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

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>

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.

The advances in additive manufacturing removed most of the limitations that were once stopping designers when it comes to the manufacturability of the design. It allowed designers to produce parts with high geometric complexity such as cellular structures. These structures are known for their high strength relative to their low mass, good energy absorption, and high thermal and acoustic insulation compared to their relative solid counter-parts. Lattice structures, a type of cellular structures, have received considerable attention due to their properties when producing light-weight with high strength parts. The design of these structures can pose a challenge to designers due to the sheer number of variables that are present. Traditional optimization approaches become an infeasible approach for designing them, which motivated researchers to search for other alternative approaches. In this research, a new method is proposed by utilizing the material density information obtained from the topology optimization of continuum structures. The efficacy of the developed method will be compared to existing methods, such as the Size Matching and Scaling (SMS) method that combines solid-body analysis and a predefined unit-cell library. The proposed method shows good potential in structures that are subjected to multiple loading conditions compared to SMS, which would be advantageous in creating reliable structures. In order to demonstrate the applicability of the proposed method to practical engineering applications, the design problem of a commercial elevator sling will be considered.

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a threedimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a threedimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17511号 / 工博第3670号 / 新制||工||1558(附属図書館) / 30277 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 田畑 修, 教授 蓮尾 昌裕 / 学位規則第4条第1項該当

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