## 4 Optimization Analysis  
To evaluate the optimal hinge configuration, optimization analysis has been performed by fusing the commercial ModeFrontier code [16] that is an integration platform for multi-objective and multi-disciplinary optimization. It provides an easy coupling method with third-party engineering tools (like Finite Element codes), enables the automation of the design simulation process, and facilitates analytic decision making. A multidisciplinary approach is key for a successful design process, especially when the constraints and the requirements are very challenging. A powerful workflow enables the execution of complex chains of design optimization and innovative algorithms to determine the set of best possible solutions that combine opposing objectives. The code is widely used in engineering applications and is demonstrated to be suitable for several technical problems [17; 18; 19; 20]. Figure 10: Boundary conditions with global and local reference systems. Figure 9: FE model. (**A**) Global Model; (**B**) Hinge detail. Figure 11 shows the defined workflow. The latter is composed of \"nodes\" connected to each other to define the logic data path. The input variable nodes are used to define the design variables, their allowable ranges and increments (in this case the variables are treat as discrete variables): the input file node is the APDL macro and it is used to translate the design variables in a format that ANSYS can manage, and, thus, it is the link between ModeFrontier and ANSYS; the DOS node is a simple shell dos that is used to call on demand ANSYS to execute the numerical simulation; the DOE (design of experiment) node is used to define the starting generation and connected to this node there is a Scheduler node that is the optimization algorithm to be used; the output file nodes have the same function of the input file nodes, but, in this case, the link is from ANSYS to ModeFrontier; the output variable nodes represent all data from the solver that are available for the optimization process (but can be also used simply as checking data); the constraint nodes are used to define the constraint functions and can be applied both in output and input variable; finally, the objective function nodes are used to define whether the process has to minimize or maximize well-defined output variables. The design variables consist of the coordinates of the centers of the holes C1, C2, C4, and C5, which are specifically defined in Table 3. The coordinates of points C3 and C6, relative to the folded configuration, are defined by the previous points and by the folding angle. The variables H1-X and H2-X are defined in a dimensionless way, in order to avoid unfeasible configurations, they are then converted into physical dimensions by the calculation routine. They can range from 0 to 1 with a step increment equal to 0.025. The variables H1-Z and H2-Z can range from 10 mm up to 50 mm with a step increment equal to 2.5 mm. The developed APDL macro is the core of the optimization procedure as it can manage the design variable and translate them into an FE model ready to be solved by ANSYS,  
Figure 11: Optimization workflow. and, at the end of each design evaluation, it uses ANSYS to extract the output data that are then used in ModeFrontier as constraint and objective functions. The initial sampling, named _generation 0_, was done with a SOBOL algorithm (it is based on a pseudo-random SOBOL sequence and enables the uniform distribution having of the experiments in the design space), and all generations were composed by 30 elements each, so-called _individuals_. The adopted optimization algorithm is MOGAII, which is a genetic multi-objective algorithm that supports geographical selection and directional cross-over, implements Elitism for multi-objective search, defines constraints by objective function penalization, and allows generational or steady state evolution. The evolution process is defined by 10 generations and the following main parameters are reported:  
1.