تحلیل استاتیکی خمش و کمانش ورق متخلخل تابعی با استفاده از تئوری برشی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، دانشکده فنی و مهندسی، دانشگاه اراک، اراک، ایران

2 کارشناسی ارشد، دانشکده فنی و مهندسی، دانشگاه اراک، اراک، ایران

چکیده

در این مطالعه کمانش الاستیک و خمش استاتیک ناشی از تغییر شکل برشی یک ورق متخلخل مدرج تابعی بر اساس تئوری تغییر شکل برشی، بررسی‌ شده است. تأثیر نوع و میزان تخلخل بر رفتار مکانیکی ورق با استفاده از اصل انرژی پتانسیل، هدف اصلی این تحقیق می‌باشد. مدول الاستیسیته و چگالی جرمی ورق متخلخل با توجه به دو الگوی توزیع مشخص، در جهت ضخامت درجه‌بندی شده‌اند. سیستم معادلات دیفرانسیل جزئی حاکم بر رفتار کمانش و رفتار خمشی ورق‌ از اصل همیلتون به‌دست آمده‌ و برای محاسبه بارهای بحرانی کمانش و انحنای خمش عرضی، روش ریتز به کار برده ‌شده است. جهت اعتبارسنجی روش و نتایج ارائه‌شده این پژوهش، مقایسه با نتایج ارائه‌شده در مراجع و مقالات معتبر انجام شده است. علاوه بر آن، نتایج مدل‌سازی المان محدود با تحلیل حاضر مقایسه شده است؛ همچنین مطالعه پارامتری برای بررسی اثرات ضریب تخلخل و نسبت طول به ضخامت ورق بر کمانش و خواص خمشی ورق‌های متخلخل دارای تکیه‌گاه ساده در چهار طرف انجام شده است. در این تحقیق مقدار بار کمانش و رفتار خمشی ورق متخلخل مدرج تابعی با الگوی توزیع تخلخل مشخصی بررسی شده و با توجه به دو الگو توزیع تخلخل متفاوت و در نظر گرفتن اندازه‌های مختلف صفحات، بار بحرانی کمانش و اندازه خمش این صفحات محاسبه شده است. طبق نتایج مطالعه پارامتری ورق‌های متخلخل، با افزایش ضریب تخلخل و نسبت طول به ضخامت، اندازه کمانش و میزان خمش افزایش می‌یابد. نتایج این پژوهش در راستای انتخاب درست میزان و نحوه توزیع تخلخل در طراحی‌های مختلف مانند ایمپلنت‌ها کاربرد دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Buckling and bending analysis of functional porous plate using shear deformation theory

نویسندگان [English]

  • mohammad javad khoshgoftar 1
  • Mona Hajiveiseh 2
1 Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran
2 Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran
چکیده [English]

In this study, the elastic buckling and static bending of a functionally graded porous plate based on shear deformation theory have been investigated. The effect of the type and degree of porosity on the mechanical behavior of the plate using the principle of potential energy is the main goal of this research. The modulus of elasticity and mass density of the porous sheet are graded in terms of thickness according to two different distribution patterns. The system of partial differential equations governing the buckling and bending behavior of the plate is derived from Hamilton's principle. The Ritz method is used to calculate the critical buckling loads and transverse bending curvature. In order to validate the method and the results presented in this research, a comparison was made with the results presented in authoritative references and articles. In addition, the finite element modeling results have been compared with the present analysis. Also, a parametric study has been performed to investigate the effects of porosity coefficient and length to thickness ratio of plate on buckling and flexural properties of porous sheets with simply support boundaries. The effect of different porosity distributions on plate performance is discussed. In this research, by applying different porosity coefficients and changes in length to thickness ratio, buckling load and flexural behavior of a graded porous plate with a specific porosity distribution pattern has been investigated. According to parametric study of porous plate, the buckling load and the maximum transverse displacement on bending increase with increasing the porosity coefficient and the ratio of length to thickness. The results of this study are used to design of porous plate in various designs such as implants.

کلیدواژه‌ها [English]

  • Buckling
  • Static bending
  • Porous sheet
  • Functional graded
  • Shear deformation theory
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