تحليل كمانش سازه‌هاي استوانه‌يي كركره‌يي براي دست‌يابي به بالاترين «نسبت استحكام به وزن»

Buckling analysis of corrugated cylindrical structures to achieve the highest strength-to-weight ratio

يكي از مشخصه‌هاي سازه‌هاي كركره‌يي ــ كه در مقايسه با سازه‌هاي مشابه «نسبت استحكام به وزن بالايي» دارند ــ استحكام كمانشي آنهاست و از اين جهت در صنايع مختلف مورد توجه قرار گرفته اند. در مطالعه‌ي حاضر، كمانش سازه‌هاي كركره‌يي استوانه‌يي با الگوي هندسي ذوزنقه تحت بار محوري با شرايط مرزي تكيه گاه ساده-ساده مورد بررسي قرار گرفته است. معادلات تعادل سازه با استفاده از نظريه‌ي مرتبه‌ اول برشي استخراج شده است. خواص مكانيكي استوانه ي كركره‌يي به‌كمك استوانه ي مدور اورتوتروپيك معادل آن به دست آمده است. به‌منظور صحه‌گذاري نتايج تحليلي، از يك مدل اجزا محدود استفاده شده و نيز تاثير پارامترهاي مختلف شامل تعداد كركره، ضخامت استوانه، طول استوانه، شعاع استوانه، زاويه‌ي كركره و ضريب شكل بر رفتار كمانشي استوانه كركره‌يي مورد بررسي قرار گرفته است. نتايج حاضر، دقت و كارايي طراحي اين‌گونه سازه‌ها را براي مهندسان بالاتر خواهد برد.

Increasing the buckling strength-to-weight ratio is of particular importance in aerospace, mechanical, nuclear, and civil engineering. Corrugated structures with trapezoidal geometric pattern have higher amount of the buckling strength-to-weight ratio with respect to other similar structures; hence, these generations of structures are widely used in several industries. Static stability of corrugated cylindrical structures with trapezoidal geometric pattern was investigated here under axial loading for simply supported boundary condition. Using first-order shear deformation theory of Mindlin, equilibrium equations of the problem were derived. Mechanical properties of corrugated cylindrical structure were achieved by the mechanical properties of equivalent orthotropic circular cylinder. Then, critical buckling load was obtained for both simple circular and corrugated cylinders. The present analytical results are validated by the finite element models. These validations report very good agreement between the present results and those obtained by the finite element analysis. Effect of different parameters including number of corrugations, cylinder thickness, cylinder length, cylinder radius, corrugation angle, and shape factor was investigated numerically on buckling behavior of corrugated cylindrical structure. The results of finite element reveal that buckling mode shapes can be divided into two types as local and global buckling modes. Graphical shapes of local and global modes are presented to make the better physical sense. In this article, the present analytical method can solve the global buckling problem of a corrugated cylinder. According to the comparison between present modeling results and those obtained by finite element analysis, increasing the corrugation angle and cylinder radius and decreasing the number of corrugations, the cylinder thickness, the cylinder length, and shape factor led to an increase in the buckling load of corrugated cylinder with respect to circular cylinder on the condition that local buckling had not been occurred. The present results and procedure can help engineers and designers to achieve a best performance for their structures, especially related to aerospace structures.