Flexure Design Optimization for Foldable Structures: Pseudo-Rigid Body Modeling and Multi-Objective Optimization

Compliant mechanisms have found their way in more and more applications in recent years, particularly in the aerospace and microsystems sectors. The benefits of compliant mechanisms stretch far, and can be exploited for large scale applications as well. Little research has been performed on the use of compliant mechanisms in large scale structures, where large deflections are in play. This while the interest in foldable structures is increasing, take for example the foldable container concept and origami inspired structures. The required hinges can be made compliant, such a hinge is called a flexure. The aim of this research is to give insight in the design of flexures for large scale applications and large deflections, to aid researchers when designing large foldable structures. The research question that is answered in this report is: how can flexure design be optimized for foldable structures? To answer the research question a PseudoRigid Body Model (PRBM) is made in Python, along with a multiobjective optimization. Compliant mechanisms can offer increased performance, however, the design of compliant mechanisms is more complicated than rigid body mechanisms. Therefore, an intuitive method for designing compliant mechanisms is required. The FiniteElement Method is considered for this purpose, but is too complex and not suited for initial design stages. Therefore, a PRBM is selected for the design analysis, as it is less complex and well suited for large deflection members and ideal for initial design stages. A PRBM with two revolute joints is used, because it provides a higher accuracy than a model with one revolute joint and it simplifies the iterative process of a model with three revolute joints, while maintaining a similar level of accuracy. The load case that is evaluated in this research is a moment end load. A sensitivity analysis is performed for the flexure behaviour regarding the flexure’s Young’s modulus, length, width, thickness and end moment load. This analysis shows that the flexure length and moment load, linearly influence the flexure deflection, i.e. twice the length, gives twice the deflection. Furthermore, the flexure deflection is reverse linearly dependant on the Young’s modulus and width, i.e. twice the width, gives a twice as small deflection. The flexure is most sensitive to a change in thickness. For a thickness increase of factor 𝑛, the deflection decreases by a factor 𝑛3. Furthermore, the design of the flexure is evaluated for three material types, being aluminium, rubber and a Nickel–Titanium Shape Memory Alloy (SMA). The material changes the behaviour of the flexure because of the material’s Young’s modulus and yield strength, which prescribes the allowed load. Therefore, it is shown that the measure of flexibility, 𝐹 = 𝜎𝑦 𝐸 , is a good indicator for suitable flexure materials. When taking the results from the sensitivity analysis and implementing the importance of the flexure material’s yield strength, a design constant can be deduced for viable and intuitive flexure design. This constant considers all the variables influencing the flexure design and assumes maximum allowable load on the flexure. With this constant researchers can quickly identify feasible flexure designs and the result of parameter changes are made more intuitive. The multiobjective optimization for the flexure design is performed with Nondominated Sorting Genetic Algorithm II. The optimization can find the Paretooptimal solutions for the objectives of shape error, stress and volume, while varying the flexure thickness. The evaluated configurations are for a single flexure and for flexures implemented in a large scale compliant mechanism. For the single flexure target shape, a clear Paretofront is found, depicting the required tradeoff between the objective functions. Furthermore, the optimization visualizes the super elastic properties of the SMA and its effect on the deflection when actuated optimally. The results for the use of SMA flexures in a compliant mechanisms are shown as well. It shows that with the right boundary conditions the superelasticity properties of the SMA can be exploited for optimal compliant structure design. From this it can be concluded that this optimization can be used for design of complicated foldable structures, while taking into account the accuracy of the compliant mechanism’s motion. For future research it is proposed to visualize the behaviour of a flexure with a different crosssection than a rectangular beamlike crosssection. Furthermore, more research is required into the practicality of flexures for large scale applications, since the out of plane stiffness can become too low, risking the planar motion of flexures. Other directions that require more research, are the influence of micro slip and unloading effects on the flexure behaviour. Marine Technology | Transport Engineering and Logistic