【摘要】 本文首先从弹性波动方程及其弱形式、空间离散、单元内插函数及积分、全局聚合计算、时间离散以及算法的精度和稳定性等多个方面,对谱元法的理论进行了详细的总结,然后对其在地震动模拟中的应用现状进行了归纳,最后采用该法简单分析了埋藏基岩凸起地形对地表地震动的影响作用.总的来说,谱元法不仅具有有限单元法处理复杂结构的几何灵活性,还具有伪谱法的高精度性和快速收敛性,用其进行数值模拟计算能大大减少内存需求和计算时间.在合理考虑区域地质构造、局部场地条件、介质各向异性以及地震波传播特性等多种影响因素的基础上,建立正确的计算模型,用该法研究盆地效应、地形效应以及烈度异常现象等是可行的.根据目前掌握的资料,在国内应用谱元法进行地震动模拟的研究不多,对谱元法理论进行详细分析和总结的更少.因此,本文不仅对推动谱元法在国内的应用具有重要的理论意义,还对开展全面的地震动模拟工作具有重要的参考价值.更多还原

【Abstract】 This paper firstly makes a detailed summary of the theory of spectral element method from elastic wave equation and the weak formulation,spatial discretization,element interpolation function and integral, global aggregate computation,time discretization and the precision and stability of the code.Then,it is also summary the application status of spectral element method in the area of seismic ground motion simulation.Finally,makes a simple analysis of the role of underlying convex bedrock terrain on ground motion.In general,the spectral element method combines the flexibility of a finite element method with the accuracy and convergence of a spectral method, which could greatly reduce the memory requirements and computation times of the numerical simulation.On the basis of considering the regional geological structure,local site conditions,media anisotropy and seismic wave propagation characteristics correctly,this method might be suitable for studying basin effect,terrain effect and abnormal intensity for establishing reasonable model.According to the present information,there is not much study on ground motion simulation of using the spectral element method in domestic,and it is not make a detailed analysis and summary about the theory of spectral element method.This paper not only has a great theoretical significance for promoting the application of the spectral element method in domestic,but also has a crucial reference value to carry out more comprehensive seismic ground motion simulation research work in the future.更多还原