Compression performance of hollow structures: From topology optimisation to design 3D printing

https://doi.org/10.1016/j.ijmecsci.2017.09.033Get rights and content

Highlights

  • Inequivalent designs from CAD-based topology optimisation for additive manufacturing.

  • Filament-based simulation explains differences between FDM-based hallow designs.

  • Anisotropic space filling offers potential to tune hallow designs performance.

Abstract

In this work, we experimentally evaluate the rendering of topology optimisation through the design of hollow structures manufactured using a 3D printing technique. The moving asymptote method is used as a mathematical optimisation strategy to virtually minimise the volume of 2D designs subject to hydrostatic pressure by half. Designs are converted to 3D models by extrusion in the building direction and printed using the Fused Deposition Modelling technique. Compression testing up to densification is performed and designs are evaluated. The results show that extrusion of the design in the building direction provides the best option to avoid mechanical anisotropy induced by processing. Depending on the type and extent of excluded regions, mechanical performance proves to be adapted to a wide range of designs and different types of mechanical anisotropies can be derived. Comparison with finite element results shows differences in behaviour related to mechanical instabilities that occur as a result of the lack of inter-filament cohesion and external frame unsoldering.

Introduction

Recent manufacturing routes use increasingly digitalised features to improve the added value of products and to save costs. This trend contributes other benefits for the organisation and replication of product development outcomes such as decreasing the time to market, as well as customising and designing more innovative products with smart features. New concepts have emerged from this trend, all revolving around to the notion of industrial Internet or digitally enabled technologies. Robotics and 3D printing are typical examples of these technologies with their potential to create added value through product design [1]. Additive manufacturing, for instance, allows a large degree of freedom for design creativity, with limited dependence on manufacturing tooling [2], [3]. This distinct feature can be bridged with reverse engineering solutions to adapt the design to the desired product functionalities and constraints. The analysis of the previous literature in additive manufacturing shows that direct schemes are instead used to optimise part performance. Design of experiments generally targets the optimisation of process conditions and the decrease of the dependency on the anisotropy of printed parts [4], [5], [6], [7], [8], [9], [10]. Sood et al. [5] show that surface response representation provides a robust way to rank the process parameters and improve the mechanical response of printed parts. Mohamed et al. [11] extend the same approach to more criteria such as the building time, material cost and performance. Due to the possible cross effects and process parameter inter-dependence, some contributors use artificial intelligence tools such as genetic algorithms, fuzzy logics and neural networks to obtain a better understanding of the results of design of experiments [12], [13], [14], [15], [16]. This type of approach is more suitable to handling multiple design criteria [8], [14], [17]. Typical examples that can be found in the literature concern deposition orientation vs. cost and accuracy [8], [17], [18], slicing and hatching of CAD models vs. building time and geometry tolerance [19], [20], [21], [22], and support structure generation vs. part orientation and material consumption [23], [24].

The above-cited contributions consider design as a known feature and most of the work is dedicated to finding the optimal way to manufacture it. Some other routes exist when only the building constraints but the designs are not known. The method of choice used in this type of situation is topology optimisation. It has been recently considered for the case of additive manufacturing [3], [25]–27]. Leary et al. [25] considered this approach to design FDM-based structures with limited dependence on support material. Gardan and Schneider [26] explored the use of topology optimisation for different design scenarios of structural parts. Langelaar [27] adapted topology optimisation to AM constraints like AM overhang limitations for the design of self-supporting structures. Robbins et al. [28] demonstrated the relevance of topology optimisation to design cellular structures with the help of homogenisation principles.

These contributions appear to be successful proofs of concept but generally lack experimental validation. Although printability of the optimal designs is fully justified, the constitutive mechanical models on which the minimisation procedure is built are not submitted to experimental testing. This can be a drawback, especially knowing that AM technologies such as FDM generate significant mechanical anisotropy. To better illustrate this statement, Fig. 1a shows the classical approach adopted for design optimisation. According to the classical implementation of topology optimisation, CAD reconstruction is used as an input model for finite element computation. The performance of the final design should reflect only the result of the CAD-based simulation. This is a clear limitation knowing that another important step in additive manufacturing, namely the slicing, is neglected in this classical scheme.

It is thus the purpose of this study to show the potential of using topology optimisation to design hollow structures based on experimental analysis of the rendering of predicted optimal designs. The intention of this paper is not to illustrate a new optimisation method. It is, however, about the safe use of topology optimisation within the context of additive manufacturing. The authors observed the gap in the literature between people working on optimisation and the specialists of additive manufacturing. On the one hand, optimal designs rely on CAD-based computations and, on the other, 3D printed parts are not always in conformity with CAD models. This gap can be closed if some guidelines are established for the appropriate use of topology optimisation. It is thus the idea of this paper to provide these guidelines by considering the relevant scale for mechanical property predictions. In the case of fused deposition modelling, the relevant scale should be coherent with the filament packing, which determines most of the spatial heterogeneities. This viewpoint is illustrated in Fig. 1b, which shows the alternative proposed in this study to provide reliable optimisation results. Indeed, the source of mismatch that can possibly lead to misleading results is the use of CAD models as input geometries for the evaluation of the objective function. In this study, we propose the input geometry as the one issued from the slicing step. This provides a safe framework for the selected topology optimisation paradigm to adapt to additive manufacturing specifications. In the following, the differences between both implementation approaches of topology optimisation (Fig. 1a and b) are discussed and the superior results of the new approach are further demonstrated.

Section snippets

An overview of topology optimisation

Topology optimization consists in finding the best material distribution within a design domain with respect to a desired mechanical performance (Fig. 2). This mathematical approach deals with load configurations through a constitutive modelling process that primarily involves mostly finite element computation. Design constraints can be numerous but must be quantified and predefined from the outset.

Topology optimisation can be expressed as a minimisation problem: minimizef(y)subjecttog(y)0

Topology optimisation outcome

Fig. 2 shows a typical topology optimisation process leading to various forms of hollow structures. The starting point represents a domain with excluded regions in blue. The red represents the regions with the highest density value. The positioning and extent of the excluded regions is decided either manually or using mathematical operators (the case of the bottom design in Fig. 2). The design evolves by restoring the highest density on the edges because of the hydrostatic load configurations.

Conclusions

This study shows the applicability of topology optimisation in one particular additive manufacturing route, Fused Deposition Modelling. The printability of the considered hollow structures is demonstrated through the successful implementation of the digitalised models as input geometries in the topology optimisation routine and the slicing of optimal designs. We demonstrate, however, the limit of using CAD models as input geometries to optimise the hollow designs. Differences in mechanical

Conflict of interest

The authors declare no conflict of interest.

Author contributions

Dr. Sofiane Guessasma contributed to the overall management of the FDM processing, topology optimisation, experimental protocols and campaign designs. He participated in the mechanical testing experiments and performed the analysis and interpretation of optical imaging, finite element computations, experimental results and the drafting of the article. Dr. Sofiane Belhabib implemented the topology optimisation procedure, performed the design of the hollow structures and mechanical testing, and

References (37)

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