基于ANN的混凝土均匀化方法解析解

Analytical Solution of the Concrete Homogenization Method Based on the ANN

通过自定义人工神经网络(artificial neural network,ANN),借助其优秀的函数拟合功能,针对骨料/砂浆基质二相混凝土,求解间接均匀化理论中微分法的高度非线性耦合微分方程的解析解,得到了混凝土体积模量和剪切模量分别与骨料体积分数的函数关系,并与数值模拟的结果进行了对比.结果表明,基于ANN的求解方法快速且具有更高的精度.此外,通过解构ANN的方法给出了在细观力学参数不变的条件下由骨料体积分数、初始孔隙率直接计算骨料/砂浆基质/孔隙三相混凝土弹性模量的公式.结果表明,对于不同骨料体积分数和初始孔隙率的混凝土样本,该公式均有较高的计算精度,同时避免了传统均匀化方法的复杂分析和大量假设,为复合材料均匀化方法研究提供了新思路.

By means of the self-defined artificial neural network(ANN)and its excellent function fitting func-tion,aimed at aggregate-mortar matrix 2-phase concrete,the analytical solutions of the highly nonlinear cou-pling differential equation of the differential method in the indirect homogenization theory were given,the func-tional relations between the volume modulus and the shear modulus of concrete and the volume fractions of ag-gregate were obtained respectively,and the results were compared with those of numerical simulation.The re-sults show that,the method based on the ANN is fast and has higher precision.In addition,the method of de-constructing ANN provides the formula of calculating the elastic modulus of aggregate-mortar matrix-pore 3-phase concrete directly from aggregate volume fractions and initial porosities under constant meso-mechanical parameters.For concrete samples with different aggregate volume fractions and initial porosities,the formula has higher calculation accuracy,and avoids the complex analysis and many assumptions of the traditional hom-ogenization method.The work provides a new idea of homogenization method for composite materials.