In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.

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Abstract:To stabilize infrastructures such as tall buildings, bridges, etc., piles are used to resist lateral loads created from earth pressure, wind, waves and earthquake extensively. Pile design requires understanding of how the load is transferred from a pile to surrounding soil and vice versa. Pile properties, soil stress-strain behavior and pile-soil interaction play important roles in pile-response subjected to lateral loads. A study was carried out to investigate the effects of above-mentioned parameters on pile-soil behavior subjected to lateral forces. A comparison was made between the results derived from finite difference and equivalent spring methods by writing a computer program and using a civil engineering package, respectively.

One of the main tasks in performance‐based seismic risk assessment and design of structures is the quantification of uncertainty due to earthquake ground motion (GM) records. Therefore, there is an optimal suite of GMs for each structure, selection of which can be an elusive task complicated by—among other things—the fact that structural behavior migrates into load‐path‐dependent inelastic regimes as damage begins to accumulate. To facilitate the selection of an optimal GM suite, the GM selection based on a generalized conditional single‐intensity‐measure approach will be enhanced herein to allow users to select GMs based on two and average of more‐than‐two conditioning intensity measures. To formulate this task, an intensity measure vector consisting of several intensity measures will be populated to represent earthquake's amplitude‐, duration‐based, and cumulative characteristics. The idea of two and average conditioning intensity measures will then be formulated by considering the correlation between the intensity measures in the vector with two and average of more‐than‐two intensity measures, simultaneously. The cross‐correlation between the intensity measures in the vector will also be considered to ultimately form a conditional multivariate distribution from which one could draw any number of realization samples to find matching earthquake records so that the hazard consistency concept can be fully enforced.

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