During the two last decades, topology optimization has grown to be an accepted and used method to produce conceptual designs. Topology optimization is traditionally carried out on a component level, but in this project, the possibility to apply it to airframe design on a full scale aeroplane model is evaluated. The project features a conceptual flying-wing design on which the study is to be carried out. Inertia Relief is used to constrain the aeroplane instead of traditional single point constraints with rigid body motion being suppressed by the application of accelerations instead of traditional forces and moments. The inertia relief method utilized the inertia of the aeroplane to achieve a state of quasi-equilibrium such that static finite element analysis can be carried out. Two load cases are used: a steep pitch-up manoeuvre and a landing scenario. Aerodynamic forces are calculated for the pitch-up load case via an in-house solver, with the pressure being mapped to the finite element mesh via a Matlab-script to account for different mesh sizes. Increased gravitational loads are used in the landing load case to simulate the dynamic loading caused in a real landing scenario, which is unable to be accounted for directly in the topology optimization. It can be concluded that the optimization is unable to account for one of the major design limitations: buckling of the outer skin. Approaches to account for the buckling of the outer skin are introduced and analysed, with a focus on local compression constraints throughout the wing. The compression constraints produce some promising results but are not without major drawbacks and complications. In general, a one-step topology optimization to produce a mature conceptual airframe design is not possible with optimization algorithms today. It may be possible to adopt a multiple-step optimization approach utilizing topology optimization with following size and shape optimization to achieve a design, which could be expanded on in a future project.

Structural topology optimization methods have existing and been improving theoretically since 1980s; however, in industry, with respect to the certain conditions, proper modification is always desired. This study develops a specific method to utilize topology optimization for gearbox housing design. Gearbox housing maintains the position of the shafts to ensure the precision of gear engagement in all operational states (Naunheimer, et al., 2010). The current housing design processing used in Vicura AB, a Swedish powertrain company, is able to achieve stiff optimal housing material distribution, but difficult to fulfil gear misalignment requirement. This work overcomes the above shortages to develop a new methodology for gearbox housing topology optimization concerning the gear misalignment as well. The paper is starting with an introduction of the previous method and its defects, followed by a discussion of three possible improvements. Only one of them is feasible and two main difficulties need to be resolved to make it applicable. One of the difficulties is finding a linear assumption of the non-linear components and the other is deriving an approach for topology optimization involving both external forces and non-zero prescribed displacements. The corresponding solutions are described subsequently in detail both theoretically and practically. Then the results by implementing the new method and also the comparison with the results getting from the old method are presented. Finally, a validation of the new method is discussed and the conclusions and comments are given.

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abstract: Investigation into research literature was conducted in order to understand the impacts of traditional concrete construction and explore recent advancements in 3D printing technologies and methodologies. The research project focuses on the relationship between computer modeling, testing, and verification to reduce concrete usage in flexural elements. The project features small-scale and large-scale printing applications modelled by finite element analysis software and printed for laboratory testing. The laboratory testing included mortar cylinder testing, digital image correlation (DIC), and four pointbending tests. Results demonstrated comparable performance between casted, printed solid, and printed optimized flexural elements. Results additionally mimicked finite element models regarding failure regions. / Dissertation/Thesis / Masters Thesis Engineering 2020

Indiana University-Purdue University Indianapolis (IUPUI) / Topology Optimization is a technique that allows for the obtaining structures which maximize the use of the material. This is done by intelligently deciding the binary distribution of solid material and void, in a discretized given space. Several researchers have provided methods to tackle binary topology optimization. New ef- forts are focused on extending the application for multi-phase optimizations. At the industrial level, several components designed are made up of more than one material to reduce weight and production costs. The objective of this work is to implement the algorithm of Hybrid Cellular Automaton for multi-material topology optimiza- tion. The commonly used interpolation rule SIMP, which allows to relate the design variables to the mechanical properties of the material, is replaced by ordered SIMP interpolation function. The multiple volume constraints are applied sequentially, starting with the most elastic material. When a constraint is satisfied, the elements assigned to this material remain passive by a defined number of iterations to promote the convergence of the solution. Examples are shown for static and dynamic loads. The work demonstrates the versatility of algorithms based on control systems to solve problems of multiple phases and transient response fields.

In this research, a new zeroth-order (non-gradient based) topology optimization methodology for compliance minimization was developed. It is called the Element Exchange Method (EEM). The principal operation in this method is to convert the less effective solid elements into void elements and the more effective void elements into solid elements while maintaining the overall volume fraction constant. The methodology can be integrated with existing FEA codes to determine the stiffness or other structural characteristics of each candidate design during the optimization process. This thesis provides details of the EEM algorithm, the element exchange strategy, checkerboard control, and the convergence criteria. The results for several two- and three-dimensional benchmark problems are presented with comparisons to those found using other stochastic and gradient-based approaches. Although EEM is not as efficient as some gradient-based methods, it is found to be significantly more efficient than many other non-gradient methods reported in the literature such as GA and PSO.

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<div>New approaches in topology optimization and manufacturing techniques are generating multi-scale, physically realized mechanical components from advanced materials. Current optimization formulations do not consider the dependence of strength on feature size. By failing to account for the mechanical models of this behavior, sub-optimal structures are generated.</div><div><br></div><div>A currently available academic density-based topology optimization code is extended to incorporate strength constraints. A continuum theory of failure novel to the optimization field is implemented to account for both general yielding and fracture dominated failure. The fracture limit is then formulated in terms of well-established models of brittle and quasi-brittle size dependence. Additional models of size dependence based on assumed flaw sizes are considered using the theory of linear elastic fracture mechanics. To unify the optimized topology and the empirical geometric-scaling models used, a novel geometric measure of local size is proposed. This measure interprets the evolving density field using a consistent domain of support and maintains consistency with gradient-based methods of optimization. The geometric measure is evaluated using test-problems which consider a minimum compliance objective under geometric constraints.</div><div><br></div><div>The resulting optimized structures are presented for the geometric and size-dependent strength constrained formulations. The geometrically constrained results illustrate the flexibility and robustness of the proposed local size measure. The various models of size-dependent strength illustrate the impact and necessity of considering physical models of material within the topology optimization formulation. Results which exhibit clear "micro-structural" features and scale transitioning architectures are presented for limited multi-scale optimization studies.</div><div><br></div><div>An attempt at physical validation considering a single model of quasi-brittle material failure is made. Existing approaches for generating 3D volumetric meshes from image data are leveraged to yield CAD interpretations of optimized structures. Structures are then printed using a 3D printing PolyJet process with a previously established size-dependent material. Structures are destructively evaluated under displacement controlled load testing. The resulting tests indicate that the stress states in the structure fail to induce the expected size-dependent material characteristics. Furthermore, the testing results indicate the difficulty in properly accounting for boundary conditions in the topology optimization approach.</div>

This thesis discusses how to use topology and shape optimization, specifically the level set method, for innovative design. The level set method is a numerical algorithm that simulates the expansion of dynamic implicit surfaces. In this research, the equations for manufacturability are generated and solved through use of the level set method joined with the COMSOL multi-physics package. Specific constraints are added to make the optimization practical for engineering design. The resulting method was applied to design the best underlying support structure, conforming to both curvature and manufacturability constraints, for the longerons used with the International Space Station solar panels.

Compliant mechanisms (CMs) take advantage of the deformation of their flexible members to transfer motion, force, or energy, offering attractive advantages in terms of manufacturing and performance over traditional rigid-body mechanisms (RBMs). This dissertation aims to advance the topology optimization (TO) technique (1) to design CMs that are more effective in performing their functions while being sufficiently strong to resist yield or fatigue failure; and (2) to design CMs from the perspective of mechanisms rather than that of structures, particularly with the insight into the concepts of joints, actuations, and functions of mechanisms. The existing TO frameworks generally result in CMs that are much like load-bearing structures, limiting the applications of CMs. These CMs (1) do not have joints, (2) are actuated by a translational force, and (3) can only do simple work such as amplifying motion or gripping. Three TO frameworks for the synthesis of CMs are proposed in this dissertation and they are summarized below. First, a framework was developed for the design of efficient and strong CMs. The widely used stiffness-flexibility criterion for CM design with TO results in lumped CMs that are intrinsically efficient in transferring motion, force, or energy but are prone to high localized stress and thus weak to resist yield or fatigue failure. Indeed, distributed CMs may have a better stress distribution than lumped CMs but have the weakness of being less efficient in motion, force, or energy transfer than lumped CMs. Based on this observation, the proposed framework rendered the concept of hybrid systems, hybrid CMs in this case. Further, the hybridization was achieved by a proposed super flexure hinge element and a design criterion called input stroke criterion in addition to the traditional stiffness-flexibility criterion. Both theoretical exploration and CM design examples are presented to show the effectiveness of the proposed approach. The proposed framework has two main contributions to the field of CMs: (1) a new design philosophy, i.e., hybrid CMs through TO techniques and (2) a new design criterion—input stroke. Second, a systematic framework was developed for the integrated design of CMs and actuators for the motion generation task. Both rotary actuators and bending actuators were considered. The approach can simultaneously synthesize the optimal structural topology and actuator placement for the desired position, orientation, and shape of the target link in the system while satisfying the constraints such as buckling constraint, yield stress constraint and valid connectivity constraint. A geometrically nonlinear finite element analysis was performed for CMs driven by a bending actuator and CMs driven by a rotary actuator. Novel parameterization schemes were developed to represent the placements of both types of actuators. A new valid connectivity scheme was also developed to check whether a design has valid connectivity among regions of interest based on the concept of directed graphs. Three design examples were constructed and a compliant finger was designed and fabricated. The results demonstrated that the proposed approach is able to simultaneously determine the structure of a CM and the optimal locations of actuators, either a bending actuator or a rotary actuator, to guide a flexible link into desired configurations. Third, the concept of a module view of mechanisms was proposed to represent RBMs and CMs in a general way, particularly using five basic modules: compliant link, rigid link, pin joint, compliant joint, and rigid joint; this concept was further developed for the unified synthesis of the two types of mechanisms, and the synthesis approach was thus coined as module optimization technique—a generalization of TO. Based on the hinge element in the finite element approach developed at TU Delft (Netherlands in early 1970), a beam-hinge model was proposed to describe the connection among modules, which result in a finite element model for both RBMs and CMs. Then, the concept of TO was borrowed to module optimization, particularly to determine the “stay” or “leave” of modules that mesh a design domain. The salient merits with the hinge element include (1) a natural way to describe various types of connections between two elements or modules and (2) a provision of the possibility to specify the rotational input and output motion as a design problem. Several examples were constructed to demonstrate that one may obtain a RBM, or a partially CM, or a fully CM for a given mechanical task using the module optimization approach.