Optimal size, shape, and control design in dynamics of planar frame structures under large displacements and rotations

摘要

Size, shape, and drive optimization procedures are combined with an energy-conserving time-integration scheme for the dynamic analysis of planar geometrically non-linear frame structures undergoing large overall motions. The solution method is based on the finite-element formulation, employing the classical displacement-based planar beam finite elements described in an inertial frame. Finite axial, bending, and shear strains are taken into account. If the system is conservative, the energy and momenta conservation in the discrete system during motion is guaranteed. Size, shape, and drive design variables are introduced into the model. Shape parameterization is achieved by the design element technique, using Bezier patches. The sensitivity analysis is performed by the discrete approach and the analytical direct differentiation method. A gradient-based optimization method, using an automatically adjustable convex approximation technique, is employed. The efficiency and the applicability of the approach are demonstrated via numerical examples. The shape and the driving function of a load-moving robot arm are optimized to reduce oscillations in its final position. The shape of a steel frame is optimized to reduce oscillations after an idealized ground motion jerk.