相关论文: Moving frames applied to shell elasticity

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures…

Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding…

Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference…

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for…

Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…

Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…

The locomotion of flexible membrane-like organisms on top of curved surfaces appears in different contexts and scales. Still, such dynamics have not yet been quantitatively modeled and no realization of such motion in manmade systems has…

Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…

We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…

A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows of matching…

The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…

Unified geometric approach to describing kinematics of elastic and plastic deformations of continuous media is suggested. On the base of this approach we study mechanical deformations, viscous flow, and heat transport in glassy plastic…

The effect of the frame dragging on the equation of motions, depends on the approaches that have been considered. Accordingly, additional force terms may appear or disappear. To understand the effect of radial and non-radial perturbations…

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well…

In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is…

Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net…

A thin plate or slab, prepared so that opposite faces have different surface stresses, will bend as a result of the stress difference. We have developed a classical molecular dynamics (MD) formulation where (similar in spirit to…

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and…

In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…