Publicou 6 edições por ano
ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352
Indexed in
BUCKLING ANALYSIS OF RECTANGULAR FLEXURAL MICROPLATES USING HIGHER CONTINUITY P-VERSION FINITE-ELEMENT METHOD
RESUMO
In this article, elastic buckling of rectangular flexural micro plates (FMPs), using a higher continuity p-version finite-element framework based on Galerkin formulation, is investigated. The invariant form of governing equation for microplates with nonlocal effects based on "modified couple stress theory" is extended for buckling analysis of FMPs by considering the strain gradient effects, for which the constitutive equation of the strain gradient model contains only one constant. The Galerkin weak form of the governing equation is derived and subsequently solved for a variety of boundary conditions, using higher continuity p finite elements, to extract critical buckling loads. Here the computational procedure is verified by comparing the results to those of the classical theory and microplate studies reported in literature. Investigations indicate that the length scale parameter affects the computed flexural stiffness of a plate directly proportional to the value of gradient coefficient considered for that plate. Hence there is a strong influence of length scale parameter on the value of the buckling load. Depending on boundary conditions and the length scale parameter value, the classical plate model severely underestimates (up to 90%) the buckling load of microplates. Therefore it is concluded that the classical plate theory cannot be used to predict structural response when length scale effects are present.
-
Aifantis, E., The physics of plastic deformation. DOI: 10.1016/0749-6419(87)90021-0
-
Chong, A. C. M. and Lam, D. C. C., Strain gradient plasticity effect in indentation hardness of polymers. DOI: 10.1557/JMR.1999.0554
-
Clarke, D. R. and Ma, Q., Size dependent hardness of silver single crystals. DOI: 10.1557/JMR.1995.0853
-
Cosserat, E. and Cosserat, F., Theorie des Corps Deformables.
-
Eringen, C. A., Linear theory of micropolar elasticity.
-
Eshelby, J. D. and Stroh, A. N., Dislocations in thin plates.
-
Exadaktylos, G. E. and Vardoulakis, I., Microstructure in linear elasticity and scale effects: A reconsideration of basic rock mechanics and rock fracture mechanics. DOI: 10.1016/S0040-1951(01)00047-6
-
Farahmand, H. and Arabnejad, S., Developing a novel finite elastic approach in strain gradient theory for microstructures. DOI: 10.1615/IntJMultCompEng.v8.i4
-
Fischer, F. D., Rammerstorfer, F. G., and Friedl, N., Residual stress-induced centre wave buckling of rolled strip metal. DOI: 10.1115/1.1532322
-
Fish, J. and Kuznetsov, S., Computational continua. DOI: 10.1002/nme.2918
-
Fleck, N. A., Muller, G. M., Ashby, M. F., and Hutchinson, J. W., Strain gradient plasticity: Theory and experiment. DOI: 10.1016/0956-7151(94)90502-9
-
Freund, L. B. and Suresh, S., Thin Film Materials.
-
Gorman, D. J. and Singhal, R. K., A superposition Rayleigh-Ritz method for free vibration analysis of non-uniformly tensioned membranes. DOI: 10.1006/jsvi.1993.1135
-
Koiter, W. T., Couple stresses in the theory of elasticity.
-
Lakes, R., Experimental methods for study of Cosserat elastic solids and other generalized elastic continua.
-
Mindlin, R. D., Micro-structure in linear elasticity. DOI: 10.1007/BF00248490
-
Mindlin, R. D. and Eshel, N. N., On first strain-gradient theories in linear elasticity. DOI: 10.1016/0020-7683(68)90036-X
-
Mitchell, L. H. and Head, A. K., Buckling of a dislocated plate. DOI: 10.1016/0022-5096(61)90030-8
-
Nix, W. D., Mechanical properties of thin films. DOI: 10.1007/BF02666659
-
Papargyri-Beskou, S. and Beskos, D. E., Static, stability and dynamic analysis of gradient elastic fexural Kirchhof plates. DOI: 10.1007/s00419-007-0166-5
-
Poole, W. J., Ashby, M. F., and Fleck, N. A., Micro-hardness of annealed and work-hardened copper polycrystals. DOI: 10.1016/1359-6462(95)00524-2
-
Rammerstorfer, F. G., Fischer, F. D., and Friedl, N., Buckling of free infinite strips under residual stresses and global tension. DOI: 10.1115/1.1357519
-
Stelmashenko, N. A., Walls, M. G., Brown, L. M., and Milman, Y. V., Microindentations on W and Mo oriented single crystals: An STM study. DOI: 10.1016/0956-7151(93)90100-7
-
Steolken, J. S. and Evans, A. G., A microbend test method for measuring the plasticity length scale. DOI: 10.1016/S1359-6454(98)00153-0
-
Surana, K. S., Petti, S. R., Ahmadi, A. R., and Reddy, J. N., On p-version hierarchical interpolation functions for higher order continuity finite element models.
-
Tiersten, H. F. and Bleustein, J. L., Generalized elastic continua.
-
Toupin, R. A., Elastic materials with couple-stresses. DOI: 10.1007/BF00253945
-
Vardoulakis, I. and Sulem, J., Bifurcation Analysis in Geomechanics.
-
Ansari R., Shojaei M. Faghih, Mohammadi V., Gholami R., Rouhi H., Size-Dependent Thermal Buckling and Postbuckling of Functionally Graded Annular Microplates Based on the Modified Strain Gradient Theory, Journal of Thermal Stresses, 37, 2, 2014. Crossref
-
Ke L.L., Yang J., Kitipornchai S., Bradford M.A., Wang Y.S., Axisymmetric nonlinear free vibration of size-dependent functionally graded annular microplates, Composites Part B: Engineering, 53, 2013. Crossref
-
Kolahchi Reza, Bidgoli Mahmood Rabani, Beygipoor Gholamhossein, Fakhar Mohammad Hosein, A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field, Journal of Mechanical Science and Technology, 29, 9, 2015. Crossref
-
Arani A. G., Jafari G. S., Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM, Applied Mathematics and Mechanics, 36, 8, 2015. Crossref
-
Ansari R., Shojaei M. Faghih, Mohammadi V., Gholami R., Rouhi H., Nonlinear Vibration Analysis of Microscale Functionally Graded Timoshenko Beams using the Most General form of Strain Gradient Elasticity, Journal of Mechanics, 30, 2, 2014. Crossref
-
Ansari R., Shojaei M. Faghih, Rouhi H., Small-scale Timoshenko beam element, European Journal of Mechanics - A/Solids, 53, 2015. Crossref
-
Barzoki Ali Akbar Mosallaie, Loghman Abbas, Arani Ali Ghorbanpour, Temperature-dependent nonlocal nonlinear buckling analysis of functionally graded SWCNT-reinforced microplates embedded in an orthotropic elastomeric medium, Structural Engineering and Mechanics, 53, 3, 2015. Crossref
-
Farahmand H., A variational approach for analytical buckling solution of moderately thick microplate using strain gradient theory incorporating two-variable refined plate theory: a benchmark study, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 3, 2021. Crossref
-
Farahmand H., Yasaie P., Instability analysis of moderately thick porous micro-plate via two-variable strain gradient theory, Archive of Applied Mechanics, 91, 11, 2021. Crossref
-
Ghalami Yasaman, Askari Amir R., Awrejcewicz Jan, Tahani Masoud, Strain gradient bistability of bimorph piezoelectric curved beam interacting with a curved electrode, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44, 5, 2022. Crossref