Aztec在混凝土细观数值模拟中的应用研究

细观数值模拟是混凝土性能研究的一种重要手段,但稀疏线性方程组求解在总体模拟时间中所占比重很大。由于属于三维问题,且规模很大,所以采用预条件Krylov子空间迭代是必由之路。Aztec是国际上专门设计用于求解稀疏线性方程组的软件包之一,由于目前混凝土细观数值模拟中的稀疏线性方程组对称正定,所以利用Aztec中提供的CG迭代法进行求解,并对多种能保持对称性的预条件选项进行了实验比较。结果表明,在基于区域分解的并行不完全Cholesky分解、无重叠对称化GS迭代、最小二乘等预条件技术中,第一种的效率最高,且在重叠度为0,填充层次为0时,效果最好;实验结果还表明,在本应用问题中,用RCM排序一般导致求解时间更长,从而没有必要采用。

排序对重叠区域分解型并行ILU的影响分析

对Krylov子空间迭代法,高效预条件的构造是核心问题之一,而重叠区域分解是一种很有效的并行化技术。通过模型偏微分方程离散求解以及混凝土细观数值模拟中的线性方程组求解,对商图,就自然排序、RCM排序、Sloan排序、GPS排序、谱排序和随机排序等多种重排算法进行了比较。对子区域内顶点的重排方案,进行了自然排序、RCM排序、谱排序、随机排序和一种新排序算法间的比较。结果表明,预条件效果对商图排序不敏感。局部排序对预条件质量具有明显影响,局部采用随机排序时效果一般较差,而带宽缩减算法对加性Schwarz影响很小,对块Jacobi并行化预条件影响较大,对因子组合型并行预条件采用自然排序和新排序时效果较好。

Improved parameter selection method for mesoscopic numerical simulation test of direct tensile failure of rock and concrete

In order to numerically simulate the failure process of rock and concrete under uniaxial tension,an improved method of selecting the mechanical properties of materials was presented for the random mechanic parameter model based on the mesoscopic damage mechanics.The product of strength and elastic modulus of mesoscale representative volume element was considered to be one of the mechanical property parameters of materials and assumed to conform to specified probability distributions to reflect the heterogeneity of mechanical property in materials.With the improved property parameter selection method,a numerical program was developed and the simulation of the failure process of the rock and concrete specimens under static tensile loading condition was carried out.The failure process and complete stress-strain curves of a class of rock and concrete in stable fracture propagation manner under uniaxial tension were obtained.The simulated macroscopic mechanical behavior was compared with the available laboratory experimental observation,and a reasonable agreement was obtained.Verification shows that the improved parameter selection method is suitable for mesoscopic numerical simulation in the failure process of rock and concrete.