단면 변형의 영향을 포함하는 샤시 프레임 경량화 위상 최적 설계 방법론 = Topology Optimization for Lightweight Chassis Frame Design Including Joint Flexibility

다국어 초록 (Multilingual Abstract)

This study proposes a novel topology optimization methodology based on higher-order beam theory. The proposed method accurately accounts for the joint flexibility of thin-walled box beam structures and addresses previous limitations related to member connectivity. Classical beam theories fail to predict complex cross-sectional deformations and joint flexibility. Although existing higher-order beam studies have addressed these issues, defining joint matching conditions within the topology optimization remains a challenging task. Consequently, previous studies have been limited to simple structures. To address these issues, the proposed methodology defines joint matching conditions that include warping and distortion degrees of freedom at a single joint-centered node, which allows for modeling independent of the number of joint members and angles. Furthermore, the proposed methodology establishes a transformation from local to global matching conditions, ensuring physical consistency even as design variables approach zero. By introducing an interpolation function based on member density, the proposed method ensures that changes in joint stiffness are monotonic, simulating diaphragm formation at joint interfaces as the member density approaches zero. Numerical examples, including vehicle chassis frames, demonstrate the effectiveness of the proposed methodology. The results demonstrate approximately 4.6 times higher stiffness compared to earlier work at the same volume. Furthermore, unlike Timoshenko beam-based methods, the proposed approach strictly satisfies compliance constraints and reduces weight by approximately 23%. In conclusion, we found the first topology optimization methodology for thin-walled structures that integrates joint flexibility with unrestricted connectivity. The methodology offers significant potential for the initial design of 3D automotive body frames.

목차 (Table of Contents)

• 1. Introduction 1
• 2. One-Dimensional Higher-Order Beam Theory 3
• 2.1 Fundamental Theory 3
• 2.2 Finite Element Formulation 6
• 2.3 Static Condensation 8
• 3. Joint Matching Conditions 10
• 4. Globalization of Local Matching Conditions 15
• 5. Interpolation of Distortional Stiffness at a Joint 21
• 6. Topology Optimization Formulation 25
• 7. Numerical Examples 29
• 7.1 Comparison with Earlier works 29
• 7.2 Comparison with Timoshenko beam-based approach 33
• 7.3 Chassis Frame Topology Optimization 36
• 8. Conclusion 41
• References 43
• Abstract (English) 45
• Appendices 47