Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 27, No. 6 (June 2014) 951-960   

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  A SIZE-DEPENDENT BERNOULLI-EULER BEAM FORMULATION BASED ON A NEW MODEL OF COUPLE STRESS THEORY
 
R. Akbari Alashti and A. H. Abolghasemi
 
( Received: September 14, 2013 – Accepted: November 07, 2013 )
 
 

Abstract    In this paper, a size-dependent formulation for the Bernoulli-Euler beam is developed based on a new model of couple stress theory presented by Hadjesfandiari and Dargush. The constitutive equation obtained in this new model, consists of only one length scale parameter that is capable of capturing the micro-structural size effect in predicting the mechanical behavior of the structure. Having one length scale parameter is claimed to be an advantage of the model in comparison with the classical couple stress theory. The governing equations and boundary conditions of the Bernoulli-Euler beam are developed using the variational formulation and the Hamilton principle. The static bending and free vibration problems of a Bernoulli-Euler beam with various boundary conditions are solved. Numerical results demonstrate that the value of deflection predicted by the new model is lower than that of the classical theory. It is also found that natural frequencies obtained by the present couple stress model are higher than those predicted by the classical theory. The differences between results obtained by the present model and the classical theory become significant as the thickness of the beam gets close to the length scale parameter of the beam material.

 

Keywords    Bernoulli-Euler beam, couple stress theory, microstructural effect, static bending, free vibration

 

چکیده    در اين مقاله، با استفاده از مدل جديد کوپل تنش ارائه شده توسط Hadjesfandiari و Dargush، فرمول بندي وابسته به اثر اندازه ريزساختار ماده براي يک تير اويلر- برنولي توسعه داده شده است. روابط ساختاري بدست آمده در اين مدل جديد، شامل يک پارامتر مقياس طولي ماده است که اين تئوري را قادر به پيش بيني رفتار مکانيکي مواد ناشي از تاثير اندازه ريزساختار مي سازد. داشتن تنها يک پارامتر مقياس طولي ماده يکي از مزيت هاي اين مدل در مقايسه با تئوري کلاسيک کوپل تنش عنوان شده است. معادلات حاکم و شرايط مرزي تير اويلر- برنولي با استفاده از روش وردشي و اصل هميلتون بدست آمده و مسائل خمش استاتيکي و ارتعاش آزاد يک تير اويلر- برنولي با شرايط مرزي مختلف حل شده اند. نتايج عددي نشان مي دهند که مقدار خيز پيش بيني شده در مدل جديد کمتر از مقدار پيش بيني شده در تئوري الاستيسيته کلاسيک مي باشد. همچنين فرکانس هاي ارتعاش آزاد بدست آمده در اين تئوري بالاتر از تئوري کلاسيک مي باشد. تفاوت بين جوابهاي بدست آمده از تئوري کوپل تنش حاضر و تئوری کلاسيک با نزديک شدن مقدار ضخامت تير به پارامتر مقياس طولي ماده، زياد مي شود.

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