A Hybrid Experimental–Differential Equation Model for Predicting Mechanical Properties of FDM-Printed PLA Using Lucas Polynomial Collocation

Baykuş Savaşaneril N., Çevik M.

MATHEMATICS AND MECHANICS OF SOLIDS, cilt.1, sa.2, ss.10-35, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 1 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1177/10812865261466674
  • Dergi Adı: MATHEMATICS AND MECHANICS OF SOLIDS
  • Derginin Tarandığı İndeksler: Academic Search Ultimate (EBSCO), Natural Science Collection (ProQuest), Earth, Atmospheric, & Aquatic Science Collection (ProQuest), Engineering Source (EBSCO), Scopus, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest), Aerospace Database, Science Citation Index Expanded (SCI-EXPANDED), Compendex, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.10-35
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

A hybrid experimental–mathematical framework is proposed for predicting and optimizing the mechanical properties of fused deposition modeling (FDM) printed polylactic acid (PLA) components. A Taguchi L9 orthogonal array experiment characterizes tensile and Charpy impact strengths as functions of infill density, layer thickness, and filling structure; analysis of variance identifies infill density as the dominant parameter. A first-order saturating ordinary differential equation (ODE) is formulated to model each mechanical property as a continuous function of infill density, with parameters identified analytically from mean experimental values. The ODE is solved both analytically and numerically via Lucas polynomial collocation, providing independent verification of the numerical scheme. A Pareto-based multi-objective optimization confirms that both strengths are simultaneously maximized at 60% infill density. The model achieves near-perfect predictive accuracy against calibration data for both tensile and impact strengths. The proposed ODE–Lucas framework offers a compact, physically interpretable predictive tool bridging statistical experimental design and continuous mathematical modeling for additive manufacturing.