Abstract:A new triangular cylindrical shell finite element is used to obtain an elastic linear analysis of a cylindrical shell roof. The element's displacement fields are in terms of curvilinear coordinates, satisfy the exact requirement of rigid body modes of deformation and have five degrees of freedom at each of the three corner nodes. The efficiency of the developed element is first tested and then applied to analyze stiffened cylindrical shell roof. The results of the displacement and stress resultant along the stiffener are presented and a parametric study is carried out to find the effect of the varying geometry of the stiffener and the effect of axis rotation of the beam on the level of the internal forces.
Abstract:A new spherical triangular finite element based on shallow shell formulation is developed in this paper. The element has six degrees of freedom at each corner node, five of which are the essential external degrees of freedom and the additional sixth is associated with the in-plane shell rotation. The displacement fields of the element satisfy the exact requirement of rigid body modes of motion. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated by applying it to the analysis of a benchmark problem involving a standard spherical shell with simply supported edges. The results of the analysis showed that reasonably accurate results were obtained even when modeling the shells using fewer elements compared to other shell element types. The element is then used in a finite element model to analyze polygon shaped spherical roof structures. The distribution of the various components of deflection and stress is obtained. Furthermore, the effect of introducing circular arched beams as stiffeners spanning the two diagonally opposite end corners is investigated. It is found that the stiffeners reduced the deflections and the stresses in the roof structure by considerable value.
A new hyperbolic parabolic triangular finite element is developed in this paper. The element has only five essential nodal degrees of freedom (three general external degrees of freedom and two rotations) at each of the three corner nodes. The displacement fields of the element satisfy the exact requirements of rigid body modes of motion. Shallow shell formulation is used and the element is based on an independent strain assumption insofar as it is allowed by the compatibility equations. A hyperbolic Paraboloid shell dam for which a previous solution exists is first analyzed using this new element to validate the program and to compute the results. The element is then used in the analysis of a complex type of hyperbolic Paraboloid shell roof, which normally referred to as hyperbolic Paraboloid groined vault. It is usually made up of a combination of four of intersecting hyper Paraboloids joined together to form a square shape in plan view. This form of structure is often used by architects to roof large span exhibition halls and public buildings. The distribution of various components of forces is obtained to give designers an in–sight of the behavior of such complex structures.
تم في هذه الدراسة تطوير واشتقاق معادلات الإزاحة باستخدام طريقة العناصر المحددة لعنصر مثلثي جديد على شكل قطع (Hyper)، يحتوي هذا العنصر على خمس درجات حرية عند كل نقطة طرفية (Nodes)، وهي (حركات الإزاحة الثلاثة الرئيسية بالإضافة إلى حركتي الدوران)، ومعادلات الإزاحة للعنصر تلبي المتطلبات الدقيقة لأنماط الحركة للأجسام الصلبة، في هذا الاشتقاق تم استخدام صيغ المعادلات الخاصة بالقشريات الضحلة العمق (shallow) اعتمد العنصر على استقلالية التشوه ضمن حدود المعادلات الانسجامية. تم استخدام المعادلات المشتقة لحل منشأ هندسي عبارة عن سد (Hyper dam) حيث يوجد حل سابق لهذا المنشأ وذلك للتأكد من دقة معادلات العنصر الجديد المستخدم وكذلك للحصول على نتائج باستخدام العنصر الثلاثي الجديد، بعد ذلك تم توسيع العمل في هذا البحث باستخدام معادلات العنصر الجديد لحل منشأ هندسي معقد على شكل قبو منحني مطلق عليه (H.P groin vault)، وهذا النشأ يتكون من تجميع أربع أشكال هايبر (Hyper) متصلة مع بعضها ولتكون شكل مربع في مسقطها الأفقي. هذا النوع من المنشآت يستخدمها عادة المعماريون لتغطية قاعات المعارض والمباني العامة ذات الأبعاد الواسعة، وقد تم الحصول على نتائج للقوة الداخلية للمنشأ والتي من شأنها أن تعطي المهندسين المصممين من خلالها نظرة حول تصرف وسلوك مثل هذا النوع من المنشآت المعقدة.
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