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

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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.



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