A new energy-based structural design optimization concept under seismic actions

Abstract

A new optimization concept is introduced which involves the optimization of non-linear planar shear buildings by using gradients based on equivalent linear structures, instead of the traditional practice of calculating the gradients from the non-linear objective function. The optimization problem is formulated as an equivalent linear system of equations in which a target fundamental eigenfrequency and equal dissipated energy distribution within the storeys of the building are the components of the objective function. The concept is applied in a modified Newton–Raphson algorithm in order to find the optimum stiffness distribution of two representative linear or non-linear MDOF shear buildings, so that the distribution of viscously damped and hysteretically dissipated energy, respectively, over the structural height is uniform. A number of optimization results are presented in which the effect of the earthquake excitation, the critical modal damping ratio, and the normalized yield inter-storey drift limit on the optimum stiffness distributions is studied. Structural design based on the proposed approach is more rational and technically feasible compared to other optimization strategies (e.g., uniform ductility concept), whereas it is expected to provide increased protection against global collapse and loss of life during strong earthquake events. Finally, it is proven that the new optimization concept not only reduces running times by as much as 91% compared to the classical optimization algorithms but also can be applied in other optimization algorithms which use gradient information to proceed to the optimum point.