Abstract
A new optimization concept is introduced which involves the optimization of nonlinear planar shear buildings by using gradients based on equivalent linear structures, instead of the traditional practice of calculating the gradients from the nonlinear 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 nonlinear 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 interstorey 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 it can be applied in other optimization algorithms which use gradient information to proceed to the optimum point.
Highlights
Optimization techniques play an important role in various occasions in structural design, where they can be used by engineers, decision makers, etc. to find the best possible solution
The objective of the optimization procedure employed in this study is to find the stiffness distribution that corresponds to uniform energy dissipation over the structural height, either in terms of energy dissipation due to viscous damping for linear elastic structures, or in terms of energy dissipation due to hysteresis for elastic-perfectly plastic structures
It is shown that there exist unique optimum stiffness distributions which correspond to equidistributed viscous damping and hysteretic energy dissipation for linear elastic and elastoplastic planar shear building structures, respectively
Summary
Specialty section: This article was submitted to Earthquake Engineering, a section of the journal Frontiers in Built Environment. 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.
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