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Three-dimensional continuum point cloud method for large deformation and its verification
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-08-30 , DOI: 10.1016/j.cma.2024.117307 Peter M. Schaefferkoetter , Young-Cheol Yoon , Jeong-Hoon Song
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-08-30 , DOI: 10.1016/j.cma.2024.117307 Peter M. Schaefferkoetter , Young-Cheol Yoon , Jeong-Hoon Song
This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Finally, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.
中文翻译:
大变形的三维连续点云方法及其验证
本研究提出了一种基于强形式的无网格搭配方法,称为连续体点云方法,用于求解从经典力学中推导出的三维欧几里得空间中变形体的非线性场方程。该方法及其实现使用制造的解针对非线性矢量场进行了基准测试。力学场的分析首先集中在 St. Venant Kirchhoff 和可压缩新 Hookean 材料的研究上。介绍了各种初始边界值问题的结果,包括涉及单向拉伸和简单剪切的基准情况。随后,该研究对可压缩新胡克材料的位移控制模拟进行了分析,特别是被拉到其原始长度的 50% 并旋转 90° 的杆。纯拉伸工况在计算值和预期值之间的位移误差为 1.5%,而拉伸和扭转组合载荷工况可以进一步了解复杂载荷条件下的材料行为。还给出了由此产生的法向轴向和横向应力-应变曲线。最后,通过各种数值实验成功地证明了所提出的非线性数值方案的一致性和鲁棒性。
更新日期:2024-08-30
中文翻译:
大变形的三维连续点云方法及其验证
本研究提出了一种基于强形式的无网格搭配方法,称为连续体点云方法,用于求解从经典力学中推导出的三维欧几里得空间中变形体的非线性场方程。该方法及其实现使用制造的解针对非线性矢量场进行了基准测试。力学场的分析首先集中在 St. Venant Kirchhoff 和可压缩新 Hookean 材料的研究上。介绍了各种初始边界值问题的结果,包括涉及单向拉伸和简单剪切的基准情况。随后,该研究对可压缩新胡克材料的位移控制模拟进行了分析,特别是被拉到其原始长度的 50% 并旋转 90° 的杆。纯拉伸工况在计算值和预期值之间的位移误差为 1.5%,而拉伸和扭转组合载荷工况可以进一步了解复杂载荷条件下的材料行为。还给出了由此产生的法向轴向和横向应力-应变曲线。最后,通过各种数值实验成功地证明了所提出的非线性数值方案的一致性和鲁棒性。