<div>The objective of this dissertation is to develop new methods in the areas of multiscale topology optimization, thermomechanical topology optimization including heat convection, and thermal-fluid topology optimization. The dissertation mainly focuses on developing five innovative topology optimization algorithms with respect to structure and multistructure coupling fluid, thermal and mechanical analysis, in order to solve customary design requirements. Most of algorithms are coded as in-house code in MATLAB.</div><div><br></div><div><div>In Chapter One, a brief introduction of topology optimization, a brief literature review and the objective is presented. Five innovative algorithms are illustrated in Chapter Two</div><div>to Six. From Chapter Two to Four, the methods with respect to multiscale approach are presneted. and Chapter Five and Six aims to contribute further research associated with</div><div>topology optimization considering heat convection. In Chapter Two, a multiphse topology optimization of thermomechanical structures is presented, in which the optimized structure is composed of several phases of prescribed lattice unit cells. Chapter Three presents a</div><div>Multiscale, thermomechanical topology optimization of self-supporting cellular structures. Each lattice unit cell have a optimised porousity and diamond shape that benefit additive</div><div>manufacturing. In Chapter Four, the multiscale approach is extended to topology optimization involved with fluid mechanics problem to design optimized micropillar arrays in</div><div>microfludics devices. The optimised micropillars minimize the energy loss caused by local fluid drag force. In Chapter Five, a novel thermomechanical topology optimization is developed, in order to generate optimized multifunctional lattice heat transfer structure. The algorithm approximate convective heat transfer by design-dependent heat source and natural convection. In Chapter Six, an improved thermal-fluid topology optimization method is created to flexibly handle the changing of thermal-fluid parameters such as external heat source, Reynolds number, Prandtl number and thermal diffusivity. The results show the</div><div>changing of these parameters lead versatile optimized topologies. Finally, the summary and recommendations are presented in Chapter Seven.</div></div><div><br></div>

Biomineralized lattice materials with have high mineral contents (~ 99 wt%), usually "conceal" multiscale structural arrangements for unique mechanical or functional performance, such as the remarkable damage tolerance despite of the brittle nature of the constituents (e.g., biogenic silica and calcite). However, the quantitative explorations of the structure-mechanics relationships in multiscale of biomineralized lattices remain insufficient and hence hinder the leverage of the functional benefits to design architected cellular materials. In this dissertation, I selected two groups of marine animals (i.e., Hexactinellid sponges and Echinoderms) for systematic structural-mechanical study. Their biomineralized lattice skeletons exhibit three representative types of multiscale structures: 1) multiscale hierarchical structure: skeleton of Hexactinellid sponge such as Euplectella aspergillum; 2) multiscale functionally graded structure: spine of sea urchin Heterocentrotus mammillatus; and 3) dual-scale (atomic and microlattice scales) periodic structure: ossicle of starfish Protoreaster nodosus. This dissertation develops quantitatively the structural-mechanical/functional correlations in biomineralized cellular materials for bio-inspired material design. Four different species of Hexactinellid sponges have been studied with particular focus on the species E. aspergillum. As an example of the multiscale hierarchical biomineralized lattice, the extremely lightweight skeleton (~99% porosity) of E. aspergillum exhibits 1) amorphous nanoparticular biogenic silica; 2) micron-sized fibrous spicule with cylindrically laminated silica layers separated by organic interfaces; 3) spicule bundles where the individual spicules merged by secondary silica deposition; 4) a centimeter-sized Voronoi-like cellular dome known as sieve plate; and 5) a centimeter-sized cylindrically arranged rectangular lattice with double-diagonal reinforcement and external helical ridge. Here, we discovered a series of mechanical or functional properties or formation process of structures in different length scales: 1) for the biogenic silica in three different species of Hexactinellid sponge, consistent modulus and hardness of the biogenic silica throughout the cross section of the spicule are found via substantial correlation between the measured values and locations; 2) for the sieve plate, the Voronoi-like cellular dome constructed by porous branch with increased height achieves balance between improved mechanical stiffness and large pore opening for sponge's current pumping mechanism; 3) via microstructural study, the formation process of the sieve plate is proposed; and 4) for the cylindrical skeletal body, the double-diagonal configuration and the ridge structure are found to provide tendency to optimize torsional rigidity, and enhanced radial stiffening and improved permeability, respectively. The cellular structure in the spine of the H. mammillatus (i.e., stereom) made of ~99wt% of single-crystalline calcite shows a multiscale functionally graded structure. We developed and optimized a cellular network analysis workflow on the large-volume 3D lattice structure obtained from the synchrotron-based micro-Computed Tomography scan. The analysis provides quantitative descriptions of the branch, ring structure, and septum which reveals a functionally graded structure in multiscale from the center region to the edge region of the spine: 1) in microscale, the branch thickness and length increases, resulting in a significantly decreased porosity; and 2) in macroscale, the center region of the spine with galleried stereom of highly aligned branches transits to the edge region with laminar stereom of radially arranged septa and interconnecting branches. The multiscale structural variations lead to the mechanical variations the increased elastic modulus and mechanical isotropy from the center to the edge of the spine. This provides a biological pathway for designing the lightweight, strong, and tough beam with multiscale structural gradient. In previous work, we discovered that ossicle in starfish P. nodosus possesses a unique dual-scale periodic lattice structure, which means periodic single crystal calcite in nanoscale and diamond triply periodic minimal surface (diamond-TPMS) lattice in microscale. It has three unique structural features: 1) microlattice dislocations in ossicles similar to those found in crystals with diamond cubic lattice; 2) a diamond-TPMS microlattice with ca. 50% relative density; and 3) dual-scale crystallographic coalignment between c-axis of the single-crystalline constituent calcite and the [111] direction of the diamond-TPMS microlattice. Based on this work, this dissertation mainly reveals: 1) unique type and core structures of the dislocations in the ossicle for stiffness, strength, and toughness; 2) the 3D property compensation of dual-scale crystallographic coalignment for improved mechanical isotropy; and 3) mechanical benefits (improved mechanical isotropy and effective fragment jamming) and morphological benefits (minimal surface and highest surface area to volume ratio) for 50% relative density. / Doctor of Philosophy / Architected lattice materials, featured by their tailorable 3D multiscale architectures, achieve unique mechanical properties such as breaking the trade-off between strength and toughness, and mechanical isotropy reaching theoretical limit. In nature, as a result of evolutionary driving force, the biomineralized skeletons of the animals such as sea sponge, sea urchin, and starfish usually delicately control the architectural arrangements in different length scales and provide excellent templates for the design of architected lattices with desirable properties. Quantitative understanding of the 3D multiscale structures and mechanics of these natural biomineralized lattices allows the development of bio-inspired materials that are, for example, simultaneously stiff, strong, and tough. This dissertation establishes the quantitative structural-mechanical/functional relationships in multiscale of three biomineralized lattices with high mineral contents (~99 wt%) and a wide range of porosity (50~99 vol%) in Hexactinellid sponges with main emphasis on species (Euplectella aspergillum), sea urchin Heterocentrotus mammillatus, and starfish Protoreaster nodosus. They are selected for their representative multiscale structures, i.e., multiscale hierarchical structure, multiscale functionally graded structure, and dual-scale (i.e., atomic and microlattice scales) periodic structure, respectively. Study of these biomineralized lattices significantly improve our understanding of the biological strategies in structural arrangement and pave the way towards bio-inspired modeling to leverage the mechanical benefits.

Für Festigkeitsnachweise hat sich die Methode der Finiten Elemente (FEM) als Goldstandard etabliert. Zwar wird sowohl bei der Modellbildung als auch bei der Auswertung der Ergebnisse nach wie vor eine intellektuelle Eigenleistung gefordert, die Ergebnisse selbst sind aber unter dieser Voraussetzung zuverlässig und tendenziell reproduzierbar. Dank der Leistungsfähigkeit der heutigen Arbeitsplatzrechner werden zunehmend große Produkte betrachtet – Assemblies, die aus einer Vielzahl unterschiedlichster Parts bzw. Baugruppen bestehen. Hier begegnen wir einem neuen Phänomen. Es gibt oft Basisstrukturen, in denen Detailstrukturen enthalten sind, deren geometrische Abmessungen sich um mehrere Größenordnungen von den Gesamtabmessungen unterscheiden können. Eine gemeinsame Elementierung erweist sich dabei als wenig sinnvoll. Ebenso findet man oft eine große Anzahl von Gleichteilen, für die im Prinzip jeweils eine Mustervernetzung genügt. Selbst wenn die FE-Software dies zulassen sollte, bleibt das Problem der extrem unterschiedlichen Elementgrößen innerhalb eines Modells. Das häufig propagierte defeaturing, für das sogar Automatisierungsansätze existieren, ist ebenso wenig zielführend, weil es auf geometrische Details bezogen ist, die nicht notwendig physikalische Funktionselemente darstellen. Gerade die physikalischen Eigenschaften der Parts sollten ja erhalten bleiben und in die Analyse einfließen. In Einzelfällen werden physikalisch motivierte Vereinfachungen praktiziert; so werden Wellen auf Balkenstrukturen reduziert, wenn man sich nur für die mechanischen Eigenschaften von Rotoren interessiert. Eine Verallgemeinerung und Systematisierung solcher Individualansätze auf größere Klassen von Strukturkomponenten ist bisher nicht untersucht worden.

<p dir="ltr">Multiscale topology optimization is a numerical method that enables the synthesis of hierarchical structures, offering greater design flexibility than single-scale topology optimization. However, this increased flexibility also incurs higher computational costs. Recent advancements have integrated machine learning models into MSTO methods to address this issue. Unfortunately, existing machine learning-based multiscale topology optimization (ML-MSTO) approaches underutilize the potential of machine learning models to surrogate the inner optimization, analysis, and numerical homogenization of arbitrary non-periodic microstructures. This dissertation presents an ML-MSTO method featuring displacement-driven topology-optimized microstructures (TOMs). The proposed method solves an outer optimization problem to design a homogenized macroscale structure and multiple inner optimization problems to obtain spatially distributed, non-periodic TOMs. The inner problem formulation employs the macroscale element densities and nodal displacements to define constraints and boundary conditions for microscale density-based topology optimization problems. Each problem yields a free-form TOM. To reduce computational costs, artificial neural networks (ANNs) are trained to predict their homogenized constitutive tensor. The ANNs also enable sensitivity coefficients to be approximated through a variety of standard derivative methods. The effect of the neural network-based derivative methods on topology optimization results is evaluated in a comparative study. An explicit dehomogenization approach is proposed, leveraging the TOMs of the ML-MSTO method. The explicit approach also features two post-processing schemes to improve the connectivity and clean the final multiscale structure. A 2D and a 3D case study are designed with the ML-MSTO method and dehomogenized with the explicit approach. The resulting multiscale structures are non-periodic with free-form microstructures. In addition, a second implicit dehomogenization approach is developed in this dissertation that allows the projection of homogenized mechanical property fields onto a discrete lattice structure of arbitrary shape. The implicit approach is capable of dehomogenizing any homogenized design. This is done by incorporating an optimization algorithm to find the lattice thickness distribution that minimizes the difference between a local target homogenized property and a corresponding lattice homogenized stiffness tensor. The result is a well-connected, functionally graded lattice structure, that enables control over the length scale, orientation, and complexity of the final microstructured design.</p>