نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، مهندسی مکانیک، دانشگاه تربیت مدرس، تهرا ن.

2 استاد، دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران.

10.22068/jstc.2021.523813.1700

چکیده

در این تحقیق به تحلیل رفتار خمشی ورق مربعی هایپرالاستیک چندلایه با شرایط مرزی گیردار، ساده و آزاد پرداخته شده است. برای استخراج معادلات حاکم بر مسئله از تانسور تغییر شکل کوشی-گرین راست استفاده شده و به دنبال آن از تابع انرژی کرنشی نئوهوکین برای توصیف رفتار غیرخطی مادی ورق استفاده شده است. برای فرمولبندی کرنش‌های غیرخطی، تئوری تغییر شکل برشی مرتبۀ اول به کار رفته و برای استخراج معادلات حاکم بر ورق هایپرالاستیک به فرم قوی، روابط اویلر-لاگرانژ به کار رفته‌اند. برای حل معادلات غیرخطی حاکم بر مسئله از روش بدون شبکه به فرم قوی بر پایۀ درونیابی نقاط شعاعی استفاده شده است. یکی از مزایای مهم این روش، اعمال شرایط مرزی غیرخطی در فرآیند حل مسئله است. از تابع پایۀ شعاعی لگاریتمی برای استخراج توابع شکل روش بدون شبکه استفاده شده و دستگاه معادلات غیرخطی حاصل از درونیابی نقاط شعاعی با استفاده از الگوریتم طول کمان بررسی شده است. نتایج حاصل از روش بدون شبکه با نتایج نرم افزار المان محدود آباکوس مقایسه شده است. نتایج این تحقیق نشان می‌دهند که روش بدون شبکه به فرم قوی بر اساس توابع پایۀ شعاعی دارای دقت بالایی در شرایط مرزی مختلف بوده به طوری که کمترین مقدار اختلاف در شرایط مرزی گیردار با 0.93 درصد اختلاف و بیشترین مقدار اختلاف در شرایط مرزی آزاد با 8.72 درصد اختلاف است.

کلیدواژه‌ها

عنوان مقاله [English]

Nonlinear bending analysis of multi-layer hyperelastic silicon-rubber plates using meshless based on radial basis functions

نویسندگان [English]

  • Shahram Hosseini 1
  • Gholamhossein Rahimi 2

1 Department of mechanical engineering, Tarbiat Modares University, Tehran, Iran.

2 Department of mechanical engineering, Tarbiat Modares University, Tehran, Iran.

چکیده [English]

In this paper, bending analysis of a hyperelastic multi-layer square plate with clamped, simply supported, and free boundary conditions are studied. The right Cauchy-Green tensor and neo-Hookean strain energy function utilized to define the plate's physical nonlinear behaviour. The nonlinear strains formulated using first-order shear deformation plate theory, and the Euler-Lagrange equations employed to derive the strong form of the governing equations. The meshless collocation method based on radial point interpolation method used to solve the nonlinear governing equations. The nonlinear boundary conditions imposed directly on the plate in meshless collocation method. The logarithm basis function utilized for defining shape functions, and the nonlinear system of equations solved using the arc-length algorithm. The results of the meshless method compared to those of ABAQUS finite element software. The results show that the meshless collocation method based on radial basis functions are efficient in nonlinear bending analysis of the multi-layer hyperelastic plate with various boundary conditions such that the less difference between meshless method and finite element method is 0.93% for clamped and the most difference is 8.72% with free boundary conditions.

کلیدواژه‌ها [English]

  • Multi-layer hyperelastic plates
  • meshless method
  • radial basis functions
  • neo-Hookean strain energy function
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