Geometric optimization of the crashworthiness performance of 3D-printed PLA-GF tubes with square-to-circular transitions via squircle geometry

This study explores the crashworthiness performance of 3D-printed tubes composed of polylactic acid reinforced with glass fiber (PLA-GF), with particular emphasis on the geometric transition from square to circular cross-sections through the use of arc fillets. Tubes with profiles ranging from sharp-cornered squares to fully circular shapes, including intermediate transitional designs, were subjected to quasi-static axial compression testing to evaluate their structural performance. During testing, the load-displacement responses were systematically recorded, and the corresponding failure modes were carefully examined. The crashworthiness analysis focused on evaluating key indicators, including initial peak force ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , total absorbed energy ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:mrow> </mml:math> ), average force ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>v</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), crash force efficiency (CFE), and specific energy absorption (SEA). Additionally, to identify the most effective geometry, a multi-attribute decision-making framework based on the Complex Proportional Assessment (COPRAS) method was employed. The results revealed that the circular configuration achieved substantial enhancements compared with the square tube, including a 37% increase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>v</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , a 41% increase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:mrow> </mml:math> , a 33% improvement in CFE, and a 70% increase in SEA. Additionally, the SR25 structure exhibited notable improvements over the square tube, particularly in SEA (+40%) and CFE (+24%), highlighting the benefits of intermediate geometric transitions. The COPRAS evaluation further identified the circular tube as the most favorable configuration, attributed to its well-balanced across all evaluated indicators. This work provides clear experimental evidence that controlled geometric transitions between square and circular profiles can significantly affect the crashworthiness of 3D-printed PLA-GF structures.