发表机构
Swansea University; Edinburgh Napier University（斯旺西大学; 爱丁堡纳皮尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种几何精确平面梁有限元框架，通过引入面内厚度变形场并独立处理平面应力/应变条件，实现超弹性材料模型的有效集成，数值验证表明平面应力条件更优且与Neo-Hookean模型高度一致。
AI 中文摘要
本文开发了一个几何精确的平面梁有限元框架，用于分析具有超弹性本构模型的梁。首先，建立了一个具有完全几何非线性和线弹性材料定律的传统三场梁模型。然后，通过一个额外的全局场对运动学进行丰富，该场允许通过面内厚度发生变形。面外方向通过平面应变和平面应力本构约简分别纳入，使得截面变形假设和本构行为可以独立地制定。针对当前基准的数值结果表明，在所考虑的泊松比值下，平面应力条件给出了基本重合的中心线变形。相比之下，文献中广泛采用的平面应变条件使公式对泊松比耦合敏感，在较高的泊松比下梁变得明显更刚硬。圣维南-基尔霍夫和 Neo-Hookean 超弹性模型之间的比较进一步表明，在全局变形和面内厚度响应方面具有密切的一致性，而小的本构差异在局部面外拉伸中变得更加明显。所提出的方法为将超弹性材料模型集成到平面几何精确梁模型中提供了一个简单且一致的框架。
英文摘要
A geometrically-exact planar beam finite-element framework is developed for the analysis of beams with hyperelastic constitutive models. A conventional three-field beam model is first formulated with full geometrical nonlinearity and a linear elastic material law. The kinematics are then enriched by an additional global field that permits deformation through the in-plane thickness. The out-of-plane direction is incorporated separately through plane-strain and plane-stress constitutive reductions, allowing the cross-sectional deformation assumptions and constitutive behaviour to be formulated independently. Numerical results for the present benchmarks show that the plane-stress condition gives essentially coincident centreline deformations for the Poisson's ratio values considered. In contrast, the plane-strain condition, which is widely employed in the literature, makes the formulation sensitive to Poisson's ratio coupling, with the beam becoming significantly stiffer at higher Poisson's ratios. Comparisons between Saint Venant-Kirchhoff and Neo-Hookean hyperelastic models further demonstrate close agreement in the global deformation and in-plane thickness response, with small constitutive differences becoming more apparent in the local out-of-plane stretch. The proposed approach offers a simple and consistent framework to integrate hyperelastic material models into planar geometrically-exact beam models.
