Optimal sizing of piezo-actuators for minimum-deflection design of frames under uncertain loads

Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty are determined with the objective of minimizing the deflection under worst case of loading. The bending moments generated by the piezo-actuators are used for deflection control, i.e., to minimize the maximum deflection. The frame is subjected to a tip load which lies in an uncertainty domain with regard to its magnitude and direction. The specific uncertain loading studied in the present paper involves a load of given magnitude but of unknown direction, which should be determined to produce the highest deflection. The worst case of loading depends on the size and location of the actuators leading to a nested problem of optimization (design) and anti-optimization (uncertainty problem). Results are given for deterministic and uncertain loading conditions.     

Iterative algorithms for optimal design of columns subject to a stress constraint

Two algorithms based on an integral equation formulation of the buckling optimization problem are formulated and implemented. The objective of the optimization is to maximize the buckling load of an elastically restrained column by optimally designing the cross-sectional area subject to a minimum cross-section or maximum stress constraint. The first approach involves solving the resulting integral equations iteratively taking into account the boundary conditions, the optimality criterion and the imposed constraints. In the second approach an iterative finite difference approximation scheme is developed.The column is elastically restrained at both ends which produce the simple support and clamped end conditions for the limiting cases leading to the optimal design of columns under general boundary conditions. The above problems do not have analytical solutions due to the complexity of the boundary conditions, constraints and the optimality conditions necessitating the formulation of computational schemes for their solution. Several numerical results are given and compared with available results in the literature. Moreover the accuracy of the methods is studied by comparing the iterative solutions with finite element ones and with exact results when available.