تحليل استاتيك ـ خميري پوسته‌ي مركب استوانه‌يي ـ مخروطي بر اثر فشار داخلي

Static-Plastic Analysis of Cylindrical-Truncated Conical Shell under Internal Pressure

در اين نوشتار رفتار خميري پوسته‌ي استوانه‌يي ـ مخروطي جدار نازك تحت فشار استاتيكي داخلي، مورد تحليل قرار گرفت. از مدل صلب ـ خميري كامل براي رفتار مادي سازه، و از سطح تسليم مستطيلي معمول ــ شامل N? و M? ــ براي معيار تسليم استفاده شده است. سه سازوكار كلي براي فروريزش پوسته شامل فروريزش مخروطي، فروريزش با دو لولاي خميري و فروريزش با سه لولاي خميري در نظر گرفته مي‌شود كه براساس هندسه‌ي سازه، يكي از اين سه حالت در هنگام فروريزش رخ مي‌دهد. در نتايج، نمودار تغييرات فشار فروريزش سازه نسبت به تغييرات طول استوانه يا طول مخروط آمده است. سازوكار فروريزش به‌ازاي تغيير طول استوانه و يا مخروط تغيير مي‌كند به‌گونه‌يي كه فشار فروريزش سازه به مقادير مجانبي خود (فشار فروريزش سازه كاملاً استوانه‌يي يا كاملاً مخروطي) نزديك مي‌شود.

Conical shells are of interests to many engineering branches. These shells are usually used as components for bearing pressure. For instance, in civil engineering applications, structures like; silos, pressure vessels, tanks, cooling towers and chimneys, involve conical shells in their constructions. Large conical tubes have a transition cone between two cylinders of different diameter. Conical reducers are used in oil transfer tubes for connecting two cylinder pipes of different diameter, and in places that do not fit the flange. Thus, these structures could be modeled as conical shells under internal pressure loading. Also, in the field of marine engineering, a body of submarines could be modeled as cylindrical shells with rigid reinforcement rings that are blocked by a truncated cone. In the field of aerospace engineering, a spacecraft cabin can also be considered a conical shell. In two recent applications, the model of conical shells is under external pressure. Therefore, due to the use of these structures, their analysis under pressure loads is essential and must be considered. In this paper, the plastic behavior of thin-walled cylindrical-truncated conical shells under static internal pressure will be investigated analytically. Towards this aim, the material behavior is assumed rigid-perfectly plastic, and a common rectangular surface has been used as the yielding criterion composed of stress resultants, M? and N?. According to the present approach, three basic mechanisms have been defined for structural collapse. These include cone-part collapse, collapse with two plastic hinges and collapse with three plastic hinges, each of which caused structural collapse, based on geometrical specifications. Variation of the pressure collapse of the structure has been depicted versus different cylinder-part or cone-part lengths, graphically. The changing of the collapse mechanism occurs in a particular cylinder-part or cone-part length, such that the collapse pressures approach asymptotic values (pressure collapse of completely cylindrical or conical shells).