Ngày nhận bài: 02-04-2024
Ngày duyệt đăng: 23-05-2024
DOI:
Lượt xem
Download
Cách trích dẫn:
PHÂN TÍCH TĨNH TẤM SANDWICH FGM XỐPĐẶT TRÊN NỀN ĐÀN HỒI WINKLER/PASTERNAK/KERR
,
Nguyễn Thanh Hải
2
,
Lê Vũ Quân
2
Tóm tắt
Nghiên cứu này được thực hiện nhằm phân tích tĩnh kết cấu tấm sandwich với lớp lõi bằng vật liệu xốp (FGP), hai lớp bề mặt là vật liệu có cơ tính biến thiên (FGM) đặt trên nền đàn hồi Winkler/Pasternak/Kerr. Phương pháp nghiên cứu là mô hình lý thuyết bằng phương pháp giải tích dựa trên lý thuyết biến dạng cắt bậc nhất (FSDT). Ba quy luật phân bố lỗ rỗng của lớp lõi được xem xét bao gồm: phân bố đều, phân bố không đều đối xứng và phân bố không đều bất đối xứng. Hai lớp bề mặt FGM giả thiết có cơ tính biến thiên tuân theo quy luật lũy thừa. Dựa trên nguyên lý Hamilton, hệ phương trình cân bằng được thiết lập và giải bằng cách sử dụng dạng nghiệm Navier cho tấm chữ nhật liên kết khớp trên chu tuyến. Kết quả nghiên cứu mô hình lý thuyết đã thiết lập và chương trình tính được kiểm chứng bằng cách so sánh với các công bố từ các tác giả khác, qua đó đã chứng minh độ tin cậy của phương pháp giải. Bên cạnh đó, ảnh hưởng của tham số vật liệu, kích thước hình học, nền đàn hồi đến độ võng và ứng suất của tấm sandwich được khảo sát qua các ví dụ số.
Tài liệu tham khảo
Asghari M., Ahmadian M., Kahrobaiyan M. & Rahaeifard M. (2010). On the size-dependent behavior of functionally graded micro-beams. Materials & Design (1980-2015). 31(5): 2324-2329.
Daikh A.A. & Zenkour A.M. (2019). Effect of porosity on the bending analysis of various functionally graded sandwich plates. Materials Research Express. 6(6): 065703.
Daikh A.A. &d Zenkour A.M. (2019). Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory. Materials Research Express. 6(11): 115707.
Đặng Xuân Hùng, Vũ Văn Thẩm, Trần Hữu Quốc & Phommavongsa S. (2023). Phân tích dao động riêng kết cấu tấm Sandwich Auxetic áp điện có cơ tính biến thiên. Tạp chí Khoa học Công nghệ Xây dựng (TCKHCNXD)-ĐHXDHN, 17(2V): 42-60.
Filonenko-Borodich M. (1940). Some approximate theories of elastic foundation. Uchenyie Zapiski Moskovskogo Gosudarstuennogo Universiteta Mekhanika, Moscow. 46: 3-18.
Guo H., Zheng H. & Zhuang X. (2019). Numerical manifold method for vibration analysis of Kirchhoff's plates of arbitrary geometry. Applied Mathematical Modelling. 66: 695-727.
Hetenyi M. (1950). A general solution for the bending of beams on an elastic foundation of arbitrary continuity. Journal of Applied Physics. 21(1): 55-58.
Houari M.S.A., Tounsi A. & Bég O.A. (2013). Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory. International Journal of Mechanical Sciences. 76: 102-111.
Kerr A. (1984). On the formal development of elastic foundation models. Ingenieur-Archiv. 54(6): 455-464.
Kerr A.D. (1965). A study of a new foundation model. Acta Mechanica. 1(2): 135-147.
Li Y., Feng Z., Hao L., Huang L., Xin C., Wang Y., Bilotti E., Essa K., Zhang H. & Li Z. (2020). A Review on Functionally Graded Materials and Structures via Additive Manufacturing: From Multi‐Scale Design to Versatile Functional Properties. Advanced Materials Technologies. 5(6): 1900981.
Li D., Deng Z., Xiao H. & Jin P. (2018). Bending analysis of sandwich plates with different face sheet materials and functionally graded soft core. Thin-Walled Structures. 122: 8-16.
Li D., Deng Z., Xiao H. & Zhu L. (2018). Thermomechanical bending analysis of functionally graded sandwich plates with both functionally graded face sheets and functionally graded cores. Mechanics of Advanced Materials and Structures. 25(3): 179-191.
Li M., Soares C.G. & Yan R. (2021). Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT. Composite Structures. 264: 113643.
Mantari J. (2015). Refined and generalized hybrid type quasi-3D shear deformation theory for the bending analysis of functionally graded shells. Composites Part B: Engineering. 83: 142-152.
Mindlin R. (1951). Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME. J. Appl. Mech. 18(1): 31-38.
Neves A., Ferreira A., Carrera E., Cinefra M., Roque C., Jorge R. & Soares C.M. (2013). Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Composites Part B: Engineering. 44(1): 657-674.
Pasternak P. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants. Gos. Izd. Lit. po Strait i Arkh.
Quoc T.H., Tu T.M. & Van Tham V. (2021). Free vibration and dynamic response of sandwich composite plates with auxetic honeycomb core. Journal of Science and Technology in Civil Engineering (JSTCE)-HUCE. 15(4): 1-14.
Reddy J. (2000). Analysis of functionally graded plates. International Journal for numerical methods in engineering. 47(1‐3): 663-684.
Reddy J.N. (2017). Energy principles and variational methods in applied mechanics. John Wiley & Sons.
Reissner E. (1945). The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech., 12(2): A69-A77.
Rezaei A. & Saidi A. (2015). Exact solution for free vibration of thick rectangular plates made of porous materials. Composite Structures. 134: 1051-1060.
Rezaei A. & Saidi A. (2016). Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous - cellular plates. Composites Part B: Engineering. 91: 361-370.
Sokolov S. (1952). Circular plate on a generalized foundation. Inzhinierny Sbornik, Academy of Sciences USSR. 11.
Thai C.H., Zenkour A., Wahab M.A. & Nguyen-Xuan H. (2016). A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis. Composite Structures. 139: 77-95.
Thai H.-T. & Choi D.-H. (2011). A refined plate theory for functionally graded plates resting on elastic foundation. Composites Science and Technology. 71(16): 1850-1858.
Thai H.-T., Nguyen T.-K., Vo T.P. & Lee J. (2014). Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics-A/Solids. 45: 211-225.
Tlidji Y., Daouadji T.H., Hadji L., Tounsi A. & Bedia E.A.A. (2014). Elasticity solution for bending response of functionally graded sandwich plates under thermomechanical loading. Journal of Thermal Stresses. 37(7): 852-869.
Torabi J., Kiani Y. & Eslami M. (2013). Linear thermal buckling analysis of truncated hybrid FGM conical shells. Composites Part B: Engineering. 50: 265-272.
Tornabene F. (2009). Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Computer Methods in Applied Mechanics and Engineering. 198(37-40): 2911-2935.
Tounsi A., Houari M.S.A. & Benyoucef S. (2013). A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates. Aerospace science and technology. 24(1): 209-220.
Tran H.-Q., Vu V.-T. & Tran M.-T. (2023). Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method. Composite Structures. 305: 116535.
Tran H.-Q., Vu V.-T., Nguyen V.-L. & Tran M.-T. (2023). Free vibration and nonlinear dynamic response of sandwich plates with auxetic honeycomb core and piezoelectric face sheets. Thin-Walled Structures. 191: 111141.
Trinh L.C., Vo T.P., Osofero A.I. & Lee J. (2016). Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach. Composite Structures. 156: 263-275.
Vafakhah Z. & Neya B.N. (2019). An exact three dimensional solution for bending of thick rectangular FGM plate. Composites Part B: Engineering. 156: 72-87.
Vo T.P., Thai H.-T., Nguyen T.-K. & Inam F. (2014). Static and vibration analysis of functionally graded beams using refined shear deformation theory. Meccanica. 49: 155-168.
Winkler E. (1867). Die Lehre von der Elasticitaet und Festigkeit: mit besonderer Rücksicht auf ihre Anwendung in der Technik, für polytechnische Schulen, Bauakademien, Ingenieure, Maschinenbauer, Architecten, etc. H. Dominicus.
Wu D., Liu A., Huang Y., Huang Y., Pi Y. & Gao W. (2018). Dynamic analysis of functionally graded porous structures through finite element analysis. Engineering Structures. 165: 287-301.
Zaoui F.Z., Ouinas D. & Tounsi A. (2019). New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Composites Part B: Engineering. 159: 231-247.
Zenkour A. (2005). A comprehensive analysis of functionally graded sandwich plates: Part 1 - Deflection and stresses. International journal of solids and structures. 42(18-19): 5224-5242.
Zenkour A. & Sobhy M. (2010). Thermal buckling of various types of FGM sandwich plates. Composite Structures. 93(1): 93-102.
Zenkour A.M. (2006). Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling. 30(1): 67-84.
Zhao X., Lee Y. & Liew K.M. (2009). Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. Journal of sound and Vibration. 319(3-5): 918-939.