Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to...Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to miniaturization of electronic components,it is challenging to directly measure or numerically predict the mechanical response of small-sized critical interconnections in board-level packaging structures to ensure the mechanical reliability of electronic devices in projectiles under harsh working conditions.To address this issue,an indirect measurement method using the Bayesian regularization-based load identification was proposed in this study based on finite element(FE)pre-dictions to estimate the load applied on critical interconnections of board-level packaging structures during the process of projectile penetration.For predicting the high-strain-rate penetration process,an FE model was established with elasto-plastic constitutive models of the representative packaging ma-terials(that is,solder material and epoxy molding compound)in which material constitutive parameters were calibrated against the experimental results by using the split-Hopkinson pressure bar.As the impact-induced dynamic bending of the printed circuit board resulted in an alternating tensile-compressive loading on the solder joints during penetration,the corner solder joints in the edge re-gions experience the highest S11 and strain,making them more prone to failure.Based on FE predictions at different structural scales,an improved Bayesian method based on augmented Tikhonov regulariza-tion was theoretically proposed to address the issues of ill-posed matrix inversion and noise sensitivity in the load identification at the critical solder joints.By incorporating a wavelet thresholding technique,the method resolves the problem of poor load identification accuracy at high noise levels.The proposed method achieves satisfactorily small relative errors and high correlation coefficients in identifying the mechanical response of local interconnections in board-level packaging structures,while significantly balancing the smoothness of response curves with the accuracy of peak identification.At medium and low noise levels,the relative error is less than 6%,while it is less than 10%at high noise levels.The proposed method provides an effective indirect approach for the boundary conditions of localized solder joints during the projectile penetration process,and its philosophy can be readily extended to other scenarios of multiscale analysis for highly nonlinear materials and structures under extreme loading conditions.展开更多
The Baoshan Cu-Pb-Zn polymetallic deposit is lied in the central Nanling mineralization zone,and belongs to the junction area of the Chenzhou-Linwu fault zone and the Leiyang-Linwu fault zone.It is a significant part ...The Baoshan Cu-Pb-Zn polymetallic deposit is lied in the central Nanling mineralization zone,and belongs to the junction area of the Chenzhou-Linwu fault zone and the Leiyang-Linwu fault zone.It is a significant part of Nanling polymetallic deposit belt.The outcropping stratas consist of upper Devonian Shetianqiao,Xikuangshan Formation,Lower Carboniferous Menggong’ao,Shidengzi,Ceshui,and Zimenqiao Formation.Igneous rocks in the Baoshan ore area mainly comprise granodiorite porphyry.Furthermore,the radio isotopic age ranges from 123 Ma to 183 Ma,belonging to the early to middle Yanshanian.展开更多
为提高载荷识别与结构响应重构的精度及效率,提出了一种同时考虑传递矩阵误差和测量误差的改进Tikhonov正则化方法。首先,通过结构动力学模型构建状态空间方程和传递矩阵,得到结构载荷和响应的重构方程;其次,利用截断随机奇异值分解方...为提高载荷识别与结构响应重构的精度及效率,提出了一种同时考虑传递矩阵误差和测量误差的改进Tikhonov正则化方法。首先,通过结构动力学模型构建状态空间方程和传递矩阵,得到结构载荷和响应的重构方程;其次,利用截断随机奇异值分解方法计算测点位置的近似传递矩阵,同时结合总体最小二乘法(Total Least Squares Method,TLSM)和传统Tikhonov正则化方法识别载荷,再通过待重构位置的传递矩阵重构未知响应;最后,分别对二维桁架和简支梁进行数值仿真和试验分析,验证所提方法的有效性。结果表明,相较于传统Tikhonov正则化方法,所提方法可在保证重构精度的同时提升重构效率。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52475166,52175148)the Regional Collaboration Project of Shanxi Province(Grant No.202204041101044).
文摘Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to miniaturization of electronic components,it is challenging to directly measure or numerically predict the mechanical response of small-sized critical interconnections in board-level packaging structures to ensure the mechanical reliability of electronic devices in projectiles under harsh working conditions.To address this issue,an indirect measurement method using the Bayesian regularization-based load identification was proposed in this study based on finite element(FE)pre-dictions to estimate the load applied on critical interconnections of board-level packaging structures during the process of projectile penetration.For predicting the high-strain-rate penetration process,an FE model was established with elasto-plastic constitutive models of the representative packaging ma-terials(that is,solder material and epoxy molding compound)in which material constitutive parameters were calibrated against the experimental results by using the split-Hopkinson pressure bar.As the impact-induced dynamic bending of the printed circuit board resulted in an alternating tensile-compressive loading on the solder joints during penetration,the corner solder joints in the edge re-gions experience the highest S11 and strain,making them more prone to failure.Based on FE predictions at different structural scales,an improved Bayesian method based on augmented Tikhonov regulariza-tion was theoretically proposed to address the issues of ill-posed matrix inversion and noise sensitivity in the load identification at the critical solder joints.By incorporating a wavelet thresholding technique,the method resolves the problem of poor load identification accuracy at high noise levels.The proposed method achieves satisfactorily small relative errors and high correlation coefficients in identifying the mechanical response of local interconnections in board-level packaging structures,while significantly balancing the smoothness of response curves with the accuracy of peak identification.At medium and low noise levels,the relative error is less than 6%,while it is less than 10%at high noise levels.The proposed method provides an effective indirect approach for the boundary conditions of localized solder joints during the projectile penetration process,and its philosophy can be readily extended to other scenarios of multiscale analysis for highly nonlinear materials and structures under extreme loading conditions.
基金Supported by the Program of Superseding Resources Prospecting in Crisis Mines in China(20089927)
文摘The Baoshan Cu-Pb-Zn polymetallic deposit is lied in the central Nanling mineralization zone,and belongs to the junction area of the Chenzhou-Linwu fault zone and the Leiyang-Linwu fault zone.It is a significant part of Nanling polymetallic deposit belt.The outcropping stratas consist of upper Devonian Shetianqiao,Xikuangshan Formation,Lower Carboniferous Menggong’ao,Shidengzi,Ceshui,and Zimenqiao Formation.Igneous rocks in the Baoshan ore area mainly comprise granodiorite porphyry.Furthermore,the radio isotopic age ranges from 123 Ma to 183 Ma,belonging to the early to middle Yanshanian.
文摘为提高载荷识别与结构响应重构的精度及效率,提出了一种同时考虑传递矩阵误差和测量误差的改进Tikhonov正则化方法。首先,通过结构动力学模型构建状态空间方程和传递矩阵,得到结构载荷和响应的重构方程;其次,利用截断随机奇异值分解方法计算测点位置的近似传递矩阵,同时结合总体最小二乘法(Total Least Squares Method,TLSM)和传统Tikhonov正则化方法识别载荷,再通过待重构位置的传递矩阵重构未知响应;最后,分别对二维桁架和简支梁进行数值仿真和试验分析,验证所提方法的有效性。结果表明,相较于传统Tikhonov正则化方法,所提方法可在保证重构精度的同时提升重构效率。
