具有多處斷面驟變之半無限長瑞利– 洛夫桿受衝擊桿加載下之應力波傳播

簡易檢索 / 詳目顯示

回結果列表

研究生：	Nguyen Ngoc Thang Nguyen Ngoc Thang
論文名稱：	具有多處斷面驟變之半無限長瑞利– 洛夫桿受衝擊桿加載下之應力波傳播 Stress Wave Propagation in a Semi-Infinite Rayleigh–Love Rod with Multiple Sudden Cross-Sectional Area Variations Excited by a Striker Rod
指導教授：	王仲宇 Chung-Yue Wang
口試委員:
學位類別：	博士 Doctor
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2024
畢業學年度：	113
語文別：	英文
論文頁數：	181
中文關鍵詞：	應力波傳播、瑞利-洛夫桿理論、非破壞檢測（NDT）、橫截面面積變化、沖擊回聲技術、結構健康監測、拉普拉斯變換的數值逆轉換法、反射波和透射波、幾何不規則性、後張錨固系統、側向慣性和泊松比的影響
外文關鍵詞：	Stress wave propagation, Rayleigh–Love rod theory, cross-sectional area variation, impact echo techniques, post-tension anchorage systems, effects of lateral inertia and Poisson’s ratio
相關次數：	點閱：28 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本論文研究了在不同橫截面積和不同一般阻抗條件下，側向慣性和泊松比對瑞利-洛夫桿中縱向波的影響，並探討了應力波在有突變橫截面的桿中的傳播情況，導出了反射波和透射波的解析解。通過有限元分析驗證了解析解之正確性。此外，本論文提出了一種基於沖擊回聲技術的新型非破壞檢測（NDT）方法，可用於檢測具有突變橫截面結構中的缺陷位置及劣化程度。
這項研究探討了在一個包括移動擊錘桿和靜止的半無限長瑞利-洛夫桿系統中，不同阻抗對應力波傳播的影響。在這項研究中，使用拉普拉斯變換的數值逆轉換是處理與瑞利-洛夫桿中應力波傳播方程相關的複雜數學模型的關鍵技術。這種數值方法的可將複雜的微分方程從拉普拉斯域轉回時間域，提供了一個清楚且可行的波動行為展示。拉普拉斯變換的數值逆轉換有助於更深入地探索在阻抗變化的界面處發生的波動傳播。這種功能非常重要，因為它有助於預測材料屬性和幾何配置的變化如何影響波的特性，這對於設計有效的測試系統至關重要。它揭示了這些桿件之幾何不連續性如何顯著改變波的幅度和傳播模式，導致波形的放大或衰減。這一關鍵的理解有助於改善分離式霍普金森壓力桿（SHPB）測試的設計和校準，以獲得更好的測試結果。
最後，本研究開發了一個正算及反算分析方法，用於評估土木工程中的後張錨固系統中鋼腱的完整性。通過模擬擊錘沖擊並利用瑞利-洛夫桿理論，該模型評估張力鋼腱的完整性，通過波幅、波形和時序的變化識別腐蝕和其他缺陷的位置及尺寸。這項研究加深了對截面變化如何影響波動行為的理解，從而促進了結構健康監測方法的發展。

This dissertation studies the stress wave propagation in Rayleigh–Love rods considering the effects of lateral inertia and Poisson’s ratio on longitudinal waves in the rods under varying conditions of cross-sectional areas and different general impedances. The study explores the propagation of stress waves in rods with abrupt changes in cross-sectional area, deriving analytical solutions for reflected and transmitted waves. Theoretical findings are substantiated through finite element analysis, confirming the analytical solutions. Additionally, the research proposes a novel nondestructive testing (NDT) method based on impact echo techniques for detecting defects in structures with sudden cross-sectional changes.
This study simultaneously investigates the effects of different impedances on stress wave propagation in a system comprising a moving striker rod and a stationary semi-infinite Rayleigh–Love rod. The utilization of the numerical inversion of Laplace transformations in this research is a pivotal technique for handling the complex mathematical models related to the equation of stress wave propagation in Rayleigh–Love rods. The convenience of this numerical method allows for the transformation of complicated differential equations from the Laplace domain back to the time domain, providing a clear and actionable depiction of wave behaviors over time. The numerical inversion of Laplace transformations facilitates a deeper exploration into the wave propagation that occurs at the interfaces where general impedances vary. This capability is crucial because it helps in predicting how changes in material properties and geometrical configurations influence the wave's characteristics, which are essential for designing effective testing setups. It reveals how these discontinuities can significantly alter wave amplitude and propagation patterns, leading to either wave amplification or attenuation. This crucial understanding is instrumental in refining the design and calibration of Split-Hopkinson Pressure Bar (SHPB) tests, optimizing them for better response under test conditions.
Lastly, the research develops both forward and backward analysis methods to assess the integrity of post-tension anchorage systems in civil engineering. By simulating striker impacts and leveraging the Rayleigh–Love rod theory, this model assesses the integrity of anchorage blocks, identifying corrosion and other defects through variations in wave amplitude, waveform, and timing. This research provides a deeper understanding of how cross-sectional variations influence wave behavior, thereby facilitating the development of methodologies in structural health monitoring.

中文摘要    I
ABSTRACT    II
ACKNOWLEDGEMENTS    III
Table of Contents    V
List of Tables    VIII
List of Figures    IX
List of Abbreviations    XVI
Chapter 1. Introduction    1
1.1 Overview and Motivation    1
1.3 Research Methods    7
1.4 Organization of Dissertation    7
Chapter 2. Fundamental of Traditional Wave Theory in a rod    10
2.1 Introduction to One-Dimensional Traditional Wave Theory    10
2.2 Derivation of One-Dimensional Traditional Wave Equation    10
2.3 Analytical Solutions for Solving the Traditional Wave Equation    11
2.4 Reflection and Transmission at Boundaries    22
2.5 Applications of One-Dimensional Traditional Wave Theory    23
Chapter 3. Fundamental of Rayleigh–Love Wave Theory in a Rod    25
3.1 Introduction to Rayleigh–Love Longitudinal Wave Theory in a Rod    25
3.2 Derivation of Rayleigh–Love Wave Equation under Tension Force    26
3.3 Applications of Rayleigh–Love Wave Theory    34
3.4 Methods for Solving the Rayleigh–Love Wave Equation    35
Chapter 4. Numerical Inversion of Laplace Transformation    37
4.1 Introduction to Laplace Transform    37
4.2 Basic Conditions and Theorems of the Laplace Transform    38
4.3 Inverse Laplace Transform Using an Approximation Formula    41
4.4 Applications of Laplace Transform    45
4.5 Examples    46
Chapter 5. Analysis of Stress Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Sudden Cross-Sectional Area Variations    51
5.1 Model Description    51
5.2 Solution of the Stress Wave Propagation Equation in a Rayleigh–Love Rod with Sudden Cross-Sectional Area Variation    52
5.3 Analysis of the Stress Wave Propagation in a Rod with A1  A2    56
5.3.1 Verification of the analytical solution from Eqs. (5.11) to (5.15) with the FEM solution    56
5.3.2 Investigation of stress wave propagation in a rod at various positions    60
5.4 Analysis of the Stress Wave Propagation in a Rod with A1  A2    64
5.5 Identification of Locations with Sudden Cross-Sectional Area Changes in the Rod    66
5.5.1 Reflection and transmission of stress wave in a rod with single sudden cross-sectional area variation    66
5.5.2 Reflection and transmission of stress wave in a rod with double sudden cross-sectional area variations    71
5.6 Identification of the Corresponding Model for Sudden Cross-Sectional Area Variations in the Rod    77
Chapter 6. Analysis of Stress Wave Propagation in a Semi-Infinite Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Different General Impedances    82
6.1 Model Description    82
6.2 The Fundamental Theory of Wave Propagation in the Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod of Different General Impedances    82
6.3 Investigation of Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with the same Impedances    88
6.4 Investigation of Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Different Impedances    93
6.4.1 Investigation of stress wave propagation in a semi-infinite rod and a striker rod at the interface x = 0 m    96
6.4.2 Investigation of stress wave propagation in a semi-infinite rod at x = 0.5 m    98
6.2.3 Investigation of stress wave propagation in a striker rod at x = −0.1 m    100
6.5 Investigation of Strain Rate’s Effect on the Material of the Striker Rod and Semi-Infinite Rod Under Collinear Impact    103
6.6 Travel Time History    106
Chapter 7. Detection of Defect in a Semi-Infinite Rayleigh–Love Rod Under Tensile Force    110
7.1 Model Description    110
7.2 The Fundamental Theory of Wave Propagation in a Semi-Infinite Rayleigh–Love Rod under Tensile Force Excited by a Striker Rod    110
7.3 Example and Discussion    121
7.4. Identification of Locations with Sudden Cross-Sectional Area Changes in the Rod    127
7.4.1. Formulation of method    127
7.4.2. Validation of formula    130
7.4.3. Identification of the locations and sudden cross-sectional area variations    132
Chapter 8. Conclusions    139
Chapter 9. Future Work    141
References    146
Appendixes    154
Appendix A. Derivation of the relationship between stress and velocity in a rod.    154
Appendix B. Integration of equations for determining incident, reflected, and transmitted stresses without considering Poisson’s ratio effect.    156
Appendix C. Derivation of the wave velocity taking into account the effect of Poisson's ratio.    158
List of Publication    160

                                

[1] Tesfamariam, S., and Martín-Pérez, B. "Stress wave propagation for evaluation of reinforced concrete structures." Non-Destructive Evaluation of Reinforced Concrete Structures. Woodhead Publishing, pp. 417-440, 2010.
[2] Sawangsuriya, A. "Wave propagation methods for determining stiffness of geomaterials." Wave processes in classical and new solids, vol. 44, 2012.
[3] Ostachowicz, W. and Radzieński, M. "Structural health monitoring by means of elastic wave propagation." Journal of Physics: Conference Series, vol. 382 (1). IOP Publishing, 2012.
[4] Hu, Y. and Yang, Y. "Wave propagation modeling of the PZT sensing region for structural health monitoring." Smart Materials and Structures, vol. 16(3), pp. 706, 2007.
[5] Jamaludin, N., Mba, D. and Bannister, R.H. "Condition monitoring of slow-speed rolling element bearings using stress waves." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, vol. 215.4, pp. 245-271, 2001.
[6] Lee, B. C., and Staszewski, W. J. "Modelling of Lamb waves for damage detection in metallic structures: Part I. Wave propagation." Smart materials and structures, vol. 12(5), pp. 804, 2003.
[7] Lee, B. C., and Staszewski, W. J. "Modelling of Lamb waves for damage detection in metallic structures: Part II. Wave interactions with damage." Smart materials and structures, vol. 12(5), pp. 815, 2003.
[8] Palacz, M. and Krawczuk, M. "Analysis of longitudinal wave propagation in a cracked rod by the spectral element method." Computers & structures, vol. 80(24), pp. 1809-1816, 2002.
[9] Krawczuk, M., Grabowska, J. and Palacz, M. "Longitudinal wave propagation. Part II—Analysis of crack influence." Journal of Sound and Vibration, vol. 295(3-5), pp. 479-490, 2006.
[10] Gaul, L., Bischoff, S., Sprenger, H. and Haag, T. "Numerical and experimental investigation of wave propagation in rod-systems with cracks." Engineering fracture mechanics, vol. 77(18), pp. 3532-3540, 2010.
[11] Wang, X., Yu, T., Yan, H., Ding, J., Li, Z., Qin, Z. and Chu, F. "Application of stress wave theory for pyroshock isolation at spacecraft-rocket interface." Chinese Journal of Aeronautics, vol. 34(8), pp. 75-86, 2021.
[12] Fang, X. "A one-dimensional stress wave model for analytical design and optimization of oscillation-free force measurement in high-speed tensile test specimens." International Journal of Impact Engineering, vol. 149, pp. 103770, 2021.
[13] Love A.E.H. A treatise on the mathematical theory of elasticity. New York: Dover Publications, 1944.
[14] D’Alembert, J. "Researches on the curve that a tense cord forms when set into vibration." Hist. Acad. R. Des Sci. BL Berlin, vol. 3 pp. 214-249, 1747.
[15] Yang, H., Li, Y. and Zhou, F. "Propagation of stress pulses in a Rayleigh-Love elastic rod." International Journal of Impact Engineering, vol. 153, pp. 103854, 2021.
[16] Yang, H., Li, Y. and Zhou, F. "Stress waves generated in a Rayleigh-Love rod due to impacts." International Journal of Impact Engineering, 159, pp. 104027, 2022.
[17] Beddoe, B. "Propagation of elastic stress waves in a necked rod." Journal of Sound and Vibration, vol. 2(2), pp. 150-166, 1965.
[18] Fraige, F.Y. and Es-Saheb, M.H. "Analysis of Elastic Stress Wave Propagation in Stepped Bars, Transmission, Reflection, and Interaction: Experimental Investigation." Jordan Journal of Mechanical & Industrial Engineering, vol. 16(2), 2022.
[19] Valsa, J. and Brančik, L. "Approximate formulae for numerical inversion of Laplace transforms." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 11(3), pp. 153-166, 1998.
[20] Kolsky, H. "An investigation of the mechanical properties of materials at very high rates of loading." Proceedings of the physical society. Section B, vol. 62(11), pp. 676–700, 1949.
[21] Albertini, C., Boone, P.M. and Montagnani, M. "Development of the Hopkinson bar for testing large specimens in tension." Le Journal de Physique Colloques, vol. 46(C5), pp. C5-499, 1985.
[22] Nemat-Nasser, S., Isaacs, J.B. and Starrett, J.E. "Hopkinson techniques for dynamic recovery experiments." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, vol. 435(1894), pp. 371-391, 1991.
[23] Al-Mousawi, M.M., Reid, S.R. and Deans, W.F. "The use of the split Hopkinson pressure bar techniques in high strain rate materials testing." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 211(4), pp. 273-292, 1997.
[24] Verleysen, P. and Degrieck, J. "Experimental investigation of the deformation of Hopkinson bar specimens." International journal of impact engineering, vol. 30(3), pp. 239-253, 2004.
[25] Gama, B.A., Lopatnikov, S.L. and Gillespie Jr, J.W. "Hopkinson bar experimental technique: a critical review." Appl. Mech. Rev., vol. 57(4), pp. 223-250, 2004.
[26] Yang, L.M. and Shim, V.P.W. "An analysis of stress uniformity in split Hopkinson bar test specimens." International Journal of Impact Engineering, vol. 31(2), pp. 129-150, 2005.
[27] Kolsky, H. "Stress waves in solids." Journal of Sound and Vibration, vol. 1(1), pp. 88-110, 1964.
[28] Siviour, C. R. "A measurement of wave propagation in the split Hopkinson pressure bar." Measurement Science and Technology, vol. 20(6), pp. 065702, 2009.
[29] Othman, R., editor. The Kolsky-Hopkinson bar machine: selected topics. Springer, 2018.
[30] Khosravani, M.R. and Weinberg, K. "A review on split Hopkinson bar experiments on the dynamic characterisation of concrete." Construction and Building Materials, vol. 190, pp. 1264-1283, 2018.
[31] Majzoobi, G.H., Rahmani, K. and Lahmi, S. "Determination of length to diameter ratio of the bars in torsional Split Hopkinson bar." Measurement, vol. 143, pp. 144-154, 2019.
[32] Shin, H. and Kim, J.B. "Evolution of specimen strain rate in split Hopkinson bar test." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 233(13), pp. 4667-4687, 2019.
[33] Maassen, S.F., Niekamp, R., Bergmann, J.A., Pöhl, F., Schröder, J. and Wiederkehr, P. "Modeling of the Split-Hopkinson-Pressure-Bar experiment with the explicit material point method." Computational Particle Mechanics, pp. 1-14, 2021.
[34] Miyambo, M.E., Von Kallon, D.V., Pandelani, T. and Reinecke, J.D. "Review of the development of the split Hopkinson pressure bar." Procedia CIRP, vol. 119, pp. 800-808, 2023.
[35] Shin, H. "Sound speed and Poisson’s ratio calibration of (split) Hopkinson bar via iterative dispersion correction of elastic wave." Journal of Applied Mechanics, vol. 89(6), pp. 061007, 2022.
[36] American Concrete Institute (ACI). "Corrosion and repair of unbonded single strand tendons.", ACI, pp. 1-20, 1998.
[37] Salas, R.M., Schokker, A.J., West, J.S., Breen, J.E. and Kreger, M.E. "Corrosion risk of bonded, post-tensioned concrete elements." Pci journal, vol. 53(1), pp. 89, 2008.
[38] Xu, J. and Chen, W. "Behavior of wires in parallel wire stayed cable under general corrosion effects." Journal of Constructional Steel Research, vol. 85, pp. 40-47, 2013.
[39] Carsana, M. and Bertolini, L. "Corrosion failure of post-tensioning tendons in alkaline and chloride-free segregated grout: a case study." Structure and Infrastructure Engineering, vol. 11(3), pp. 402-411, 2015.
[40] Ebeling, R.M., White, B.C., Evans, J.A., Haskins, R.W. and Miller, E.L. Corrosion induced loss of capacity of post-tensioned seven wire strand cable used in multistrand anchor systems installed at corps projects. US Army Engineer Research and Development Center, Information Technology Laboratory, 2016.
[41] Miller, E.L., White, B.C., Haskins, R.W., Ebeling, R.M. and Evans, J.A. "An investigation of corrosion mitigation strategies for aging post-tensioned cables.", US Army Engineer Research and Development Center, Information Technology Laboratory, 2017.
[42] Lan, C., Xu, Y., Liu, C., Li, H. and Spencer Jr, B.F. "Fatigue life prediction for parallel-wire stay cables considering corrosion effects." International Journal of Fatigue, vol. 114, pp. 81-91, 2018.
[43] Wu, S., Chen, H., Ramandi, H.L., Hagan, P.C., Hebblewhite, B., Crosky, A. and Saydam, S. "Investigation of cable bolts for stress corrosion cracking failure." Construction and Building Materials, vol. 187, pp. 1224-1231, 2018.
[44] Wang, Y., Zheng, Y.Q., Zhang, W.H. and Lu, Q.R. "Analysis on damage evolution and corrosion fatigue performance of high-strength steel wire for bridge cable: Experiments and numerical simulation." Theoretical and Applied Fracture Mechanics, vol. 107, pp. 102571, 2020.
[45] Yin, T., Sun, X., Wang, Y., Zhao, Y., Wang, S., Liu, L. and Chen, H. "Corrosion characteristics of anchor cables in electrolytic corrosion test and the applicability of the test method in study of anchor cable corrosion." Advances in Civil Engineering, vol. 2021 (1), pp. 6695288, 2021.
[46] Hollkamp, J.P., Sen, M. and Semperlotti, F. "Analysis of dispersion and propagation properties in a periodic rod using a space-fractional wave equation." Journal of Sound and Vibration, vol. 441, pp. 204-220, 2019.
[47] Yang, K. "A unified solution for longitudinal wave propagation in an elastic rod." Journal of Sound and Vibration, vol. 314(1-2), pp. 307-329, 2008.
[48] Hull, A.J. "A closed form solution of a longitudinal bar with a viscous boundary condition." Journal of Sound and Vibration, vol. 169, pp. 19-19, 1994.
[49] Wheeler, G.F. and Crummett, W.P. "The vibrating string controversy." American Journal of Physics, vol. 55(1), pp. 33-37, 1987.
[50] Sirota, L. and Halevi, Y. "Extended D'Alembert solution of finite length second order flexible structures with damped boundaries." Mechanical Systems and Signal Processing, vol. 39(1-2), pp. 47-58, 2013.
[51] Tanaka, K., Kurokawa, T. and Ueda, K. "Plastic stress wave propagation in a circular bar induced by a longitudinal impact." Macro-and Micro-Mechanics of High Velocity Deformation and Fracture: IUTAM Symposium on MMMHVDF Tokyo, Japan, pp. 317-326, 1985.
[52] Gopalakrishnan, S. "A deep rod finite element for structural dynamics and wave propagation problems." International Journal for numerical methods in Engineering, vol. 48(5), pp. 731-744, 2000.
[53] Grote, M.J., Schneebeli, A. and Schötzau, D. "Discontinuous Galerkin finite element method for the wave equation." SIAM Journal on Numerical Analysis, vol. 44(6), pp. 2408-2431, 2006.
[54] Ramírez, H. and Rubio-Gonzalez, C. "Finite-element simulation of wave propagation and dispersion in Hopkinson bar test." Materials & design, vol. 27(1), pp. 36-44, 2006.
[55] Idesman, A.V., Subramanian, K., Schmidt, M., Foley, J.R., Tu, Y. and Sierakowski, R.L. "Finite element simulation of wave propagation in an axisymmetric bar." Journal of sound and vibration, vol. 329(14), pp. 2851-2872, 2010.
[56] Keramat, A. and Ahmadi, A. "Axial wave propagation in viscoelastic bars using a new finite-element-based method." Journal of Engineering Mathematics, vol. 77(1), pp. 105-117, 2012.
[57] Steinbach, O. and Zank, M. "A stabilized space–time finite element method for the wave equation." Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, Springer International Publishing, pp. 341-370, 2019.
[58] Mirzajani, M., Khaji, N. and Hori, M. "Stress wave propagation analysis in one-dimensional micropolar rods with variable cross-section using micropolar wave finite element method." International Journal of Applied Mechanics, vol. 10(04), pp. 1850039, 2018.
[59] Lu, T. and Legrand, M. "Nonsmooth modal analysis via the boundary element method for one-dimensional bar systems." Nonlinear Dynamics, pp. 1-20, 2021.
[60] Aral, M.M. and Gülçat, Ü. "A finite element Laplace transform solution technique for the wave equation." International Journal for Numerical Methods in Engineering, vol. 11(11), pp. 1719-1732, 1977.
[61] Davies, A. "The solution of differential equations using numerical Laplace transforms." International Journal of Mathematical Education in Science and Technology, vol. 30(1), pp. 65-79, 1999.
[62] Agrawal, O.P. "Solution for a fractional diffusion-wave equation defined in a bounded domain." Nonlinear Dynamics, vol. 29, pp. 145-155, 2002.
[63] Agrawal, O.P. "A general solution for a fourth-order fractional diffusion–wave equation defined in a bounded domain." Computers & Structures, vol. 79(16), pp. 1497-1501, 2001.
[64] Huynh, D.P., Knezevic, D.J. and Patera, A.T. Patera. "A Laplace transform certified reduced basis method; application to the heat equation and wave equation." Comptes Rendus. Mathématique, vol. 349(7-8), pp. 401-405, 2011.
[65] Jafari, H., Khalique, C.M. and Nazari, M. "Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion–wave equations." Applied Mathematics Letters, vol. 24(11), pp. 1799-1805, 2011.
[66] Schiff, J.L. The Laplace transform: theory and applications. Springer Science & Business Media, 2013.
[67] Zheng, Y. and Zhou, F. "Using Laplace transform to solve the viscoelastic wave problems in the dynamic material property tests." EPJ Web of Conferences, vol. 94, 2015.
[68] Schiff, J. L. The Laplace transform: theory and applications. Springer, Berlin. 1999.
[69] Carrier, G.F., Krook, M. and Pearson, C.E. Functions of a complex variable: theory and technique. Society for Industrial and Applied Mathematics, 2005.
[70] Siauw, T. and Bayen, A. An introduction to MATLAB® programming and numerical methods for engineers. Academic Press, 2014.
[71] Esfandiari, R.S. Numerical methods for engineers and scientists using MATLAB®. Crc Press, 2017.
[72] Yang, W.Y., Cao, W., Kim, J., Park, K.W., Park, H.H., Joung, J., Ro, J.S., Lee, H.L., Hong, C.H. and Im, T. Applied numerical methods using MATLAB. John Wiley & Sons, 2020.
[73] Dupac, M. and Marghitu, D.B. Engineering Applications: Analytical and Numerical Calculation with MATLAB. John Wiley & Sons, 2021.
[74] Al-Furjan, M.S.H., Bidgoli, M.R., Kolahchi, R., Farrokhian, A. and Bayati, M.R. Application of Numerical Methods in Engineering Problems using MATLAB®. CRC Press, 2023.
[75] Juraj, V. "Numerical inversion of Laplace transforms in Matlab." MATLAB Central File ID: # 32824, 2011.
[76] Dassault Systèmes. Abaqus Analysis User's Guide, Volume II: Analysis. Providence, RI, USA, 2016.
[77] Shin, H. and Kim, D. "One-dimensional analyses of striker impact on bar with different general impedance." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 234(2), pp. 589-608, 2020.
[78] Johnson, G.R. "A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures." Proceedings of the 7th International Symposium on Ballistics, The Hague, Netherlands, 1983.
[79] Tanimura, S., Tsuda, T., Abe, A., Hayashi, H. and Jones, N. "Comparison of rate-dependent constitutive models with experimental data." International Journal of Impact Engineering, vol. 69, pp. 104-113, 2014.
[80] Zhao, Y., Sun, J., Li, J., Yan, Y. and Wang, P. "A comparative study on Johnson-Cook and modified Johnson-Cook constitutive material model to predict the dynamic behavior laser additive manufacturing FeCr alloy." Journal of Alloys and Compounds, vol. 723, pp. 179-187, 2017.
[81] Jang, T.J., Yoon, J.W. and Kim, J.B. "Determination of Johnson-Cook constitutive model coefficients considering initial gap between contact faces in SHPB test." Journal of Materials Research and Technology, vol. 24, pp. 7242-7257, 2023.
[82] Chen, G., Ke, Z., Ren, C. and Li, J. "Constitutive modeling for Ti-6Al-4V alloy machining based on the SHPB tests and simulation." Chinese Journal of Mechanical Engineering, vol. 29(5), pp. 962-970, 2016.
[83] Tang, W., Liu, C. and Zhang, K. "The Johnson-Cook Constitutive Model of TA19 Titanium Alloy." Journal of Physics: Conference Series, vol. 2557(1), pp. 012041, 2023.

簡易檢索 / 詳目顯示

相關論文