纸张如何折叠：使用局部约束进行弯曲
How paper folds: bending with local constraints
摘要：
一个变分的框架被引入到描述如何弯曲的表面时，它是受其几何形状的局部约束。这个框架被应用于描述一张折叠的纸的图案。纸的不可拉伸性意味着对表面度量的约束;弯曲受到平均曲率的能量平方的惩罚。执行约束的局部拉格朗日乘子被确定与保守的切向应力耦合到外部曲率的片材。该框架是说明通过检查变形的平板成一个广义的圆锥。
英文摘要：
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
