Modeling of the Mechanical Behavior of Nonplanar Multi-Axis Fdm-Printed Parts with Local Material Anisotropy

N. V. Piatkovsky; M. A. Tashkinov

doi:10.17804/2410-9908.2026.2.073-086

N. V. Piatkovsky, M. A. Tashkinov

MODELING OF THE MECHANICAL BEHAVIOR OF NONPLANAR MULTI-AXIS FDM-PRINTED PARTS WITH LOCAL MATERIAL ANISOTROPY

DOI: 10.17804/2410-9908.2026.2.073-086

The paper presents an approach to finite element modeling of parts manufactured by non-planar multi-axis FDM printing, taking into account the local spatial anisotropy of the material. A software algorithm is developed for the parametric generation of print paths for thin-walled hollow tubes without preliminary slicing. The main contribution of the study lies in the comparative modeling of two layer deposition strategies, namely planar and non-planar, using geometrically oriented local coordinate systems reflecting the expected orientation of orthotropic properties in the walls of a curved tube. The methodology is validated using the example of thin-walled hollow square-section tubes made of ABS plastic. The numerical analysis of the stress-strain state under static three-point bending shows that non-planar deposition, in which non-parallel layers follow the geometry of the part, provides a more uniform stress distribution and reduces local stress concentrations induced by unfavorable layer orientation, but is at the same time more susceptible to delamination.

Acknowledgement: The study was performed at Perm National Research Polytechnic University and supported by the Russian Science Foundation (project No. 22-79-10350-П).

Keywords: additive manufacturing, multi-axis printing, non-planar printing, FDM printing (fused deposition modeling), finite element method (FEM), three-point bending

References:

Gleadall, A. FullControl GCode Designer: open-source software for unconstrained design in additive manufacturing. Additive Manufacturing, 2021, 46, 102109. DOI: 10.1016/j.addma.2021.102109.
Wang, M., Zhang, H., Hu, Q., Liu, D., and Lammer, H. Research and implementation of a non-supporting 3D printing method based on 5-axis dynamic slice algorithm. Robotics and Computer-Integrated Manufacturing, 2019, 57, 496–505. DOI: 10.1016/j.rcim.2019.01.007.
Fortunato, G.M., Nicoletta, M., Batoni, E., Vozzi, G., and De Maria, C. A fully automatic non-planar slicing algorithm for the additive manufacturing of complex geometries. Additive Manufacturing, 2023, 69, 103541. DOI: 10.1016/j.addma.2023.103541.
Lettori, J., Raffaeli, R., Bilancia, P., Peruzzini, M., and Pellicciari, M. A review of geometry representation and processing methods for cartesian and multiaxial robot-based additive manufacturing. The International Journal of Advanced Manufacturing Technology, 2022, 123, 3767–3794. DOI: 10.1007/s00170-022-10432-8.
Gajdoš, I., Sobaszek, Ł., Štefčák, P., Varga, J., and Slota, J. A novel parametrical approach to the ribbed element slicing process in robotic additive manufacturing. Polymers (Basel), 2025, 17 (14), 1965. DOI: 10.3390/polym17141965.
Morita, T., Watanabe, S., and Sasaki, S. Multiaxis printing method for bent tubular structured gels in support bath for achieving high dimension and shape accuracy. Precision Engineering, 2023, 79, 109–118. DOI: 10.1016/j.precisioneng.2022.09.004.
Murtezaoglu, Y., Plakhotnik, D., Stautner, M., Vaneker, T., and Van Houten, F.J.A.M. Geometry-based process planning for multi-axis support-free additive manufacturing. Procedia CIRP, 2018, 78, 73–78. DOI: 10.1016/j.procir.2018.08.175.
E-project-042717-111547, Worcester Polytechnic Institute, 2017, 80 p.
Geuy, M., Martin, J., Simpson, T., and Meisel, N. Path planning for non-planar robotic additive manufacturing. In: Solid Freeform Fabrication 2023: Proceedings of the 34th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference, 2023, 865–880.
Nayyeri, P., Zareinia, K., and Bougherara, H. Planar and nonplanar slicing algorithms for fused deposition modeling technology: a critical review. The International Journal of Advanced Manufacturing Technology, 2022, 119, 2785–2810. DOI: 10.1007/s00170-021-08347-x.
Wüthrich, M., Gubser, M., Elspass, W.J., and Jaeger, C. A novel slicing strategy to print overhangs without support material. Applied Sciences, 2021, 11 (18), 8760. DOI: 10.3390/app11188760.
Li, X., Liu, W., Hu, Z., He, C., Ding, J., Chen, W., Wang, S., and Dong, W. Supportless 3D-printing of non-planar thin-walled structures with the multi-axis screw-extrusion additive manufacturing system. Materials & Design, 2024, 240, 112860. DOI: 10.1016/j.matdes.2024.112860.
Zhang, H., Lei, X., Hu, Q., Wu, S., Aburaia, M., Gonzalez-Gutierrez, J., and Lammer, H. Hybrid printing method of polymer and continuous fiber-reinforced thermoplastic composites (CFRT PCs) for pipes through double-nozzle five-axis printer. Polymers, 2022, 14 (4), 819. DOI: 10.3390/polym14040819.
Chen, L., Chung, M.-F., Tian, Y., Joneja, A., and Tang, K. Variable-depth curved layer fused deposition modeling of thin-shells. Robotics and Computer-Integrated Manufacturing, 2019, 57, 422–434. DOI: 10.1016/j.rcim.2018.12.016.
Yao, Y., Zhang, Y., Aburaia, M., and Lackner, M. 3D printing of objects with continuous spatial paths by a multi-axis robotic FFF platform. Applied Sciences, 2021, 11 (11), 4825. DOI: 10.3390/app11114825.
Guidetti, X., Balta, E.C., Nagel, Y., Yin, H., Rupenyan, A., and Lygeros, J. Stress flow guided non-planar print trajectory optimization for additive manufacturing of anisotropic polymers. Additive Manufacturing, 2023, 72, 103628. DOI: 10.1016/j.addma.2023.103628.
Pyatkovskiy, N.V. RF Software Registration Certificate No. 2025663622, 2025.
Entner, E. Mechanical Properties of Some FDM 3D-printed Infill Structures: Master’s Thesis, UiT The Arctic University of Norway, 2024, 96 p.

Н. В. Пятковский, М. А. Ташкинов

МОДЕЛИРОВАНИЕ МЕХАНИЧЕСКОГО ПОВЕДЕНИЯ ИЗДЕЛИЙ, ИЗГОТОВЛЕННЫХ МЕТОДОМ НЕПЛАНАРНОЙ МНОГООСЕВОЙ FDM-ПЕЧАТИ, С УЧЕТОМ ЛОКАЛЬНОЙ АНИЗОТРОПИИ МАТЕРИАЛА

В статье представлен подход к конечно-элементному моделированию изделий, полученных методом многоосевой непланарной FDM-печати, с учетом локальной пространственной анизотропии материала. Разработан программный алгоритм для параметрической генерации траектории печати полых тонкостенных трубок без предварительного слайсинга. Основной вклад работы состоит в сравнительном моделировании двух схем укладки слоев (планарной и непланарной) с использованием геометрически ориентированных локальных систем координат, отражающих предполагаемую ориентацию ортотропных свойств в стенках изогнутой трубы. Методика протестирована на примере тонкостенных полых труб квадратного сечения, изготовленных с использованием ABS-пластика. Численный анализ напряженно-деформированного состояния при статическом трехточечном изгибе показывает, что непланарная укладка (формирование непараллельных друг другу слоев, повторяющих геометрию изделия) обеспечивает более равномерное распределение напряжений и снижает связанные с неблагоприятной ориентацией слоев локальные концентрации, но при этом более уязвима к расслоению.

Благодарность: Исследование выполнено в Пермском национальном исследовательском политехниче-ском университете при поддержке Российского научного фонда (проект № 22-79-10350-П).

Ключевые слова: аддитивное производство, многоосевая печать, непланарная печать, FDM-печать, метод конечных элементов, трехточечный изгиб

Библиография:

Gleadall A. FullControl GCode Designer: open-source software for unconstrained design in additive manufacturing // Additive Manufacturing. – 2021. – Vol. 46. – P. 102109. – DOI: 10.1016/j.addma.2021.102109.
Research and implementation of a non-supporting 3D printing method based on 5-axis dynamic slice algorithm / M. Wang, H. Zhang, Q. Hu, D. Liu, H. Lammer // Robotics and Computer-Integrated Manufacturing. – 2019. – Vol. 57. – P. 496–505. – DOI: 10.1016/j.rcim.2019.01.007.
A fully automatic non-planar slicing algorithm for the additive manufacturing of complex geometries / G. M. Fortunato, M. Nicoletta, E. Batoni, G. Vozzi, C. De Maria // Additive Manufacturing. – 2023. – Vol. 69. – P. 103541. – DOI: 10.1016/j.addma.2023.103541.
A review of geometry representation and processing methods for cartesian and multiaxial robot-based additive manufacturing / J. Lettori, R. Raffaeli, P. Bilancia, M. Peruzzini, M. Pellicciari // The International Journal of Advanced Manufacturing Technology. – 2022. – Vol. 123 (11–12). – P. 3767–3794. – DOI: 10.1007/s00170-022-10432-8.
A novel parametrical approach to the ribbed element slicing process in robotic additive manufacturing / I. Gajdoš, Ł. Sobaszek, P. Štefčák, J. Varga, J. Slota // Polymers (Basel). – 2025. – Vol. 17 (14). – P. 1965. – DOI: 10.3390/polym17141965.
Morita T., Watanabe S., Sasaki S. Multiaxis printing method for bent tubular structured gels in support bath for achieving high dimension and shape accuracy // Precision Engineering. – 2023. – Vol. 79. – P. 109–118. – DOI: 10.1016/j.precisioneng.2022.09.004.
Geometry-based process planning for multi-axis support-free additive manufacturing / Y. Murtezaoglu, D. Plakhotnik, M. Stautner, T. Vaneker, F. J. A. M. van Houten // Procedia CIRP. – 2018. – Vol. 78. – 73–78. DOI: 10.1016/j.procir.2018.08.175.
E-project-042717-111547. – Worcester Polytechnic Institute, 2017. – 80 p.
Path planning for non-planar robotic additive manufacturing / M. Geuy, J. Martin, T. Simpson, N. Meisel // Solid Freeform Fabrication 2023 : Proceedings of the 34th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference. – 2023. – P. 865–880.
Nayyeri P., Zareinia K., Bougherara H. Planar and nonplanar slicing algorithms for fused deposition modeling technology: a critical review // The International Journal of Advanced Manufacturing Technology. – 2022. – Vol. 119. – P. 2785–2810. – DOI: 10.1007/s00170-021-08347-x.
A novel slicing strategy to print overhangs without support material / M. Wüthrich, M. Gubser, W. J. Elspass, C. Jaeger // Applied Sciences. – 2021. – Vol. 11 (18). – P. 8760. – DOI: 10.3390/app11188760.
Supportless 3D-printing of non-planar thin-walled structures with the multi-axis screw-extrusion additive manufacturing system / X. Li, W. Liu, Z. Hu, C. He, J. Ding, W. Chen, S. Wang, W. Dong // Materials & Design. – 2024. – Vol. 240. – P. 112860. – DOI: 10.1016/j.matdes.2024.112860.
Hybrid printing method of polymer and continuous fiber-reinforced thermoplastic composites (CFRTPCs) for pipes through double-nozzle five-axis printer / H. Zhang, X. Lei, Q. Hu, S. Wu, M. Aburaia, J. Gonzalez-Gutierrez, H. Lammer // Polymers. – 2022. – Vol. 14 (4). – P. 819. – DOI: 10.3390/polym14040819.
Variable-depth curved layer fused deposition modeling of thin-shells / L. Chen, M.-F. Chung, Y. Tian, A. Joneja, K. Tang // Robotics and Computer-Integrated Manufacturing. – 2019. – Vol. 57. – P. 422–434. – DOI: 10.1016/j.rcim.2018.12.016.
3D printing of objects with continuous spatial paths by a multi-axis robotic FFF platform / Y. Yao, Y. Zhang, M. Aburaia, M. Lackner // Applied Sciences. – 2021. – Vol. 11 (11). – P. 4825. – DOI: 10.3390/app11114825.
Stress flow guided non-planar print trajectory optimization for additive manufacturing of anisotropic polymers / X. Guidetti, E. C. Balta, Y. Nagel, H. Yin, A. Rupenyan, J. Lygeros // Additive Manufacturing. – 2023. – Vol. 72. – P. 103628. – DOI: 10.1016/j.addma.2023.103628.
Свидетельство о регистрации программы для ЭВМ № 2025664392 Рос. Федерация. Программный продукт для генерации 4-х осевого G-кода для печати полых труб круглого сечения : № 2025663622 : регистрация 04.06.2025 : опубл. 04.06.2025 / Пятковский Н. В.
Entner E. Mechanical Properties of Some FDM 3D-printed Infill Structures : Master’s Thesis. – UiT The Arctic University of Norway, 2024. – 96 p.

Библиографическая ссылка на статью

Piatkovsky N. V., Tashkinov M. A. Modeling of the Mechanical Behavior of Nonplanar Multi-Axis Fdm-Printed Parts with Local Material Anisotropy // Diagnostics, Resource and Mechanics of materials and structures. - 2026. - Iss. 2. - P. 73-86. -
DOI: 10.17804/2410-9908.2026.2.073-086. -
URL: http://dream-journal.org/issues/2026-2/2026-2_565.html
(accessed: 26.09.2026).