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Geometrically Nonlinear analysis using Plane Stress / strain Elements based on Alternative Strain Measures

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pro.Abdelrahman Elzubair Mohmed Hamad,Dr. Rashid Ahmed Mohammed Hussien,Dr.Nuha Moawia Akasha Hilal,Qussay Hameed Alslami ,Basim Hussein Khudair ,Ghassan khalaf khalid ,Mohamed Sharif Abd Allah ,2012, Geometrically Nonlinear analysis using Plane Stress / strain Elements based on Alternative Strain Measures,Journal of Science and Technology,13 (1) ,pp:1-12

Authors:
By pro.Abdelrahman Elzubair Mohmed Hamad,Dr. Rashid Ahmed Mohammed Hussien,Dr.Nuha Moawia Akasha Hilal,Qussay Hameed Alslami ,Basim Hussein Khudair ,Ghassan khalaf khalid ,Mohamed Sharif Abd Allah ,
Year:
2012
Keywords
Geometric Nonlinear, Logarithmic, Geometric, strain measures
Abstract
The description of deformation and the measure of strain are essential parts of nonlinear continuum mechanics. In this paper, a new formulation for geometric nonlinear plane stress/strain based on Logarithmic strains (GNLGS) is presented. This is coupled with a formulation based on the well known Greens strains and coupled with modifying a formulation based on geometric strains (conventional strains). A geometric nonlinear total lagrangian formulation applied on two-dimensional elasticity using 4-node plane finite elements is used. The formulations were implemented into the finite element program (NUSAP), which is developed for the analysis of plane stress/strain problems subjected to static loading. The solution of nonlinear equations was obtained by the Newton-Raphson method. The program was applied to obtain displacements for the different strain measures. The accuracy of the results was demonstrated by using two numerical examples and the results are in good agreement with other available published solutions and those obtained using commercial finite element solvers such as ANSYS. It could be concluded that the geometrically nonlinear formulations converge to the correct solution with coarse meshes and are computationally efficient. In addition, the resulting displacements clearly showed the effect of the nonlinearity in the deflected shape. It is also observed that all results were approximately identical when applying a small value of load and when a large value of a load was applied there was a difference between the results of the three strain measures.
الملخص
وصف التشوه وقياس الانفعال من المكونات الاساسية للميكانيكا اللاخطية للاجسام المتصلة. تعرض هذه الورقة تقنين جديد للاَّخطية الهندسية للاجهاد/الانفعال المستوى بُنى على الانفعالات اللوغرثمية . تُزاوج الورقة بين هذا التقنين وبين التقنين المعلوم لانفعالات قرين(Green) وبين تقنين مستحدث تم الحصول عليه بتعديل تقنين مبنى على الانفعالات الهندسية (المتعارف عليها) استخدام تقنين لاقرانج (Lagrange) الكلِّى للاَّخطية الهندسية تطبيقاً على المرونة ثنائية الابعاد لعنصر محدد مستوى ذى أربعة عقـد. تمت حوسبة التقنينات الثلاثة بوضعها فـى برنامـج العنصر المحدد (N U S A P) الذى طُوِّر لتحليل مسائل الاجهاد/ الانفعال المستوى المعرضة لأحمال ساكنة. تم الحصول على حل المعادلات اللاَّخطية باستخدام طريقة نيوتن – رابسون. طُبق البرنامج للحصول على الازاحات الناتجة عن قياسات الانفعال المختلفة. وبُينت دقة النتائج بناءً على مثالين عدديين ، وأظهرت النتائج توافقاً جيداً مع الحلول المنشورة ومع التى تم الحصول عليها باستخدام برامج العنصر المحدد التجارية مثل (A N S Y S). تخلص الورقة الى أن تقنينات اللاَّخطية الهندسية تتقارب الى الحل الصحيح باستخدام عناصر محددة قليلة وهى ذات كفاءة محوسبة مناسبة. وبالاضافة لهذا تُظهر الازاحات المتحصل عليها بوضوح أثر اللاَّخطية على الشكل المنحنى. ويلاحظ ، ايضاً ، أن كل النتائج متطابقة تقريباً عند تطبيق الاحمال الصغيرة ، وهنالك فرق واضح بين نتائج قياسات الانفعالات الثلاثة عند تطبيق الأحمال العاليه.
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