Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 27, No. 8 (August 2014) 1277-1286   

downloaded Downloaded: 285   viewed Viewed: 2095

  ELASTIC/PLASTIC BUCKLING ANALYSIS OF SKEW THIN PLATES BASED ON INCREMENTAL AND DEFORMATION THEORIES OF PLASTICITY USING GENERALIZED DIFFERENTIAL QUADRATURE METHOD
 
M. Maarefdoust and M. Kadkhodayan
 
( Received: December 30, 2013 – Accepted: April 17, 2014 )
 
 

Abstract    Abstract In this study, generalized differential quadrature analysis of elastic/plastic buckling of skew thin plates is presented. The governing equations are derived for the first time based on the incremental and deformation theories of plasticity and classical plate theory (CPT). The elastic/plastic behavior of plates is described by the Ramberg-Osgood model. The ranges of plate geometries are 0.5 a/b 2.5 and 0.001 h/b 0.05 under uniaxial uniform compression or biaxial compression/tension. GDQ discretization rules in association with an exact coordinate transformation are simultaneously used to transform and discretize the equilibrium equations and the related boundary conditions. Based on comparison with previously published results, the accuracy of the results is shown. Finally, the effects of aspect, loading and thickness ratios, skew angle, incremental and deformation theories and different types of boundary conditions on the buckling coefficient are presented. Moreover, the effect of skew angle and thickness ratio on the convergence and accuracy of the method are studied. Due to the lack of published solutions for plastic buckling of skew thin plates and the high accuracy of the present approach, the solutions obtained may serve as benchmark values for further studies.

 

Keywords    Skew Plates, GDQ, Deformation Theory, Elastic/plastic Buckling, CPT, Incremental Theory.

 

چکیده    در این مقاله تحليل یک چهارم تفاضلی تعمیم یافته کمانش الاستيك-پلاستیک صفحات نازك اريب مورد بحث قرار گرفته است. معادلات حاكم بر كمانش الاستيك – پلاستيك صفحات نازك مورب براي اولين بار بوسيلة تئوري ­ای پلاستيسيته تغيير‏شكل و نموي و تئوري صفحات كلاسيك استخراج گرديده است. رفتار الاستيك – پلاستيك صفحه بوسيله مدل رامبرگ ازگود مدلسازي شده است. بار به صورت فشاري محوري يا كششي/ فشاري دومحوري وارد مي‏شود و هندسه مورد نظر صفحه و می‏باشد. معادلات استخراجي در سيستم دكارتي به سيستم اريب انتقال داده شده و در سيستم یک چهارم تفاضلی تعمیم یافته نوشته شده است و نتايج حاصل با كارهاي گذشتگان مورد مقايسه قرار گرفته است. اثرات نسبت ابعادي، زاويه اريب، ضريب ضخامت صفحه، ضريب بار، تئوري تغييرشكل و تئوري نموي و شرايط مرزي مختلف بر تعيين ضريب كمانشي بررسی شده و نتايج حاصل ارائه گرديده است. همچنين اثر زاويه اريب و ضريب ضخامت بر همگرايي و صحت روش مورد استفاده، سنجيده شده است. با توجه به اينكه نتايج كمانش پلاستيك صفحات نازك اريب بدست آمده داراي دقت و صحت خوبي مي‏باشند مي­توانند براي كارهاي آيندگان مورد استفاده قرار گيرند.

References   

 

1.     Anderson, R.A., "Charts giving critical compressive stress of continuous flat sheet divided into parallelogram-shaped panels, National Advisory Committee for Aeronautics,  (1951).

2.     Durvasula, S., "Buckling of clamped skew plates", AIAA Journal,  Vol. 8, No. 1, (1970), 178-181.

3.     Durvasula, S., "Buckling of simply supported skew plates", Journal of the Engineering Mechanics Division,  Vol. 97, No. 3, (1971), 967-979.

4.     Fried, I. and Schmitt, K., Numerical results from application of gradient iterative techniques to finite element vibration and stability analysis of skew plates. 1972, ROYAL AERONAUTICAL SOC 4 HAMILTON PL, LONDON W1V OBQ, ENGLAND. p. 166-&.

5.     Mizusawa, T., Kajita, T. and Naruoka, M., "Analysis of skew plate problems with various constraints", Journal of Sound and Vibration,  Vol. 73, No. 4, (1980), 575-584.

6.     Mizusawa, T., Kajita, T. and Naruoka, M., "Buckling of skew plate structures using bspline functions", International Journal for Numerical Methods in Engineering,  Vol. 15, No. 1, (1980), 87-96.

7.     Mizusawa, T. and Kajita, T., "Vibration and buckling of skew plates with edges elastically restrained against rotation", Computers & structures,  Vol. 22, No. 6, (1986), 987-994.

8.     Xiang, Y. and Wang, C., "Buckling of skew mindlin plates subjected to in-plane shear loadings", International journal of mechanical sciences,  Vol. 37, No. 10, (1995), 1089-1101.

9.     York, C., "Influence of continuity and aspect-ratio on the buckling of skew plates and plate assemblies", International journal of solids and structures,  Vol. 33, No. 15, (1996), 2133-2159.

10.   Huyton, P. and York, C., "Buckling of skew plates with continuity or rotational edge restraint", Journal of Aerospace Engineering,  Vol. 14, No. 3, (2001), 92-101.

11.   Wang, X., Tan, M. and Zhou, Y., "Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method", Thin-Walled Structures,  Vol. 41, No. 1, (2003), 15-29.

12.   Wu, W., Shu, C., Wang, C. and Xiang, Y., "Free vibration and buckling analysis of highly skewed plates by least squares-based finite difference method", International Journal of Structural Stability and Dynamics,  Vol. 10, No. 02, (2010), 225-252.

13.   Durban, D., "Plastic buckling of plates and shells", NASA,  Vol., No. 19980019030, (1998).

14.   Durban, D. and Zuckerman, Z., "Elastoplastic buckling of rectangular plates in biaxial compression/tension", International journal of mechanical sciences,  Vol. 41, No. 7, (1999), 751-765.

15.   Wang, C., Xiang, Y. and Chakrabarty, J., "Elastic/plastic buckling of thick plates", International journal of solids and structures,  Vol. 38, No. 48, (2001), 8617-8640.

16.   Wang, C. and Aung, T.M., "Plastic buckling analysis of thick plates using p-ritz method", International journal of solids and structures,  Vol. 44, No. 18, (2007), 6239-6255.

17.   Chakrabarty, J., "Applied plasticity, Springer,  (2010).

18.   Shanmugam, N., "Elastic buckling of uniaxially loaded skew plates containing openings", Thin-Walled Structures,  Vol. 49, No. 10, (2011), 1208-1216.

19.   Jaberzadeh, E., Azhari, M. and Boroomand, B., "Inelastic buckling of skew and rhombic thin thickness-tapered plates with and without intermediate supports using the element-free galerkin method", Applied Mathematical Modelling,  Vol. 37, No. 10, (2013), 6838-6854.

20.   Maarefdoust, M. and Kadkhodayan, M., "Elastoplastic buckling analysis of plates involving free edges by deformation theory of plasticity", International Journal of Engineering (1025-2495),  Vol. 26, No. 4, (2013).

21.   Kadkhodayan, M. and Maarefdoust, M., "Elastic/plastic buckling of isotropic thin plates subjected to uniform and linearly varying in-plane loading using incremental and deformation theories", Aerospace Science and Technology,  Vol. 32, No. 1, (2014), 66-83.

22.   Bellman, R. and Casti, J., "Differential quadrature and long-term integration", Journal of Mathematical Analysis and Applications,  Vol. 34, No. 2, (1971), 235-238.

23.   Bert, C.W. and Malik, M., "Differential quadrature method in computational mechanics: A review", Applied Mechanics Reviews,  Vol. 49, No. 1, (1996), 1-28.

24.   Shu, C. and Richards, B.E., "Application of generalized differential quadrature to solve twodimensional incompressible navierstokes equations", International Journal for Numerical Methods in Fluids,  Vol. 15, No. 7, (1992), 791-798.

25.   Shu, C., Chen, W., Xue, H. and Du, H., "Numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation", International Journal for Numerical Methods in Engineering,  Vol. 51, No. 2, (2001), 159-179.

26.   Kennedy, J. and Prabhakara, M., "Buckling of simply supported orthotropic skew plates", Aeronautical Quarterly,  Vol. 29, No., (1978), 161-174.

27.   Guest, J., "The buckling of uniformly compressed parallelogram plates having all edges clamped", Aeronautical Research Laboratories Report SM,  Vol. 172, No., (1951).

28.   Wittrick, W., "Buckling of oblique plates with clamped edges under uniform compression", Aeronautical Quarterly,  Vol. 4, No. 2, (1953), 151-163.

29.   Krishna Reddy, A. and Palaninathan, R., "Buckling of laminated skew plates", Thin-Walled Structures,  Vol. 22, No. 4, (1995), 241-259.

30.           Tham, L. and Szeto, H., "Buckling analysis of arbitrarily shaped plates by spline finite strip method", Computers & structures,  Vol. 36, No. 4, (1990), 729-735.     





International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir