Related papers: Stress in Rotating Disks and Cylinders
The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics…
The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a…
In standard textbooks of college physics, the Work Energy Theorem is usually presented for inertial frames of references and it is clear that energy is conserved when there is not net work of interaction forces. But what happens when energy…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
The three-dimensional axisymmetric Boussinesq problem of an isotropic half-space subjected to a concentrated normal quasi-static load is studied within the framework of linear dipolar gradient elasticity. Our main concern is to determine…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
For a given external loading on a structure we consider the optimal stresses. Ignoring the material properties the structure may have, we look for the distribution of internal forces or stresses that is in equilibrium with the external…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
We consider the angular momentum exchange at the corotation resonance between a two-dimensional gaseous disk and a uniformly rotating external potential, assuming that the disk flow is adiabatic. We first consider the linear case for an…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
The Dirac equation in curved spacetimes is formulated using coordinate-free notation. A Lagrangean density which corresponds to the subject equation is presented. The subject equation is invariant under a local rotation of the coframe. The…
The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves…
The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light,…
A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy…
The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…
The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is…
A crystal plasticity theory was developed for use in simulations of dynamic loading at high pressures and strain rates. At pressures of the order of the bulk modulus, compressions o(100%) may be induced. At strain rates o(10^9)/s or higher,…
We consider classical closed string with $N$ particles inside. Taking collisions into account, we consider dynamics of this $N$-particle system under the influence of constant external force. We get Euler equations and explicit formula for…
One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and…