A random parameter can be transformed into an interval number in the structural analysis with the concept of the confidence interval. Hence, analyses of uncertain structural systems can be used in the traditional FE...A random parameter can be transformed into an interval number in the structural analysis with the concept of the confidence interval. Hence, analyses of uncertain structural systems can be used in the traditional FEM software. In some cases, the amount of solutions in stochastic structures is nearly as many as that in the traditional structural problems. In addition, a new method to evaluate the failure probability of structures is presented for the needs of the modern engineering design.展开更多
Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by...Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.展开更多
Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications.A numerical experimental method of determining resonant frequencies and Young’s modulus of nanobeams by ...Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications.A numerical experimental method of determining resonant frequencies and Young’s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper.Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process,which inevitably generates the undercut of the nanobeam clamping.In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut,dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L,which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data.By using a least-square fit expression including △L,we finally extract Young’s modulus from the measured resonance frequency versus effective length dependency and find that Young’s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon.This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.展开更多
岩石的短期和长期力学性能和变形特性对工程长期稳定与安全有着重要的影响。传统的本构模型难以统一描述不同岩石材料的短长期力学特性,而基于深度学习方法的理论可在不引入其他弹塑性参数以及本构规律的情况下预测不同岩石的力学特性...岩石的短期和长期力学性能和变形特性对工程长期稳定与安全有着重要的影响。传统的本构模型难以统一描述不同岩石材料的短长期力学特性,而基于深度学习方法的理论可在不引入其他弹塑性参数以及本构规律的情况下预测不同岩石的力学特性。长短期记忆(long short-term mernory,简称LSTM)深度学习算法适用于处理具有时间序列的数据任务,用于预测岩石短长期力学特性具有显著优势。通过引入LSTM算法,分别根据三轴压缩加载路径和应力松弛随时间变化的规律构建序列数据,建立了灰砂岩在常规三轴压缩以及应力松弛下的力学特性预测模型。与试验数据进行对比,可以证明基于深度学习的岩石短长期力学预测本构模型的准确性。为进一步提升模型工程应用价值,将LSTM本构模型嵌入到有限元法(finite element method,简称FEM)框架中进行数值实现,并应用于灰砂岩变形特性的模拟。对比结果表明,LSTM-FEM方法具有较好地预测岩石短长期变形特性的能力。展开更多
基金TheNationalNaturalScienceandChinesePhysicsResearchInstituteFoundationofChina (No .10 0 76 0 14 )andtheSWJTUFoundation (No .2 0 0 2B0 8) .
文摘A random parameter can be transformed into an interval number in the structural analysis with the concept of the confidence interval. Hence, analyses of uncertain structural systems can be used in the traditional FEM software. In some cases, the amount of solutions in stochastic structures is nearly as many as that in the traditional structural problems. In addition, a new method to evaluate the failure probability of structures is presented for the needs of the modern engineering design.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 41075026 and 61001044)the Open Re-search Fund of Key Laboratory of Microelectromechanical System of Ministry of Education,Southeast University,China (Grant Nos. 2009-03 and 2010-02)+1 种基金the Special Fund for Meteorology Research in the Public Interest,China (Grant No. GYHY200906037)the Priority Academic Program Development of Sensor Networks and Modern Meteorological Equipment of Jiangsu Provincial Higher Education Institutions
文摘Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 41075026 and 61001044)the Open Re-search Fund of Key Laboratory of Microelectromechanical System of Ministry of Education,Southeast University,China (Grant Nos. 2009-03 and 2010-02)+1 种基金the Special Fund for Meteorology Research in the Public Interest,China (Grant No. GYHY200906037)the Priority Academic Program Development of Sensor Networks and Modern Meteorological Equipment of Jiangsu Provincial Higher Education Institutions
文摘Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications.A numerical experimental method of determining resonant frequencies and Young’s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper.Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process,which inevitably generates the undercut of the nanobeam clamping.In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut,dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L,which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data.By using a least-square fit expression including △L,we finally extract Young’s modulus from the measured resonance frequency versus effective length dependency and find that Young’s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon.This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.
文摘岩石的短期和长期力学性能和变形特性对工程长期稳定与安全有着重要的影响。传统的本构模型难以统一描述不同岩石材料的短长期力学特性,而基于深度学习方法的理论可在不引入其他弹塑性参数以及本构规律的情况下预测不同岩石的力学特性。长短期记忆(long short-term mernory,简称LSTM)深度学习算法适用于处理具有时间序列的数据任务,用于预测岩石短长期力学特性具有显著优势。通过引入LSTM算法,分别根据三轴压缩加载路径和应力松弛随时间变化的规律构建序列数据,建立了灰砂岩在常规三轴压缩以及应力松弛下的力学特性预测模型。与试验数据进行对比,可以证明基于深度学习的岩石短长期力学预测本构模型的准确性。为进一步提升模型工程应用价值,将LSTM本构模型嵌入到有限元法(finite element method,简称FEM)框架中进行数值实现,并应用于灰砂岩变形特性的模拟。对比结果表明,LSTM-FEM方法具有较好地预测岩石短长期变形特性的能力。
