摘要
微极弹性有限元法在分析具有复杂微结构的材料上有着广泛应用。针对现有实现通常采用完全积分方案而导致的计算效率低以及弯曲工况下出现剪切锁定的问题,提出一种通用高效的缩减积分一阶六面体微极有限单元,并通过海洋结构物通用分析软件SAM进行算例验证。单元算法结合标准拉格朗日插值和均匀应变与曲率公式,能够通过单元分片检验并保证畸形单元计算的准确性。同时,引入一种人工刚度方法,有效抑制缩减积分微极单元的位移和旋转沙漏失稳模式。通过数值验证,包括力和位移分片检验确认单元的收敛性,悬臂梁纯弯曲测试评估单元在剪切锁定问题上的改善效果,以及对船舶常用夹芯结构进行振动响应模态分析,验证了该单元在船舶结构有限元分析中相较于传统实体单元的有效性和优势。
The micropolar elastic finite element method has found extensive applications in analyzing materials with complex microstructures.To address the problems of low computational efficiency and shear locking under bending conditions caused by the fully integrated scheme commonly adopted in existing implementations,a universal and efficient reduced-integration first-order hexahedral micropolar finite element was proposed and verified using SAM,a general analysis software for marine structures.The element algorithm,combined with the standard Lagrange interpolation and uniform-strain and curvature formulas,passed the element patch test and ensured the calculation accuracy for distorted elements.Additionally,an artificial stiffness method was introduced to effectively suppress displacement and rotational hourglass instability modes in the reduced-integration micropolar elements.Numerical validation,including force and displacement patch tests for convergence,cantilever-beam tests for shear locking,and modal analysis of vibration responses of sandwich structures used in shipbuilding,demonstrated the proposed element’s effectiveness and advantages over traditional solid elements in finite-element analysis of ship structures.
作者
周天齐
丁军
姚宇
ZHOU Tianqi;DING Jun;YAO Yu(China Ship Scientific Research Center,Wuxi Jiangsu 214000,China;Taihu Laboratory of Deepsea Technological Science,Wuxi Jiangsu 214000,China)
出处
《图学学报》
北大核心
2025年第6期1153-1160,共8页
Journal of Graphics
基金
国家重点研发计划项目(2022YFB3306200)。
关键词
微极弹性理论
有限单元开发
减缩积分法
沙漏稳定技术
数值验证
micropolar elasticity theory
development of finite element
reduced integration
hourglass instabilities
numerical validations
