Large Deformation Analysis of Continuum Compliant Mechanisms.
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos.
Compliant mechanisms (CMs) above the traditional rigid-body mechanisms have the sole merit of no relative moving parts hence preventing any form of wear, backlash, noise and need for lubrication. Its applications are versatile and fully domicile in such sectors as medicine, robotics, aerospace, biomechanics, food processing and automotive industries to mention a few. The Pseudo Rigid Body (PRB) equivalence of compliant mechanisms have been the conventional approach used by earlier researchers to analyse compliant mechanisms. Attempts at direct analyses often assume linearity and static conditions. These are justifiable in several situations where compliant mechanisms have been successful in replacing materials with several moving parts. The application domain of compliant mechanisms is widening to dynamic environment where the deformations are relatively large. It is therefore necessary to consider nonlinearities resulting from geometry and hyperelasticity. This work presents a systematic model for the analyses of compliant mechanisms. Methods of continuum mechanics and finite element method were used to model compliant mechanisms. Static and dynamic analyses were carried out using the proposed model. Compliant mechanism (CM) examples are presented. Results from linear, geometric nonlinear together with combined geometric and material nonlinearities assumptions were compared with published laboratory investigated compliant mechanisms. It is revealed that while geometric nonlinear or even linear model could capture the CM output displacement when input load or displacement is 20% of the total input, the results obtained herein have shown that for large input load or displacement, the only reliable result is that from hyperelasticity. The dynamic analysis of CMs show that neglecting material nonlinearity could lead to failure due to end point effect. A Continuum Damage Mechanics (CDM) model is also proposed to assess the fatigue life of polymeric compliant material. The elastic strain energy is computed on the basis of a nearly incompressible hyperelastic constitutive relation. The damage evolution equation is used to develop a Mathematical formula that describes the fatigue life as a function of the nominal strain amplitude. Fatigue tests experiment were conducted on polymeric compliant materials. The result from the prediction formula shows a strong agreement with that of experiment. It was established that for strain amplitude lower than 0.100 mm/mm, the developed model is more appropriate to predict the fatigue life of polymeric CMs than other compared models. It is expected that the models and results presented here will have a wide spectrum of applications and will effectively facilitate the process of design and optimization of compliant mechanisms.