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Numerical Investigation of Flexural Properties of Curved Layer FDM Parts

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Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 817))

Abstract

The printing approach of curved layer fused deposition modelling (CLFDM) is gaining popularity for its superior part properties when compared to those obtained from conventional FDM approach. Past studies reveal that the study of effects of fill gap (FG) on these two approaches (CLFDM and conventional FDM) with different printing directions needs a thorough numerical investigation. Therefore, the present work introduces numerical modelling based on genetic programming for investigating the flexural strength of the fabricated parts from FDM and CLFDM. It was found that the GP-based flexural strength models are able to generalize both processes satisfactorily. It was also noticed that the GP-based flexural strength models for horizontal printed parts predict with higher accuracy than those for parts printed in vertical directions. Experiments were performed to validate the GP models.

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Acknowledgements

We would like to thank the Hong Kong Polytechnic University under the project code: G-YM77 titled “An Innovative Approach to Additive Manufacturing” for their support. This study is supported by Shantou University Scientific Research Foundation (NTF 16002, NTF 16011). Authors would also like to acknowledge Guangdong Sailing Plan Talent fund of the year 2016. Authors also like to acknowledge Guangdong University Youth Innovation Talent Project (2016KQNCX053) Supported by Department of Education of Guangdong Province.

Author information

Authors and Affiliations

  1. Intelligent Manufacturing Key Laboratory of Ministry of Education, Shantou University, Shantou, China

    Xiongbin Peng & Akhil Garg

  2. Department of Industrial Design, National Institute of Technology, Rourkela, Rourkela, India

    Biranchi Panda

  3. Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong

    H. Guan & M. M. Savalani

Authors
  1. Xiongbin Peng
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  2. Biranchi Panda
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  3. Akhil Garg
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  4. H. Guan
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  5. M. M. Savalani
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Corresponding author

Correspondence to Akhil Garg .

Editor information

Editors and Affiliations

  1. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  2. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, India

    Kedar Nath Das

  3. Department of Mathematics and Computer Science, Faculty of Science, Liverpool Hope University, Liverpool, UK

    Atulya Nagar

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  5. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India

    Akshay Kumar Ojha

Appendix

Appendix

$$ \begin{aligned} & {\text{Flexural}}\,{\text{strength}}\,{\text{Horizontal}}\_{\text{CLFDM}}\_{\text{GP}} \\ & \quad = - 1611.6967 + ( - 14.945)*({ \cos }({ \cos }(\left( {{ \tan }\left( {\left( {{\text{x}}1} \right) + \left( {\left( {16.361923} \right)} \right)} \right)} \right) \\ & \quad + (( - 18.517307))))) + \left( {193.3434} \right)*\left( {{ \tan }\left( {\left( {{ \tanh }\left( {\left( {{\text{x}}1} \right) + \left( {\left( { - 18.517307} \right)} \right)} \right)} \right)*\left( {{\text{plog}}\left( {{\text{x}}1} \right)} \right)} \right)} \right) \\ & \quad + ( - 5.6196)*\left( {{ \sin }\left( {{ \exp }\left( {{ \exp }\left( {{\text{x}}1} \right)} \right)} \right)} \right) + \left( {64.4466} \right)*\left( {{\text{plog}}\left( {{ \tan }\left( {\left( {{ \sin }\left( {{ \sin }\left( {{ \tanh }\left( {{\text{x}}1} \right)} \right)} \right)} \right)*\left( {{\text{plog}}\left( {{ \tanh }\left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {1.4019} \right)*(\left( {\left( {{\text{plog}}\left( {{ \tan }\left( {{\text{x}}1} \right)} \right)} \right) - \left( {{ \tan }\left( {\left( {\left( {15.521232} \right)} \right) - \left( {x1} \right)} \right)} \right)} \right)*({\text{plog}}({ \tan }((( - 18.517307)) \\ & \quad *\left( {{\text{x}}1} \right))))) + ( - 57.8947)*\left( {{\text{plog}}\left( {{ \tan }\left( {\left( {{ \exp }\left( {{ \cos }\left( {{ \cos }\left( {{\text{x}}1} \right)} \right)} \right)} \right)*\left( {{\text{plog}}\left( {{ \tanh }\left( {\left( {{\text{x}}1} \right) + \left( {\left( {16.361923} \right)} \right)} \right)} \right)} \right)} \right)} \right)} \right); \\ \end{aligned} $$
(A1)
$$ \begin{aligned} & {\text{Flexural}}\,{\text{strength}}\,{\text{Horizontal}}\_{\text{FDM}}\_{\text{GP}} \\ & \quad = 23.6759 + \left( {3.9216} \right).*\left( {{ \sin }\left( {{ \cos }\left( {{ \tan }\left( {\left( {{\text{plog}}\left( {{ \tan }\left( {{\text{x}}1} \right)} \right)} \right) + \left( {{ \exp }\left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + ( - 55.6616).*\left( {{\text{plog}}\left( {\left( {{ \tan }\left( {{\text{x}}1} \right)} \right).*\left( {\left( {{ \cos }\left( {{ \tan }\left( {{ \cos }\left( {{\text{x}}1} \right)} \right)} \right)} \right) + \left( {{\text{x}}1} \right)} \right)} \right)} \right) + \left( {63.1144} \right). \\ & \quad *({\text{plog}}((( - 0.816101)).*\left( {\left( {{ \cos }\left( {{ \tan }\left( {{ \cos }\left( {{\text{x}}1} \right)} \right)} \right)} \right) + \left( {\left( { - 17.537172} \right)} \right)} \right))) \\ & \quad + \left( { - 0.15459} \right).*({ \tan }({ \tanh }({ \cos }({ \exp }((\left( {{\text{x}}1} \right) - \left( {\left( { - 17.537172} \right)} \right)) + \left( {{ \cos }\left( {{\text{x}}1} \right)} \right)))))) \\ & \quad + \left( {18.2054} \right).*(\left( {{ \sin }\left( {{ \exp }\left( {{ \tan }\left( {{ \exp }\left( {\left( { - 8.889970} \right)} \right)} \right)} \right)} \right)} \right) - \left( {{\text{x}}1} \right)) \\ & \quad + \left( {2.4745} \right).*({ \sin }({ \tanh }({ \tan }((\left( {\left( {{\text{x}}1} \right) - \left( {\left( { - 13.964471} \right)} \right)} \right) \\ & \quad - \left( {{ \cos }\left( {\left( {15.506033} \right)} \right)} \right)).*\left( {{ \sin }\left( {{ \sin }\left( {{\text{x}}1} \right)} \right)} \right))))); \\ \end{aligned} $$
(A2)
$$ \begin{aligned} & {\text{FlexuralstrengthVertical}}\_{\text{CLFDM}}\_{\text{GP}} \\ & \quad = - 223.2723 + \left( {362.7024} \right)*\left( {\exp \left( {\sin \left( {\exp \left( {\exp \left( {\tan \left( {\left( {\left( {0.157757} \right)} \right)*\left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {0.018109} \right)*((((\tan (\tan \left( {\left( {{\text{x}}1} \right)*\left( {{\text{x}}1} \right)} \right)))*\left( {\exp \left( {\sin \left( {{\text{x}}1} \right)} \right)} \right))*\left( {\exp \left( {\exp \left( {\sin \left( {\left( {{\text{x}}1} \right)*\left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)) \\ & \quad *\left( {\tan \left( {\exp \left( {{\text{plog}}\left( {\tan \left( {\exp \left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)} \right)) + \left( {0.14521} \right)*(\tan (\tan (\left( {\left( {\tanh \left( {{\text{x}}1} \right)} \right) + \left( {\exp \left( {{\text{x}}1} \right)} \right)} \right) \\ & \quad - \left( {\exp \left( {\sin \left( {\left( {{\text{x}}1} \right)*\left( {{\text{x}}1} \right)} \right)} \right)} \right)))) + \left( {31.4346} \right)*(\cos (\left( {\exp \left( {\tan \left( {\tan \left( {\left( {{\text{x}}1} \right)*\left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right)*(\exp (\cos (\left( {\cos \left( {{\text{x}}1} \right)} \right) \\ & \quad - \left( {{\text{plog}}\left( {{\text{x}}1} \right)} \right)))))) + \left( {24.5903} \right)*\left( {\cos \left( {\left( {\tan \left( {\tan \left( {\left( {{\text{x}}1} \right)*\left( {{\text{x}}1} \right)} \right)} \right)} \right)*\left( {\exp \left( {\sin \left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {0.85622} \right)*(\tan ((({\text{x}}1) + \left( {\tan \left( {{\text{x}}1} \right)} \right)) + \left( {\tan \left( {\exp \left( {\tan \left( {\left( {\left( { - 10.254681} \right)} \right) - \left( {{\text{x}}1} \right)} \right)} \right)} \right)} \right))); \\ \end{aligned} $$
(A3)
$$ \begin{aligned} & {\text{FlexuralstrengthVertical}}\_{\text{FDM}}\_{\text{GP}} \\ & \quad = 31.4187 + \left( {2.6007} \right).*\left( {{ \tan }\left( {\left( {{ \exp }\left( {\left( {{ \tan }\left( {{ \tanh }\left( {\text{x1}} \right)} \right)} \right) + \left( {{ \tanh }\left( {{\text{x}}1} \right)} \right)} \right)} \right) - \left( {{\text{plog}}\left( {{ \tanh }\left( {{ \tanh }\left( {{ \cos }\left( {\text{x1}} \right)} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + ( - 23.0296).*\left( {{ \sin }\left( {{\text{plog}}\left( {{ \tan }\left( {\text{x1}} \right)} \right)} \right)} \right) + \left( { - 28.9959} \right).*\left( {{ \tanh }\left( {\left( {{ \cos }\left( {\text{x1}} \right)} \right) - \left( {{ \exp }\left( {{ \tanh }\left( {{ \exp }\left( {\text{x1}} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + ( - 9.2956).*((\left( {{ \tanh }\left( {{ \tan }\left( {{ \sin }\left( {{ \tanh }\left( {\text{x1}} \right)} \right)} \right)} \right)} \right) - \left( {{ \tan }\left( {\left( {{ \tanh }\left( {\left( {\text{x1}} \right){ + }\left( {\text{x1}} \right)} \right)} \right).*\left( {{ \cos }\left( {{ \tan }\left( {\text{x1}} \right)} \right)} \right)} \right)} \right)). \\ & \quad *(\left( {{ \sin }\left( {{ \tan }\left( {{\text{plog}}\left( {{ \cos }\left( {\text{x1}} \right)} \right)} \right)} \right)} \right).*(((\left( {{ \exp }\left( {\text{x1}} \right)} \right) - \left( {{ \tan }\left( {\text{x1}} \right)} \right)).*\left( {{ \tan }\left( {\left( {{\text{x}}1} \right) + \left( {\left( {10.438387} \right)} \right)} \right)} \right)) \\ & \quad - ({ \sin }({\text{plog}}((( - 5.811520)).*\left( {{\text{x}}1} \right))))))) + \left( {7.487} \right).*\left( {{ \sin }\left( {\left( {{ \sin }\left( {\left( {\left( { 1 5. 7 1 2 1 2 3} \right)} \right) .*\left( {\text{x1}} \right)} \right)} \right).*\left( {{\text{x}}1} \right)} \right)} \right) \\ & \quad + \left( {15.894} \right).*({ \sin }(((({ \cos }\left( {\left( {{\text{x}}1} \right) + \left( {{\text{x}}1} \right)} \right)) - (\left( {{ \exp }\left( {\left( {11.195960} \right)} \right)} \right) \\ & \quad - \left( {\left( {\left( {19.548163} \right)} \right) + \left( {{\text{x}}1} \right)} \right))).*\left( {{ \sin }\left( {{ \tan }\left( {\text{x1}} \right)} \right)} \right)) + \left( {\left( {{ \sin }\left( {{ \sin }\left( {{ \exp }\left( {\text{x1}} \right)} \right)} \right)} \right).*\left( {{\text{plog}}\left( {{ \tan }\left( {\text{x1}} \right)} \right)} \right)} \right))); \\ \end{aligned} $$
(A4)

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Peng, X., Panda, B., Garg, A., Guan, H., Savalani, M.M. (2019). Numerical Investigation of Flexural Properties of Curved Layer FDM Parts. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 817. Springer, Singapore. https://doi.org/10.1007/978-981-13-1595-4_20

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