无限地基相互作用力时域求解的阻尼溶剂逐步抽取法

DAMPING SOLVENT STEPWISE EXTRACTION METHOD FOR EVALUTION OF INTERACTION FORCES OF UNBOUNDED SOIL IN TIME DOMAIN

无限地基相互作用力时域求解的精度及效率是面向实际工程结构动力分析的关键问题。基于阻尼抽取法模拟地基无限域动力特性的思想,从数值实现中的误差源出发,提出了一种施加较大附加人工阻尼再分步依次移频抽取的阻尼溶剂逐步抽取法,并给出了具体实现公式。该方法可以最大限度地消除反射波波动能量及抽取人工高阻尼的影响,提高了算法的精度,降低了人工高阻尼与地基区域大小的相互制约性,并能适应地基有限区域表面几何结构复杂多变的情况,具有较高的工程实用价值。最后,通过对典型三维半无限空间问题的动力反应分析,将计算结果与精确解,阻尼抽取法模型和粘弹性人工边界模型进行对比研究,证明了该方法具有良好的精度和计算效率,并对不规则地基有限域模型进行分析,验证其良好的工程适用性。

To satisfy practical requirements for dynamic analysis of engineering structures, accuracy and efficiency have played key roles in the evaluation of interaction forces of unbounded soil in the time domain. Based on the idea that the Damping Solvent Extraction Method （DSEM） simulates the dynamic characteristics of an unbounded soil, a Damping Solvent Stepwise Extraction Method （DSSEM） is proposed by first applying relatively larger artificial damping in the bounded soil and then employing a stepwise extraction process. In essence, the introduced artificial damping is divided into smaller parts to assure the convergence and then extracted step by step, which can simultaneously decrease two sources of error in the implementation of DSEM. Also, the corresponding numerical implementation of the procedure in the time domain is given within the framework of finite elements. This method provides a more efficient and accurate way to calculate the interaction forces of the unbounded soil due to the fluctuation energy of reflected waves and the undesirable effect of artificial damping are completely removed as much as possible. Additionally, the proposed method is applicable to practical engineering with an irregular soil domain, and provides the selection of the artificial damping without depending on the domain size of bounded soil. A typical 3-D strip foundation with rectangular cross-section embedded in half-space under transient excitation is analyzed as verfication. The numerical results are compared with the solution obtained by analytical formula, DSEM, and visco-elastic boundary model. It is shown that the proposed method exhibits good accuracy and efficiency. In the meantime, dynamic analysis of an irregular soil domain model is also presented to demonstrate the engineering capabilities of the method.