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  1. Free, publicly-accessible full text available March 1, 2023
  2. Editor-in-Chief: Joern Ritterbusch, Deputy Editors: (Ed.)
    Owing to the fact that effective properties of low-density cellular solids heavily rely on their underlying architecture, a variety of explicit and implicit techniques exists for designing cellular geometries. However, most of these techniques fail to present a correlation among architecture, internal forces, and effective properties. This paper introduces an alternative design strategy based on the static equilibrium of forces, equilibrium of polyhedral frames, and reciprocity of form and force. This novel approach reveals a geometric relationship among the truss system architecture, topological dual, and equilibrium of forces on the basis of 3D graphic statics. This technique is adapted tomore »devise periodic strut-based cellular architectures under certain boundary conditions and they are manipulated to construct shell-based (shellular) cells with a variety of mechanical properties. By treating the materialized unit cells as representative volume elements (RVE), multiscale homogenization is used to investigate their effective linear elastic properties. Validated by experimental tests on 3D printed funicular materials, it is shown that by manipulating the RVE topology using the proposed methodology, alternative strut materialization schemes, and rational addition of bracing struts, cellular mechanical metamaterials can be systematically architected to demonstrate properties ranging from bending- to stretching-dominated, realize metafluidic behavior, or create novel hybrid shellulars.« less
    Free, publicly-accessible full text available January 13, 2023
  3. This research investigates the design of structurally performant, lightweight architectural elements produced through concrete 3D printing (C3DP). Traditionally, concrete requires dense and sturdy formwork, whose production adds significantly to the total cost and results in massive and heavy parts after demolding. C3DP offers the unique opportunity to both eliminate the need for formwork and to create lighter parts by introducing internal voids and cavities. The advent of additive manufacturing in a broad range of scales, materials, industries, and applications, led to increased interest and intense research into different types of porous structures, their geometry, and structural performance under various boundarymore »conditions. Precise control over the sparse distribution of material allows not only for parts with similar strength at reduced mass but even for modifications of mechanical properties, like turning brittle materials into elastic or shock-absorbent ones. While with powder-based additive manufacturing processes like metal 3D printing, truss-based lattices have become very popular for the light-weighting of parts or to provide tissue growth scaffolds for medical implants, their geometry – a sparse space frame resulting in numerous individual contour islands and accentuated overhangs – cannot as easily be produced by C3DP, which is based on a continuous material extrusion. Alternative types of micro-structures, so-called triply periodic minimal surfaces (TPMS), are better suited for this process as they are, as their name suggests, consisting of one continuous surface dividing space into two separate but interwoven subspaces. TPMS are therefore very popular for the efficient design of heat exchangers. We develop and present a continuous and integrated workflow, in which the architectural elements and their structural requirements are designed through transitioning back and forth between the force and the form diagram using 3D graphic statics [1]. The members and their topology from the abstract graph of the conceptual form diagram are seamlessly connected to the volumetric modeling (VM) framework, responsible for the definition of the part geometry [2]. VM represents form assigned distance functions (SDF) and can easily handle complex topologies and flawless Boolean operations of not only the outer shell geometry but also the internal micro-structural infill patterns (Fig. 1, a). In an iterative feedback loop, the infill can be further optimized to leave the material only along certain internal stress trajectories (force flows). This functional grading controlling the relative density is done based on the FE analysis results. The stress distribution is thereby defined as a three-dimensional field (Fig. 1, b). Its values can factor into the SDF equation and be used to modify the wavelength (periodicity) of the TPMS, the local thickness of the surface shell, the solid to void fraction by shifting the threshold iso-value or even the alignment and orientation of the unit cells (Fig. 1, c). They can be arranged in an orthogonal, polar- or even spherical coordinate system to optimally adapt to structural necessities. The TPMS pattern can also gradually transition from one type into another type along the gradient of a spatial function.« less
    Free, publicly-accessible full text available October 1, 2022
  4. The recent development of three-dimensional graphic statics (3DGS) has greatly increased the ease of designing complex and efficient spatial funicular structural forms [1]. The reciprocal diagram based 3DGS approaches not only generate highly efficient funicular structures [2], but also result in planarity constraints due to the polyhedron nature of the reciprocal diagrams [3]. Our previous research has shown the feasibility of leveraging this planarity by using planar glass sheets to materialize the 10m-span, double-layer glass bridge [3]. This paper is framed as a proof of concept for the 10m bridge and explores the form-finding, detail configuration, fabrication constraints, and assemblymore »logic by designing and constructing a small-scale bridge prototype with a span of 2.5m. The prototype is designed in a modular approach, where each polyhedral cell of the form is materialized using a hollow glass unit (HGU) (Figure 1a), which can be prefabricated and preassembled, and therefore, greatly simplifies the assembly of the whole bridge. The compression-only form of the prototype is generated using the PolyFrame beta [4] plug-in for Rhinoceros [5]. The form-finding is carried out with a comprehensive consideration of a variety of parameters, including fabrication constraints, assembly ease, construction cost, and practicality. To start the form-finding process, a group of closed convex force polyhedrons is aggregated, controlling the topology of the form diagram and the orientations of the form elements. By manipulating the face tilting angles of the force diagram, the supported edges at the end of the bridge are all made horizontal, reducing the difficulty of the support design. Then, vertex locations and edge lengths of the form diagram are constrained, determining the final dimensions of both the bridge and the cells. After getting the geometry of the bridge, the detail developments are streamlined. Each of the 13 HGUs consists of two flat deck plates and a series of side plates (Figure 1b). To interlock the adjacent cells and prevent possible sliding, a male-female connection mechanism is introduced to the conjoint side plates of the HGUs (Figure 1b). Additionally, to eliminate the direct contact of the glass parts and prevent the stress concentration, two softer transparent materials are involved for connecting purposes. Within each HGU, silicon-based binding agent is used to hold the glass parts together; between the neighboring HGUs, plastic sheets are placed as interface materials (Figure 1b). Figure 1. a) The 2.5m-span small-scale prototype dome, b) Exploded view showing deck plates, side plates, male-female connection, and interface material For the fabrication of the glass parts, 5-axis Waterjet cutting techniques are applied. While the glass sheets for the deck plates can be purchased from the market, the irregular side plates with male-female connections need to be made from kiln-cast glass. In terms of the Waterjet cutting constraints, there is a max cutting angle of 60 degrees from vertical. With respect to this, all the glass parts are examined during the design process to ensure they all satisfy the cutting angle requirements. Aiming to achieve a fast and precise assembly, several assistant techniques are developed. On the local HGU level, assembly connectors are designed and 3D-printed to help locate the glass parts. On the global prototype level, the assembly sequence of the HGUs are simulated to avoid interference. Besides, a labeling system is also established to organize the fabricated parts and guide the entire assembly process. The design and construction of this small-scale prototype provide important information for the future development of the full-scale bridge regarding the interlocking detail design, the fabrication constraints, and assembly logic. The actual structural performance of the prototype awaits further investigation through-loading experiments.« less
    Free, publicly-accessible full text available October 1, 2022
  5. This research presents an experimental program executed to understand the strength and stiffness properties of hollow built-up glass compression members that are intended for use in the modular construction of all glass, compression-dominant, shell-type structures. The proposed compression-dominant geometric form has been developed using the methods of form finding and three-dimensional graphical statics. This research takes the first steps towards a new construction methodology for glass structures where individual hollow glass units (HGU) are assembled using an interlocking system to form large, compression-dominant, shell-type structures, thereby exploiting the high compression strength of glass. In this study, an individual HGU hasmore »an elongated hexagonal prism shape and consists of two deck plates, two long side plates, and four short side plates, as is shown in Figure 1. Connections between glass plates are made using a two-sided transparent structural adhesive tape. The test matrix includes four HGUs, two each fabricated with 1 mm and 2 mm thick adhesive tape. All samples are dimensioned 64 cm on the long axis of symmetry, 51 cm on the short axis of symmetry, and are 10 cm in width. Glass plates are all 10 mm thick annealed float glass with geometric fabrication done using 5-axis abrasive water jet cutting. HGU assembly is accomplished using 3D printed truing clips and results in a rigid three-dimensional glass frame. Testing was done with the HGU oriented such that load was introduced on the short side edges of the two deck plates, resulting in an asymmetric load-support condition. A soft interface material was used between the HGU and steel plates of the hydraulic actuator and support for the purpose of avoiding premature cracking from local stress concentrations on the glass edges at the load and support locations. Force was applied in displacement control at 0.25 mm/minute with a full array of displacement and strain sensors. Test results for load vs. center deck plate transverse deflection are shown in Figure 2. All samples failed explosively by flexural buckling with no premature cracking on the load and support edges of the deck plates. Strain and deformation data clearly show the presence of second-order behavior resulting from bending deformation perpendicular to the plane of the deck plates. In general, linear axial behavior transitions to nonlinear second-order behavior, with increasing rates in deflection and strain growth, ultimately ending in glass fracture on the tension surfaces of the buckled deck plates. The failure resulted in near-complete disintegration of the deck plates, but with no observable cracking in any side plates and a secure connection on all adhesive tape. Results of the experimental program clearly demonstrate the feasibility of using HGUs for modular construction of compression dominant all-glass shell-type structures. This method of construction can significantly reduce the self-weight of the structure, and it will inspire the use of sustainable materials in the construction of efficient structures.« less