受迫非线性弹性单矢量曲面的全局解分支
Global Solution Branches of Forced Nonlinearly Elastic Single-Director Surfaces
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中文总结 AI 辅助
本文通过拓扑方法证明了非线性弹性单矢量曲面在有限应变和曲率下经典解的存在性，并建立了从无载荷状态出发的全局解分支。
中文摘要 AI 辅助
我们证明了具有有限中面应变和曲率的非线性弹性单矢量曲面或壳体的经典解的存在性。我们采用拓扑方法，得到了远离无载荷、无应力参考构型（即某种全局隐函数定理）的解连续统。我们首先建立局部解路径的存在性，随后证明该路径是全局解分支的一部分，即从无载荷状态出发的最大连通、局部紧致集合。
英文摘要
We prove the existence of classical solutions for nonlinearly elastic, single-director surfaces or shells characterized by finite mid-plane strains and curvature. We employ topological methods, yielding solution continua far (in norm) from an unloaded, stress-free reference configuration, i.e., a global implicit function theorem of sorts. We first establish the existence of a local solution path, which is subsequently shown to be part of a global solution branch, viz., a maximal connected, locally compact set, emanating from the unloaded state.
发表机构
- Department of Mathematics, Cornell University（康奈尔大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
