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首页> 外文会议>ASME International Mechanical Engineering Congress and Exposition >A Verified Non-Linear Regression Model For Elastic Stiffness Estimates OF Finite Composite Domains Considering Combined Effects of Volume Fractions, Shapes, Orientations, Locations, And Number Of Multiple Inclusions
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A Verified Non-Linear Regression Model For Elastic Stiffness Estimates OF Finite Composite Domains Considering Combined Effects of Volume Fractions, Shapes, Orientations, Locations, And Number Of Multiple Inclusions

机译：考虑体积分数，形状，方向，位置和多个夹杂物数量的组合效应的有限复合域弹性刚度估计的验证的非线性回归模型

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A non-linear regression model using SAS/STAT (JMP software; Proc regression module) is developed for estimating the elastic stiffness of finite composite domains considering the combined effects of volume fractions, shapes, orientations, inclusion locations, and number of multiple inclusions. These estimates are compared to numerical solutions that utilized another developed homogenization methodology by the authors (dubbed the generalized stiffness formulation, GSF) to numerically determine the elastic stiffness tensor of a composite domain having multiple inclusions with various combinations of geometric attributes. For each inclusion, these considered variables represent the inclusions' combined attributes of volume fraction, aspect ratio, orientation, number of inclusions, and their locations. The GSF methodology's solutions were compared against literature-reported solutions of simple cases according to such well-known techniques as Mori-Tanaka and generalized self-consistent type methods. In these test cases, the effect of only one variable was considered at a time: volume fraction, aspect ratio, or orientation (omitting the number and locations of inclusions). For experimental corroboration of the numerical solutions, testing (uniaxial compression) was performed on test cases of 3D printed test cubes. The regression equation returns estimates of the composite's ratio of normalized longitudinal modulus (E11) to that of the matrix modulus (Em) or E11/Em when considering any combination of all of the aforementioned inclusions' variables. All parameters were statistically analyzed with the parameters retained are only those deemed statistically significant (p-values less than 0.05). Values returned by the regression stiffness formulation solutions were compared against values returned by the GSF formulation numerical and against the experimentally found stiffness values. Results show good agreement between the regression model estimates as compared with both numerical and experimental results.
机译：使用SAS / STAT（JMP软件; PROC回归模块）的非线性回归模型用于估计有限复合域的弹性刚度，考虑体积分数，形状，方向，包容位置和多个夹杂物的数量的组合效果。将这些估计与作者（称为广义刚度制剂，GSF被称为通用刚度制剂，GSF）使用另一种开发的均质化方法来进行比较，以数值确定具有多个夹杂物的复合域的弹性刚度张量，其几何属性的各种组合。对于每个包含，这些被认为变量代表了夹杂物的体积分数，纵横比，方向，夹杂物的组合属性及其位置。将GSF方法的解决方案与文学报告的简单病例解的解决方案进行了比较，根据这种众所周知的技术，如Mori-Tanaka和广义的自我一致类型方法。在这些测试用例中，一次仅考虑一个变量的效果：体积分数，纵横比或方向（省略夹杂物的数量和位置）。对于数值溶液的实验性粗制，对3D印刷测试立方体的测试用例进行了测试（单轴压缩）。在考虑所有上述夹杂物变量的任何组合时，回归方程返回归一化纵向模量（E11）与矩阵模量（E11）的归一化纵向模量（E11）的估计数或E11 / Em的估计值。所有参数统计地分析了所保留的参数只是认为统计学上显着的那些（p值小于0.05）。将回归刚度配方溶液返回的值与GSF配方数值返回的值进行比较，并反对实验发现的刚度值。结果显示回归模型估计与数值和实验结果相比的良好一致性。

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