A Graph-based Optimization Method for the Design of Compliant Mechanisms and Structures

Abstract

This thesis investigates several aspects of the design of compliant mechanisms and structures. It focuses the structural synthesis as well as the postprocessing of the data obtained by the optimization. Finally, the adaptive care seat concept demonstrates the capability of the synthesis procedure. A method is introduced to solve compliant mechanism and structure problems that combines evolutionary optimization techniques with the ground structure approach whereas the use of graph theory and a complex-shaped, two-dimensional beam element can increase both numerical efficiency and solution space. The beam element is curved and of variable thickness so that a localized compliant region can be placed within one beam element. The ground structure topology is represented by a mathematical graph whose edges and vertices fall together with the beams and their nodes, respectively. All genetic operators, i.e., mutation and crossover, directly apply on the graph representation (vertices and edges). This implies a set of modified and new genetic operators, which are also developed within this work. The graph-based representation allows the optimization of topology, geometry, and sizing of the beam structures at the same time. Besides this, it can handle individuals of different sizes. As a further feature, the graph-based optimization is able to find solutions for highly-constrained and discrete optimization problems such as for multi-material optimization. The inverter and the gripper optimization sample problems serve to demonstrate the advantages and disadvantages of the method. Compliant mechanisms and structures often undergo large displacement, in order to provide their functionality. Therefore, geometrical nonlinear analysis is required. The presented optimization provides both options; geometrical linear as well as nonlinear analysis. Sample large displacement grippers are illustrating the difference of the linear and nonlinear analysis. The graph-based design environment helps setting up new optimizations, visualizing and analyzing the optimized results and allow a fast aftertreatment of the structures obtained by the optimization. The aftertreatment or the so-called final design interpretation step is necessary, since the outcomes of the optimization are encoded according to the graph representation and not directly real-world models. The final design interpretation maps the encoded data into CAD(Computer Aided Design) models. An adaptive car seat concept is presented as a new, possible application of large scale, shape morphing, compliant structure. The adaptive car seat consists of compliant rib-like structures, which are kept by two columns in position. The compliant rib-like structure are designed to adapt themselves to the driver by embracing the back, when he leans into the seat and applying an additional actuation force. The whole development procedure is presented starting from the design domain parametrization and the fitness formulation up to the postprocessing of the optimization result. Finally, the real-world prototype, which integrates a pneumatic actuation system, validates the structural behavior predicted by the graph-based optimization. The adaptive car seat concept serves as an example of simultaneously increasing the functionalities and decreasing the complexity of a construction (number of parts).