标题： 奇点和奇曲线在冯·卡门弹性曲面中 显示英文标题

标题： Singular Points and Singular Curves in von Kármán Elastic Surfaces

摘要： 薄弹性表面上的力学场在受到约束变形（如纸张的皱折和折叠）、奇异体力和力偶、孤立缺陷（如位错和位错环）的分布以及奇异度量异常场（如生长和热应变）的影响时，可能在孤立点和曲线上出现奇异性。 以这些考虑为动机，我们将薄弹性表面建模为冯·卡门板，并将经典冯·卡门方程推广到分段光滑的场，这些场可能在奇异曲线上集中，除了在孤立点上出现奇异性外。 冯·卡门方程的非均匀源项，以塑性应变、缺陷引起的不相容性和体力表示，同样允许在域中的孤立点和曲线上出现奇异性。 该广义框架用于讨论由于锥形变形、褶皱以及终止于奇异点的褶皱而产生的变形和应力的奇异性。 显示英文摘要

摘要： Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated defects (e.g., dislocations and disclinations), and singular metric anomaly fields (e.g., growth and thermal strains). With such concerns as our motivation, we model thin elastic surfaces as von K{\'a}rm{\'a}n plates and generalize the classical von K{\'a}rm{\'a}n equations, which are restricted to smooth fields, to fields which are piecewise smooth, and can possibly concentrate at singular curves, in addition to being singular at isolated points. The inhomogeneous sources to the von K{\'a}rm{\'a}n equations, given in terms of plastic strains, defect induced incompatibility, and body forces, are likewise allowed to be singular at isolated points and curves in the domain. The generalized framework is used to discuss the singular nature of deformation and stress arising due to conical deformations, folds, and folds terminating at a singular point.