogenize the member lengths. The proposed formulation bypasses the number of self-stress states in a tensegrity structure thus applies to both tensegrity structures with single and multiple self-stress states. Different from existing studies that are based on the minimum required rank deficiency condition of force density matrix, the proposed method can handle tensegrity structures that have a force density matrix with rank deficiency greater than the required minimum number. Several examples are presented to verify the effectiveness of the proposed method on different types of tensegrity structures.

This paper gives a new formulation to design adaptive structures through total energy optimization (TEO). This methodology enables the design of truss as well as tensegrity configurations that are equipped with linear actuators to counteract the effect of loading through active control. The design criterion is whole-life energy minimization which comprises an embodied part in the material and an operational part for structural adaptation during service. The embodied energy is minimized through simultaneous optimization of element sizing and actuator placement, which is formulated as a mixed-integer nonlinear programming problem. Optimization variables include element cross-sectional areas, actuator positions, element forces, and node displacements. For tensegrity configurations, the actuators are not only employed to counteract the effect of loading but also to apply appropriate prestress which is included in the optimization variables. Actuator commands during service are obtained through minimization of the operational energy that is required to control the state of the structure within required limits, which is formulated as a nonlinear programming problem. Embodied and operational energy minimization problems are nested within a univariate optimization process that minimizes the structure’s whole-life energy (embodied + operational). TEO has been applied to design a roof and a high-rise adaptive tensegrity structure. The adaptive tensegrity solutions are benchmarked with equivalent passive tensegrity as well as adaptive truss solutions, which are also designed through TEO. Results have shown that since cables can be kept in tension through active control, adaptive tensegrity structures require low prestress, which in turn reduces mass, embodied energy, and construction costs compared to passive tensegrity structures. However, while adaptive truss solutions achieve significant mass and energy savings compared to passive solutions, adaptive tensegrity solutions are not efficient configurations in whole-life energy cost terms. Since cable elements must be kept in tension, significant operational energy is required to maintain stable equilibrium for adaptation to loading. Generally, adaptive tensegrity solutions are not as efficient as their equivalent adaptive truss configurations in mass and energy cost terms.

2021