Dynamic and static isogeometric analysis for laminated Timoshenko curved microbeams. (English) Zbl 1521.74221
Summary: An effective computational approach that can simultaneously deal with several complexities in geometries, material properties, and size effects is of non-trivial yet important tasks for the design and optimization of device components in micro- and nano-electromechanical systems. This study is devoted to the development of such an effective computational approach, which is formed by integrating the modified couple stress theory into isogeometric analysis framework. The proposed approach is applied to mechanical problems of laminated Timoshenko curved microbeams, i.e., anazlying static bending, natural frequency and transient response. The developed method enables to describe and examine nontrivial features in both material and geometrical properties of laminated curved microbeams. Geometries of curved microbeams and displacement approximation are accurately described by the non-uniform rational B-spline basis functions. For laminated composites, the material coupling is taken into account with the use of equivalent elastic modulus; and the deepness term is properly included in laminate stiffness parameters. In addition, the small-scale size effects are captured with the use of modified couple stress theory. The accuracy and performance of proposed method are demonstrated through several numerical examples, in which the static bending, free vibration and transient response of laminated curved microbeams are considered under effects of some factors such as aspect ratios, lay-ups, boundary conditions and size dependence.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D07 | Numerical computation using splines |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74S22 | Isogeometric methods applied to problems in solid mechanics |
Keywords:
curved microbeam; laminated composite; Timoshenko theory; size effects; variable curvature; isogeometric analysisReferences:
| [1] | Arlett, J. L.; Myers, E. B.; Roukes, M. L., Comparative advantages of mechanical biosensors, Nat Nanotechnol, 6, 4, 203-215 (2011) |
| [2] | Boisen, A.; Dohn, S.; Keller, S. S.; Schmid, S.; Tenje, M., Cantilever-like micromechanical sensors, Rep Prog Phys, 74, 3, 036101 (2011) |
| [3] | Tamayo, J.; Kosaka, P. M.; Ruz, J. J.; Paulo, A. S.; Calleja, M., Biosensors based on nanomechanical systems, Chem Soc Rev, 42, 3, 1287-1311 (2013) |
| [4] | Ouakad, H. M.; Younis, M. I., On using the dynamic snap-through motion of MEMS initially curved microbeams for filtering applications, J Sound Vib, 333, 2, 555-568 (2014) |
| [5] | Alsteens, D.; Gaub, H. E.; Newton, R.; Pfreundschuh, M.; Gerber, C.; Müller, D. J., Atomic force microscopy-based characterization and design of biointerfaces, Nat Rev Mater, 2, 17008 (2017) |
| [6] | Lesuer, D. R.; Syn, C. K.; Sherby, O. D.; Wadsworth, J.; Lewandowski, J. J.; Hunt, W. H., Mechanical behaviour of laminated metal composites, Int Mater Rev, 41, 5, 169-197 (1996) |
| [7] | He, K.; Hoa, S. V.; Ganesan, R., The study of tapered laminated composite structures: a review, Compos Sci Technol, 60, 14, 2643-2657 (2000) |
| [8] | Stölken, J. S.; Evans, A. G., A microbend test method for measuring the plasticity length scale, Acta Mater, 46, 14, 5109-5115 (1998) |
| [9] | Toupin, R. A., Elastic materials with couple-stresses, Arch Ration Mech An, 11, 1, 385-414 (1962) · Zbl 0112.16805 |
| [10] | Yang, F.; Chong, A. C.M.; Lam, D. C.C.; Tong, P., Couple stress based straingradient theory for elasticity, Int J Solids Struct, 39, 10, 2731-2743 (2002) · Zbl 1037.74006 |
| [11] | Fleck, N. A.; Hutchinson, J. W., A phenomenological theory for strain gradient effects in plasticity, J Mech Phys Solids, 41, 12, 1825-1857 (1993) · Zbl 0791.73029 |
| [12] | Eringen, A. C., Linear theory of micropolar elasticity, J Math Mech, 15, 909-923 (1966) · Zbl 0145.21302 |
| [13] | Eringen, A. C., Nonlocal polar elastic continua, Int J Eng Sci, 10, 1, 1-16 (1972) · Zbl 0229.73006 |
| [14] | Qi, L.; Huang, S.; Fu, G.; Zhou, S.; Jiang, X., On the mechanics of curved flexoelectric microbeams, Int J Eng Sci, 124, 1-15 (2018) · Zbl 1423.74317 |
| [15] | Karami, B.; Shahsavari, D.; Janghorban, M.; Li, L., Influence of homogenization schemes on vibration of functionally graded curved microbeams, Compos Struct, 216, 67-79 (2019) |
| [16] | She, G. L.; Liu, H. B.; Karami, B., Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets, Thin Wall Struct, 160, 107407 (2021) |
| [17] | Zhang, B.; He, Y.; Liu, D.; Gan, Z.; Shen, L., A novel size-dependent functionally graded curved microbeam model based on the strain gradient elasticity theory, Compos Struct, 106, 374-392 (2013) |
| [18] | Zhang, B.; He, Y.; Liu, D.; Gan, Z.; Shen, L., Size-dependent functionally graded beam model based on an improved third-order shear deformation theory, Eur J Mech A-Solid, 47, 211-230 (2014) · Zbl 1406.74416 |
| [19] | Ansari, R.; Gholami, R.; Sahmani, S., Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory, Arch Appl Mech, 83, 1439-1449 (2013) · Zbl 1293.74155 |
| [20] | Allahkarami, F.; Nikkhah-Bahrami, M., The effects of agglomerated CNTs as reinforcement on the size-dependent vibration of embedded curvedmicrobeams based on modified couple stress theory, Mech Adv Mater Struct, 25, 12, 995-1008 (2018) |
| [21] | Akrami-Nia, E.; Ekhteraei-Toussi, H., Pull-in and snap-through analysis of electrically actuated viscoelastic curved microbeam, Adv Mater Sci Eng, 9107323 (2020) |
| [22] | Bakhtiari, I.; Behrouz, S. J.; Rahmani, O., Nonlinear forced vibration of a curved micro beam with a surface-mounted light-driven actuator, Commun Nonlinear Sci Numer Simul, 91, 105420 (2020) · Zbl 1453.74036 |
| [23] | Rahmani, O.; Hosseini, S. A.H.; Ghoytasi, I.; Golmohammadi, H., Free vibration of deep curved FG nano-beam based on modified couple stress theory, Steel Compos Struct, 26, 5, 607-620 (2018) |
| [24] | Akgöz, B.; Civalek, O., Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams, Compos Part B-Eng, 129, 77-87 (2017) |
| [25] | Qatu, M. S., Theories and analyse of thin and moderately thick laminated composite curved beams, Int J Solids Struct, 30, 20, 2743-2756 (1993) · Zbl 0782.73033 |
| [26] | Lin, K. C.; Hsieh, C. M., The closed form general solutions of 2-D curved laminated beams of variable curvatures, Compos Struct, 79, 4, 606-618 (2007) |
| [27] | Wang, Q.; Choe, K.; Tang, J.; Shuai, C.; Wang, A., Vibration analyses of general thin and moderately thick laminated composite curved beams with variable curvatures and general boundary conditions, Mech Adv Mater Struct, 27, 12, 991-1005 (2020) |
| [28] | Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput Methods Appl Mech Eng, 194, 39, 4135-4195 (2005) · Zbl 1151.74419 |
| [29] | Luu, A. T.; Kim, N.; Lee, J., Bending and buckling of general laminated curved beams using NURBS-based isogeometric analysis, Eur J Mech A-Solid, 54, 218-231 (2015) · Zbl 1406.74253 |
| [30] | Huynh, T. A.; Luu, A. T.; LeeBending, J., buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach, Meccanica, 52, 11-12, 2527-2546 (2017) |
| [31] | Tsiptsis, I. N.; Sapountzakis, E. J., Generalized warping and distortional analysis of curved beams with isogeometric methods, Comput Struct, 191, 33-50 (2017) |
| [32] | Vo, D.; Nanakorn, P., Geometrically nonlinear multi-patch isogeometric analysis of planar curved euler-bernoulli beams, Comput Methods Appl Mech Engrg, 366, 113078 (2020) · Zbl 1442.74108 |
| [33] | Choi, M. J.; Yoon, M.; Cho, S., Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using jaumann strain formulation, Comput Methods Appl Mech Eng, 309, 41-73 (2016) · Zbl 1439.74399 |
| [34] | Bouclier, R.; Elguedj, T.; Combescure, A., Locking free isogeometric formulations of curved thick beams, Comput Methods Appl Mech Eng, 245-246, 144-162 (2012) · Zbl 1354.74260 |
| [35] | Hosseini, S. F.; Hashemian, A.; Alessandro Reali, A., On the application of curve reparameterization in isogeometric vibration analysis of free-from curved beams, Comput Struct, 209, 117-129 (2018) |
| [36] | Zhang, G.; Alberdi, R.; Khandelwal, K., On the locking free isogeometric formulations for 3-D curved Timoshenko beams, Finite Elem Anal Des, 143, 46-65 (2018) |
| [37] | Hosseini, S. F.; Hashemian, A.; Reali, A., Studies on knot placement techniques for the geometry construction and the accurate simulation of isogeometric spatial curved beams, Comput Methods Appl Mech Eng, 360, 112705 (2020) · Zbl 1441.74247 |
| [38] | Chen, D.; Zheng, S.; Wang, Y.; Yang, L.; Li, Z., Nonlinear free vibration analysis of a rotating two-dimensional functionally graded porous micro-beam using isogeometric analysis, Eur J Mech A-Solid, 84, 104083 (2020) · Zbl 1477.74039 |
| [39] | Yu, T. T.; Zhang, J. K.; Hu, H. F.; Bui, T. Q., A novel size-dependent quasi-3D isogeometric beam model for two-directional FG microbeams analysis, Compos Struct, 211, 76-88 (2019) |
| [40] | Yu, T. T.; Hu, H. F.; Zhang, J. K.; Bui, T. Q., Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory, Thin Wall Struct, 138, 1-14 (2019) |
| [41] | Yin, S. H.; Deng, Y.; Yu, T. T.; Gu, S. T.; Zhang, G. Y., Isogeometric analysis for non-classical bernoulli-euler beam model incorporating microstructure and surface energy effects, Appl Math Model, 89, 470-485 (2021) · Zbl 1485.74094 |
| [42] | Chen, D.; Feng, K.; Zheng, S., Flapwise vibration analysis of rotating composite laminated timoshenko microbeams with geometric imperfection based on a re-modified couple stress theory and isogeometric analysis, Eur J Mech A-Solid, 76, 25-35 (2019) · Zbl 1470.74033 |
| [43] | Hu, H. F.; Yu, T. T.; Lich, L. V.; Bui, T. Q., Functionally graded curved timoshenko microbeams: anumerical study using IGA and modified couple stress theory, Compos Struct, 254, 112841 (2020) |
| [44] | Karami, B.; Janghorban, M.; Li, L., On guided wave propagation in fully clamped porous functionally graded nanoplates, Acta Astronaut, 143, 380-390 (2018) |
| [45] | Hajianmaleki, M.; Qatu, M. S., Static and vibration analyse of thick, generally laminated deep curved beams with different boundary conditions, Compos Part B-Eng, 43, 1767-1775 (2012) |
| [46] | Cottrell, J. A.; Hughes, T. J.R.; Bazilevs, Y., Isogeometric Analysis: Toward Integration of CAD and FEA (2009), Wiley & Sons · Zbl 1378.65009 |
| [47] | Piegl, L.; Tiller, W., The NURBS Book (2012), Springer Science & Business Media |
| [48] | Luu, A. T.; Kim, N.; Lee, J., NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature, Compos Struct, 119, 150-165 (2015) |
| [49] | Zupan, E.; Saje, M.; Zupan, D., Dynamics of spatial beams in quaternion description based on the newmark integration scheme, Comput Mech, 51, 47-64 (2013) · Zbl 1398.74201 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
