Multiobjective design optimization of multi-outrigger tall-timber building: Using SMA-based damper and Lagrangian model

This study proposes a shape memory alloy (SMA)-based damped outrigger system for vibration control of tall timber buildings. In this study, the core of the structure is idealized as a cantilever beam, and each floor mass is considered as a discrete mass that acts at the junction between the floor and the core of the structure. The governing equations of motion of the combined system of shear core and outrigger are derived using the Lagrange formulation. The SMA spring is installed between the outrigger beam and the column to dissipate earthquake-induced energy and reduce excessive load demand on the column. Optimal performance of the proposed system requires optimizing the outriggers' location and tuning the SMA properties in an uncertain environment. Two conflicting objective functions, minimization of acceleration and inter-storey drift ratio, are solved through a multi-objective optimization. Four different multi-objective meta-heuristic optimization algorithms (ant-lion, dragonfly, particle swarm optimization, and non-dominated sorting genetic algorithm II) are considered. Three different tall timber buildings (10-, 15-, and 20-storey) and up to two outrigger beams are considered for optimization. The seismicity of Vancouver, BC is used for the numerical simulation and vulnerability assessment. The optimum outrigger location for a one-outrigger system is found to be approximately 60%, while for a two outrigger system, the same is obtained as 33% and 68%, respectively. Finally, the fragility analysis is carried out, which shows the superiority of this passive device in terms of minimizing the probability of failure exceeding a given threshold limit, which yields an improvement in the reliability of the structure.

本研究提出了一种基于形状记忆合金（SMA）的阻尼伸臂系统，用于高层木结构建筑的振动控制。在本研究中，结构的核心被理想化为悬臂梁，每层的质量被视为作用在楼层与结构核心连接处的离散质量。采用拉格朗日公式推导了核心筒与伸臂组合系统的运动控制方程。SMA弹簧安装在伸臂梁和柱子之间，以耗散地震引起的能量并减少柱子上的过度荷载需求。所提出系统的最佳性能需要在不确定环境中优化伸臂的位置并调整SMA的性能。通过多目标优化解决了两个相互冲突的目标函数，即加速度和层间位移比的最小化。考虑了四种不同的多目标元启发式优化算法（蚁狮算法、蜻蜓算法、粒子群优化算法和非支配排序遗传算法II）。对三栋不同的高层木结构建筑（10层、15层和20层）以及最多两根伸臂梁进行了优化。数值模拟和易损性评估采用了不列颠哥伦比亚省温哥华的地震活动数据。对于单伸臂系统，最佳伸臂位置约为60%，而对于双伸臂系统，最佳位置分别为33%和68%。最后进行了易损性分析，结果表明这种被动装置在最小化超过给定阈值的失效概率方面具有优势，从而提高了结构的可靠性。