Dynamics of geometrically nonlinear rods. I: Mechanical models and equations of motion
type: Item
instance of: scholarly article
title: Dynamics of geometrically nonlinear rods. I: Mechanical models and equations of motion
zbMATH Open document ID: 1101.74040
DOI: 10.1023/A:1021268325425
author: Holger Weiss
published in: Nonlinear Dynamics
publication date: 2003-05-06T00:00:00Z
review text: The author deals with large motions of slender thread-like bodies (e.g., cables, ropes, textile threads, belts) building up a mechanical-mathematical model of homogeneous isotropic linearly elastic, geometrically nonlinear one-dimensional continua. Only small strains, but large deflections are possible. The author presents kinematics (coordinate systems, Bernoulli hypothesis, strains, volume and area alteration), kinetics (forces and stresses, balance laws, field equations, material laws, constitutive equations), equations of motion (Timoshenko beam, inextensible and extensible Euler-Bernoulli beams with circular cross-section, vanishing bending and torsional stiffness, and energy balance) and the corresponding boundary conditions. The formulations of the problems in standard and concentrated form can be applied to many technical problems as space and marine engineering.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 1906537
zbMATH Keywords: Euler-Bernoulli beam
zbMATH Keywords: Timoshenko beam
zbMATH Keywords: energy balance
reviewed by: Petre P. Teodorescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1906537