Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite struc...Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.展开更多
基金This work was supported by National Natural Science Foundation of China under Grant 11672266.
文摘Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.
文摘目的:基于瘤内及瘤周多参数磁共振成像(magnetic resonance imaging,MRI)影像组学构建术前预测浸润性乳腺癌N2-3期腋窝淋巴结(axillary lymph node,ALN)的列线图并验证模型效能。方法:回顾性分析2018年1月—2019年12月接受规范治疗前乳腺MRI检查的320例(训练集224例,验证集96例)浸润性乳腺癌患者资料。根据病理报告中腋窝转移淋巴结数量将患者分为N0-1期组(转移<4枚)和N2-3期组(转移≥4枚)。从5个MRI序列的瘤内、瘤周及瘤内+瘤周3个感兴趣区(region of interest,ROI)中分别提取并筛选与ALN分期相关的影像组学特征,通过随机森林(random forest,RF)分类器构建3个影像组学模型(瘤内模型、瘤周模型及瘤内+瘤周模型),计算各自的影像组学评分。采用单因素、多因素Logistic回归分析筛选临床独立预测因子,构建临床模型。整合最优影像组学模型和临床模型中的特征构建联合模型,并可视化为列线图。通过受试者工作特征(receiver operating characteristic,ROC)曲线、校准曲线和决策曲线分析(decision curve analysis,DCA)评估并比较各模型的预测效能和临床实用价值。结果:在单纯影像组学模型中瘤内+瘤周模型的表现最优,训练集和验证集中的曲线下面积(area under the curve,AUC)分别为0.911和0.858。整合了瘤内+瘤周组学特征和临床特征(瘤周水肿和病灶强化形态)的列线图在所有模型中具有最佳的N2-3期ALN预测效能,训练集和验证集的AUC分别为0.923和0.892。校准曲线显示列线图的预测值与实际观测值一致性良好。DCA显示列线图临床效用较高。结论:联合多区域多参数MRI影像组学特征和临床特征构建的列线图对浸润癌乳腺癌N2-3期腋窝淋巴结的个性化预测有较高价值。
