The application of stochastic design strategies to primitive and complex shapes

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Groth, Jan-Hendrik (2023) The application of stochastic design strategies to primitive and complex shapes. PhD thesis, University of Nottingham.

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Abstract

Corporations and research institutes increasingly adopt Additive Manufacturing (AM) as a complementary manufacturing process, which enables them to manufacture parts or components that either cannot be manufactured from Traditional Manufacturing (TM) processes or the cost is significantly lower. This adoption process involves rethinking design strategies to leverage the full potential of AM, namely the design of highly complex and customised parts. Inevitably, intelligent design strategies will lead to increased part or equipment performance. This raises competitiveness over companies that do not efficiently apply these design strategies. One of these design strategies is cellular material design, which is an essential part of this thesis and will be explained. Cellular material design is considered a design strategy of Biomimicry. Biomimicry assumes that natural designs provide an acceptable solution for applications such as thermal devices, body armour, etc.

Typical elements that can be found in nature are surface or volume elements. Prominent examples of surface elements are shark denticles or surface pedestals on lotus leaves. Well-known volume elements are cellular materials such as sponges or bee’s honeycomb structures. These structures are attractive for fluid dynamic and mechanical applications and have found a broad research community over the years.

An important detail is missing when the natural designs are translated from the natural world to the engineering world. This detail is the variation that can be observed in their natural counterparts. Moreover, this variation is not the same; it is instead a range. This range is mainly designed and explored in Voronoi-based cellular materials and least in other cellular materials and surface elements because only a few design software and design strategies are available.

This thesis addresses this by developing design rules and design strategies for surface elements and cellular materials by using a pseudo-random number generator (RNG) that samples a Gaussian distribution, which allows for designing different levels of stochasticity.

To design a stochastic array, it is necessary to consider the range of stochasticity to produce a feasible design. These design rules include designing structures with stochastic levels that must be larger than the manufacturing tolerance but lower than a specific stochastic level at which the structure’s performance is reduced. Moreover, rules are explained that help to determine the maximum level of stochasticity by preventing invalid volumes or overlaps.

Five design strategies are implemented for strut-based an sheet-based cellular materials, and four for surface elements. The first design strategy is Isotropic Randomness, where the stochastic level is the same for a set of parameters such as the spatial coordinates x, y, and z. The second design strategy is Anisotropic Randomness, which enables selecting different levels of stochasticity for each parameter of a parameter set. The third strategy involves the spatial variation of the level of stochasticity along a defined direction for a parameter or a parameter set, termed Graded Randomness. Fourth, Layered Randomness is demonstrated, which allows the creation of layers in 3D and bands in 2D (surface elements). Fifth, Stochastic Surface Roughness is introduced, which can modulate the surface roughness of cellular materials.

For these design strategies and elements, a Blender Plug-In provides five distinct stochastic design strategies for cellular materials and four for surface elements. The cellular materials include strut-based and sheet-based cellular materials. These are Cubic, Body Centred Cubic (BCC), a standard and modified Face Centred Cubic structure (FCC) and three Triply Periodic Minimal Surfaces (TPMS). The surface elements include shark denticles, spheres, cubes, cylinders, and cone structures.

The developed software tools and the design rules will enable other researchers to explore the influence of different levels of stochasticity on surface elements and cellular materials on the thermohydraulic performance, mechanical properties, or their ability to promote osseointegration in implants.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Clare, Adam
Tuck, Christopher
Magnini, Mirco
Keywords: stochastic design, additive manufacturing, cellular materials
Subjects: T Technology > TS Manufactures
Faculties/Schools: UK Campuses > Faculty of Engineering
UK Campuses > Faculty of Engineering > Department of Mechanical, Materials and Manufacturing Engineering
Item ID: 76584
Depositing User: Groth, Jan-Hendrik
Date Deposited: 14 Dec 2023 04:40
Last Modified: 14 Dec 2023 04:40
URI: https://eprints.nottingham.ac.uk/id/eprint/76584

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