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Numerical simulation of structural response is a challenging issue in earthquake engineering and there has been remarkable progress in this area in the last decade. Endurance Time (ET) method is a new response history based analysis procedure for seismic assessment and structural design in which structures are subjected to a gradually intensifying dynamic excitation and their seismic performance is evaluated based on their responses at different excitation levels. Generating appropriate artificial dynamic excitation is essential in this type of analysis. In this paper, an optimization procedure is presented for computation of the intensifying acceleration functions utilized in the ET method and the results of this procedure are discussed. A set of the ET acceleration functions (ETAFs) is considered which has been produced utilizing numerical optimization considering 2048 acceleration points as optimization variables by an unconstrained optimization procedure. The ET formulation is then modified from the continuous time condition into the discrete time state thus the optimization problem is reformulated as a nonlinear least squares problem. In this way, a second set of the ETAFs is generated which better satisfies the proposed objective function. Subsequently, acceleration points are increased to 4096, for 40 seconds duration, and the third set of the ETAFs is produced using a multi level optimization procedure. Improvement of the ETAFs is demonstrated by analyzing several SDOF systems.

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In this article, topology optimization of two-dimensional (2D) building frames subjected to seismic loading is performed using the polygonal finite element method. Artificial ground motion accelerograms compatible with the design response spectrum of ASCE 7-16 are generated for the response history dynamic analysis needed in the optimization. The mean compliance of structure is minimized as a typical objective function under the material volume fraction constraint. Also, the adjoint method is employed for the sensitivity analysis evaluated in terms of spatial and time discretization. The ground structures are 2D continua taking the main structural components (columns and beams) as passive regions (solid) to render planar frames with additional components. Hence, building frames with different aspect ratios are considered to assess the usefulness of the additional structural components when applying the earthquake ground motions. Furthermore, final results are obtained for different ground motions to investigate the effects of ground motion variability on the optimized topologies.