Abstract
This paper presents a new All-In-One (AIO) implementation of an existing formulation to design adaptive structures through Total Energy Optimization (TEO). The method implemented in previous work is a nested optimization process, here named TEO-Nested. Numerical simulations and experimental testing have shown that the TEO-Nested method produces structures that embody and use significantly lower energy compared to passive designs. However, TEO-Nested does not guarantee solution optimality. The formulation presented in this paper is an AIO optimization based on Mixed Integer Nonlinear Programming (MINLP), here named TEO-MINLP. Element cross-section areas, internal forces, nodal displacements and control commands are treated as continuous variables while the actuator positions as binary variables. Stress and displacement limits are included in the optimization constraints. Case studies of reticular structures are employed to benchmark the solutions with those produced by the TEO-Nested method. Results have shown that both formulations produce similar solutions which are only marginally different in energy terms thus proving that the TEO-Nested method tends to converge to optimal (local) solutions. However, the computation time required by TEO-Nested is only a fraction of that required by TEO-MINLP, which makes the former more suitable for structures of complex layout that are made of many elements.
Highlights
Adaptive structures are structural systems which have the ability to counteract actively the external loads through redirection of the internal load path and controlled changes of the external geometry
There is a relatively substantial difference (4.6%) in energy savings terms between the solution produced by the Total Energy Optimization (TEO)-Nested formulation using one-phase adaptation to that produced by considering two-phase adaptation
It has been proven that the TEO-Nested is significantly more efficient in computation time terms and it is more suitable to be employed for large-scale design problems
Summary
Adaptive structures are structural systems which have the ability to counteract actively the external loads through redirection of the internal load path (element forces) and controlled changes of the external geometry. The structure is designed to withstand normal loading conditions in a passive state (i.e. the actuators are locked in position) while it is actively controlled on the occurrence of strong loading events This allows large savings of the energy embodied in the material at the cost of a small amount of operational energy for actuation. The operational energy has been obtained by computing the energy needed for compensation of forces and displacements caused by the external load (one-phase adaptation) but without considering the energy required to control the structure into the configuration prior to actuation after the live load is removed (two-phase adaptation). This work builds on the TEO-Nested method given in [28] by reformulating the minimum energy design problem into a Mixed Integer Nonlinear Programming (MINLP) problem which can be solved directly to obtain an optimal (local) solution This new formulation is here named TEO-MINLP.
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