Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence

The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity

The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending-torsion theory for rods are deduced.

Weaving paper strips for designing of general curved surface with geometrical elasticity

This study proposes 'amigami' as a new method of creating a general curved surface. It conducts the shape optimization of weaving paper strips based on the theory of nonlinear elasticity on Riemannian manifolds. The target surface is split into small curved strips by cutting the medium along with its coordinates, and each strip is embedded into a flat paper sheet to minimize a strain energy functional due to the in-plane deformation. The weak form equilibrium equation is derived from a Lie derivative with the virtual displacement vector field, and the equation is solved numerically using the G…

Moving frames applied to shell elasticity

Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.

Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of equations of motion, viewing motion as a curve in an infinite-dimensional Banach space of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies; residual stress results from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two- dimensional curved annulus embedded in a sphere.

一维变分问题的充要条件及其在弹性力学中的应用

Necessary and sufficient conditions for one-dimensional variational problems with applications to elasticity

本文推导一维变分泛函弱、强极小元更简洁的充要条件，并应用于弹性稳定性，给出各类端点约束下自然笔直 Kirchhoff 杆稳定的最优条件，解决了既有文献中的公开问题。

Pseudomomentum: origins and consequences

The balance of pseudomomentum is discussed and applied to simple elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to position, time, and material labels yields bulk balance laws and jump conditions for momentum, energy, and pseudomomentum. The example of simple elasticity of space-filling solids is treated at length. The pseudomomentum balance in ideal fluids is shown to imply conservation of vorticity, circulation, and helicity, and a mathematical similarity is noted betw…