饱和砂土地震液化的网格自适应数值方法研究

发布时间：2018-04-11 00:24

本文选题：地震液化 + 数值模拟　；参考：《大连理工大学》2014年博士论文

【摘要】：饱和砂土液化在地震中是一种常见现象,易造成场地沉陷、流动等严重灾害。为研究其致灾机理和致灾程度,数值模拟可以有效地重现、预测地震液化过程,是一种省时省力的研究手段。然而,在有限元数值计算中,由于网格划分不当,在动力作用下变形剧烈,出现局部网格扭曲畸变,影响计算效果,甚至中止计算。因此,本文开发了两套完整的网格白适应方法对该问题进行研究,主要分为以下三个方面。首先,针对液化土体变形特性,采用了基于SPR的误差评估方法,来展现整个网格应变相对误差的分布。将双线性回归函数应用于三角形单元的网格,比常规线性回归函数获得了更稳定、更准确的误差分布,可精确指导局部网格细化或再生成,也适用于四边形和三角形单元的混合网格。其次,分别开发了基于相似形分裂的网格细化方案和基于Delaunay三角剖分的网格再生成方案。通过测试和讨论,将与液化程度相关的平均相对误差设定为合适的自适应误差阈值,以实现局部网格的有限次合理加密。最后,对应局部网格细化和再生成的方案,分别建立了与之匹配的新旧网格数据传递系统。在充分利用有限元基本规则的同时,将土体材料的塑性特征完整地从旧网格中继承到新网格中,实现了网格自适应流程中数据的准确续算。在进行上述三个方面的过程中,也探索了两种网格自适应方案的适用范围和可靠性,获得并整理了他们的优势和缺陷。通过上述工作,证明了网格自适应方案在地震液化数值模拟中能够精确地捕捉并平滑尖锐变形,极大地避免网格扭曲畸变；在有目标地、合理有序地加密局部网格的基础上降低整体计算的误差,与一致性加密的网格相比节省了大量计算资源,改善了常规有限元的数值结果,进一步发挥了基于网格计算的有限元方法的高效性。
[Abstract]:Saturated sand liquefaction is a common phenomenon in earthquakes, which can easily cause site subsidence, flow and other serious disasters.In order to study the mechanism and degree of earthquake liquefaction, numerical simulation can effectively reproduce and predict the process of earthquake liquefaction, which is a time-saving and labor-saving research method.However, in the finite element numerical calculation, due to the improper mesh division, the deformation is severe under the dynamic action, and the local mesh distortion appears, which affects the calculation effect and even suspends the calculation.Therefore, this paper develops two complete grid white adaptation methods to study the problem, mainly divided into the following three aspects.Firstly, according to the deformation characteristics of liquefaction soil, an error evaluation method based on SPR is adopted to show the relative error distribution of the whole grid strain.The bilinear regression function is applied to the mesh of triangular element, which is more stable and accurate than the conventional linear regression function, and can precisely direct the local mesh refinement or regeneration.It also applies to mixed meshes of quadrilateral and triangular elements.Secondly, a mesh refinement scheme based on similar shape splitting and a mesh regeneration scheme based on Delaunay triangulation are developed respectively.Through testing and discussing, the average relative error related to the degree of liquefaction is set as the appropriate adaptive error threshold to realize the finite reasonable encryption of the local mesh.Finally, corresponding to the scheme of local mesh refinement and regeneration, the matching new and old grid data transfer systems are established.At the same time, the plastic characteristics of soil materials are inherited from the old mesh to the new mesh completely, and the data in the adaptive mesh flow is accurately continued.In the process of the above three aspects, the applicability and reliability of the two mesh adaptive schemes are also explored, and their advantages and disadvantages are obtained and sorted out.Through the above work, it is proved that the mesh adaptive scheme can accurately capture and smooth sharp deformation in the numerical simulation of seismic liquefaction, and greatly avoid the distortion of mesh distortion.On the basis of reasonably and orderly encrypting local meshes, the error of global computation is reduced. Compared with the uniformly encrypted grids, the computational resources are saved and the numerical results of the conventional finite element method are improved.The high efficiency of the finite element method based on grid computing is further brought into play.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU441;TU435

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