تحلیل غیرخطی ورق هایپرالاستیک با استفاده از تئوری تغییر شکل برشی مرتبه اول و روش بدون شبکه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران، ایران

2 تربیت مدرس*مهندسی مکانیک

چکیده

در این مقاله تحلیل استاتیکی ورق هایپرالاستیک تحت بارگذاری‌های گستردۀ یکنواخت و سینوسی بررسی شده‌است. از تانسور تغییر شکل کوشی- گرین راست و کرنش‌های لاگرانژی برای استخراج روابط کرنش غیرخطی استفاده شده‌است. همچنین تئوری ورق برشی مرتبۀ اول برای روابط جابجایی در سه راستای اصلی به‌کاررفته‌است. برای نخستین بار، معادلات حاکم بر رفتار ورق هایپرالاستیک با استفاده از تابع انرژی کرنشی نئوهوکین به فرم قوی استخراج شده‌است. برای این منظور از رابطۀ لاگرانژ برای اعمال{Amabili, 2016 #24} روش تغییرات بر تابع انرژی پتانسیل استفاده شده‌است. معادلات دیفرانسیل غیرخطی حاکم بر مسئله به همراه شرایط مرزی حاکم بر آن، با استفاده از روش بدون شبکه به فرم قوی و توابع پایۀ شعاعی بررسی شده‌است. تابع اسپیلاین ورق نازک به عنوان تابع پایۀ شعاعی برای تشکیل توابع شکل روش بدون شبکه به‌کاررفته‌است. نتایج حاصل از روش بدون شبکه با نتایج حاصل از تحلیل المان محدود توسط نرم افزار آباکوس مقایسه شده‌است. نتایج بدست‌آمده نشان می‌دهند که مطابقت بسیار خوبی میان نتایج روش بدون شبکه و روش المان محدود در خیز ورق تحت بارگذاری‌های گستردۀ یکنواخت و سینوسی وجود دارد؛ همچنین کانتور تنش برای هر دو روش یکسان بوده و مطابقت خوبی میان آن‌ها مشاهده شده‌است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear analysis of hyperelastic plates using first-order shear deformation plate theory and a meshless method

نویسندگان [English]

  • Shahram Hosseini 1
  • Gholam Hosein Rahimi 2
  • Yavar Anani 1
1 Department of mechanics, Tarbiat Modares University, Tehran, Iran
چکیده [English]

In this paper, the static analysis of hyperelastic plates under uniform and sinusoidal distributed loading is investigated. Right Cauchy-Green deformation tensor and Lagrange strains are used to derive the nonlinear strain relations. Also, the first-order shear deformation plate theory is considered. For the first time, the governing equations of hyperelastic plates using the neo-Hookean strain energy function are derived. The Lagrange equation is utilized to implement the variational method on potential energy function. The governing nonlinear differential equations are discretized using the meshless collocation method and radial basis functions. The thin plate spline basis function is applied for deriving shape functions of the meshless method. The results are compared to the results of the finite element method. The static analysis is investigated on hyperelastic plates for uniform and sinusoidal loading and various thicknesses. Additionally, the effect of thickness is studied on the deflection of the hyperelastic plates. The results show an acceptable accuracy for static analysis of hyperelastic plates under uniform and sinusoidal loading; also, the stress contour is the same in both methods. Consequently, the meshless collocation method using the thin-plate spline basis function is an adequate method for analyzing FSDT hyperelastic plates due to no integration and imposing boundary conditions directly.

کلیدواژه‌ها [English]

  • Hyperelastic plates
  • Neo-Hookean strain energy function
  • Static analysis
  • Meshless Method
  • Radial basis functions
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