Kirchhoff Rods with Nonhomogeneous Cross Section
نویسنده
چکیده
The Kirchhoff’s theory for thin, inextensible, elastic rods with nonhomogeneous cross section is studied. The Young’s and shear moduli of the rod are considered to vary radially, and it is shown that an analytical solution for the constitutive relations can be obtained for circular cross section and constant Poisson’s ratio. We comment on possible applications of our results.
منابع مشابه
Kovalevskaya rods and Kovalevskaya waves
The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution ...
متن کاملA Symbolic-Numeric Method for Solving Boundary Value Problems of Kirchhoff Rods
We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in paramet...
متن کاملTowards a classification of Euler-Kirchhoff filaments
Euler-Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross-sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a filament can assume. Explicit formulas for the different possible configurations and specific results f...
متن کاملMechanical properties of amorphous nanosprings.
Helical amorphous nanosprings have attracted particular interest due to their special mechanical properties. In this work we present a simple model, within the framework of the Kirchhoff rod model, for investigating the structural properties of nanosprings having asymmetric cross section. We have derived expressions that can be used to obtain the Young's modulus and Poisson's ratio of the nanos...
متن کاملHeat transfer enhancement in a spiral plate heat exchanger model using continuous rods
This study presents an innovative and simple way to increase the rate of heat transfer in a spiral plate heat exchanger model. Several circular cross-section rods, as continuous vortex generators, have been inserted within the spiral plate heat exchanger in the cross-stream plane. The vortex generators are located at various azimuth angles of α=30◦, 60◦, 90◦, and 120◦ with non-dimensional diame...
متن کامل