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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 45222 (08)
- University: Sharif University of Technology
- Department: Mechanical Engineering
- Advisor(s): Naghdabadi, Reza; Baghani, Mostafa
- Abstract:
- Shape Memory Polymers (SMPs) are a class of smart materials capable of remembering multiple shapes, and transitioning between them in response to an external stimulus such as thermal or magnetic induction. SMPs have attracted significant attention of both industrial and academic researchers due to their useful and attractive functionality. This thesis aims to analytically develop Euler-Bernoulli, Timoshenko and von Karman theories for beam bending in small strain regime considering SMP constitutive equations. To properly introduce analytical solution for the problem of beam bending, the constitutive model proposed by Baghani et al. (2012) has been used. For this purpose, three dimensional constitutive model and corresponding evolution equations have been reduced to one dimensional stress strain relationships required in this work. The stress-strain formulation has been used in the axial force and moment equilibrium equations in all stages of SMP standard thermomechanical cycle, in order to obtain the position of neutral axis as well as the beam curvature at each step of the cycle. Thermomechanical standard cycle is a four-step cycle, including loading, cooling, unloading and heating stages. In the loading stage an external moment is applied to the beam at a temperature above the glass transition temperature of material (Tg). Subsequently, temperature of the beam is decreased below Tg. At the unloading stage, the external moment is removed and the beam is maintained in this deformed shape at a low temperature. This shape is being known as temporary shape of the material. The SMP beam is capable of recovering the original shape when heated above Tg. Three point bending and a cantilever under a concentrated load at the free tip have been investigated as examples for validating the derived analytical formulation for SMP beams. A good agreement has been shown between the results of the present work and those of the experiments available in the literature
- Keywords:
- Shape Memory Polymers ; Analytical Solution ; Bending ; Euler-Bernoulli Beam ; Timoshenko Beams ; Von Karman Theory
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