摘要
目的:在对土体固结问题进行求解时,如果对孔压和位移采用等阶积分,当时间步长取值很小时,得到的孔压结果会出现数值振荡,导致精度降低。本文提出一种非等阶积分的求积元孔压单元,致力于减小孔压振荡,提高单元稳定性和计算精度。创新点:1.建立了一种对于孔压和位移采用不同阶积分的求积元复合单元;2.有效降低了小时间步长引起的孔压振荡。方法:1.通过求积元法对弱形式控制方程进行数值积分,并对比奥固结方程中的位移项和孔压项采用不等阶积分;2.通过拉格朗日插值获得位移点上的孔压和孔压点上的位移值;3.通过一维及二维问题的数值算例,验证所建立方法的有效性。结论:1.通过采用复合求积元单元,大大降低了孔压的数值振荡;2.应用复合求积单元时,采用二阶精度的Crank-Nicolson积分格式不会产生随时间的孔压振荡;3.本文所建立的单元可以大大提高固结问题求解的数值计算精度和计算效率。
The weak form quadrature element method is a high-order algorithm which has been applied successfully to consolidation analysis of saturated and unsaturated soils. Its superiority over the conventional finite element method has been verified. However, in consolidation analysis, pore pressure oscillations will appear when small time increments are used due to the very small permeability and near-incompressibility of the pore water. This can produce almost zero values of main diagonal elements in the coefficient matrix. To overcome the pressure oscillations, we propose a coupled composite quadrature element in which different orders of integration are employed for the pore pressure and the displacement. Its performance is evaluated and compared with that of the standard element through 1 D and 2 D numerical tests. Our results show that pressure oscillations can be effectively alleviated and stability and accuracy can be significantly enhanced by using the proposed element.
引文
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