IJE TRANSACTIONS A: Basics Vol. 26, No. 10 (October 2013) 1191-1202   

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G. H. Majzoobi and B. Sharifi Hamadani
( Received: November 26, 2012 – Accepted: April 18, 2013 )

Abstract    The performance of an 8-noded hexahedron C1* element in elasticity is investigated. Three translational displacements and their derivatives as strain in each direction are considered as degrees of freedom (d.o.f.’s) at each node. The geometric mapping is enforced using a C0 element with no derivative as nodal d.o.f.’s . The stiffness matrix of the element is also computed using a transformation matrix obtained from an equivalent C0 element. The results obtained from elastic stress analysis of a cantilever show that: (i) the convergence rate of 8-noded C1* element is nearly equal to its equivalent C0 element, while it consumes less CPU time with respect to the C0 element; (ii) the element has successfully passed the patch and distortion tests; (iii) the condition number of the stiffness matrix for C1* element is less than the C0 element; (iv) the directly computation of strains as derivative degrees of freedom at the nodes along with excellent convergence makes the C1* element superior compared with its equivalent C0 element.


Keywords    Elasticity, Finite element method, elements, Convergence, elements.


چکیده    عملکرد یک المان مکعبی هشت گره ای نوع C1* در الاستیسیته بررسی گردیده است. سه تغییر مکان انتقالی و مشتقات آن ها به عنوان کرنش در هرجهت به عنوان درجات آزادی در هر گره در نظر گرفته شده است. نگاشت هندسی با استفاده از المان C0 که هیچ مشتقی به عنوان درجات آزادی گره ای ندارد اعمال می گردد. همچنین ماتریس سختی المان با استفاده از یک ماتریس تبدیل که از المان C0 معادل آن به دست می آید محاسبه گردیده است. نتایج به دست آمده از تحلیل تنش الاستیک یک تیر یک سرگیردار نشان می دهد که : (1) نرخ همگرایی المان هشت گره ای نوع C1* تقریباً معادل المان معادل نوع C0 آن است در حالی که زمان پردازش کمتری نسبت به المان C0 صرف می گردد. (2) المان به طور موفقیت آمیز تست های مسیر و اعوجاج را پشت سر گذاشته است. (3) عدد حالت مربوط به ماتریس سختی المان C1* کمتر از المان C0 است. (4) محاسبه کرنش ها به طور مستقیم و تحت عنوان مشتقات درجات آزادی گره ها همراه با همگرایی عالی، المان C1* را در مقایسه با المان C0 معادل آن برتر می سازد.


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