Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures

Abstract

Buckling of slender bars subject to axial compressive loads represents a critical design constraint for light-weight truss structures. Active buckling control by actuators provides a possibility to increase the maximum bearable axial load of individual bars and, thus, to stabilize the truss structure.For reasons of cost, it is in general not economically viable to use such actuators in each bar of the truss structure. Hence, it is an important practical question where to place these active bars. Optimized structures, especially when coupled with active elements to further decrease the number of necessary bars, however, lead to designs, which, while cost-efficient, are especially prone to bardamages, caused, e.g., by material failures. Therefore, this paper presents a mathematical optimization approach to optimally place active bars for buckling control in a way that secures both buckling and general stability constraints even after failure of any combination of a certain number of bars. This allows us to increase the resilience of the system and guarantee stable behavior even in case of failures.

Strategies for Mastering Uncertainty

“…[111]. In the third model, we apply actuators with the aim to achieve an improvement of the buckling resistance of trusses, which is based on [64]. In the last paragraph, we introduce the fourth model, namely the optimal design of shunt damping for vibration attenuation as presented in [112].…”

“…In the following, we show its inclusion presented in [64], for the case of discrete cross-sectional areas for each bar indicated by binary variables x a e , where x a e is 1 if and only if bar e ∈ E has the cross-sectional area a ∈ A, which we assume to be of circular shape, see also Sect. 6.1.1.…”

Resilience in Mechanical Engineering - A Concept for Controlling Uncertainty during Design, Production and Usage Phase of Load-Carrying Structures

“…Note that problem (7) consists of an exponential number of SDP-constraints which can make its solution computationally challenging. For a more in-depth discussion of this approach, see [29]. In Fig.…”

Bridging mixed integer linear programming for truss topology optimization and additive manufacturing

“…Furthermore it is shown that non-linear mixed 0-1 TO problems can equivalently be cast as either linear or convex quadratic mixed 0-1 problems (Stolpe 2007). Gally et al (2018) provide a Mixed-Integer Semidefinite Program (MISDP) for a optimal placement of active beams for buckling control in truss structures under beam failures. Also a robust TTD with beams via a Mixed-Integer Nonlinear Semidefinite Program (MINSDP) is stated (Gally et al 2015).…”

“…Beside the problem of optimum TTD considering an equilibrium of forces and stress constraints based on the ground structure method (Achtziger 1996), a MILP, a QP and a Semidefinite Program (SDP) have their advantages (Gally et al 2015). These programs can be partly extended for discrete beam thicknesses, vibrations, active elements, multiple load cases, time-invariant systems and an uncertainty set implemented by an ellipsoid containing nominal loads (Gally et al 2015;Kuttich 2018). The control of uncertainties in load-bearing lattice structures, with the use of mathematical programs and the optimal combination of passive and active structural elements within lattice structures, appear to be of particular importance for mechanical engineering (Kuttich 2018).…”