رئوس مطالب

  • چکیده
  • کلیدواژه ها
  • 1. مقدمه
  • 2. تابع پاسخ تنش نامتقارن
  • 3. تغییرشکل‌های متقارن کروی
  • 4. تورم یا تراکم
  • 5. نوسان شعاعی
  • 6. واژگونی
  • 7. تورم یا تراکم کره‌ای واژگون شده
  • 8. نوسان شعاعی کره واژگون شده
  • 9. مواد‌هارمونیک و تراکم‌پذیر وارگا
  • 9.1. مواد‌هارمونیک
  • 9.2. مواد تراکم‌پذیر وارگا
  • 10. حالات حدّی (محدودکننده)
  • 11. نتیجه‌ گیری

Abstract

Radial inflation–compaction and radial oscillation solutions are presented for hollow spheres of isotropic elastic material that are radially inextensible. The solutions for radial inflation–compaction and radial oscillation are obtained also for everted radially inextensible hollow spheres of isotropic elastic material. The static and dynamic results for everted and inverted radially inextensible hollow spheres are then compared. Harmonic and compressible Varga materials are used to demonstrate the solutions.

Keywords: - - -

Conclusions

Radial deformations and motions, with or without eversion, are controllable for radially inextensible hollow spheres that are isotropic or locally transversely isotropic. The relevant material response property is the axi-symmetric stress response function T(λ) and integration of the equations of equilibrium or motion introduces additional functions F(β; R1, R2) and G(β; R1, R2), the latter describing eversion and post-eversion behavior. Comparison of the static and dynamic solutions in Sections 4 and 5 with their post-eversion counterparts in Sections 7 and 8 allows an assessment of the effects of pre-stress on mechanical response for any particular strain energy, i.e., for any particular T(λ). The stiffness of the response in radial deformation naturally increases as the wall thickness increases and it becomes effectively rigid for a spherical cavity in an infinite medium.

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