Symplectic Hamiltonian finite element methods for linear elastodynamics

2021 ◽  
Vol 381 ◽  
pp. 113843
Author(s):  
Manuel A. Sánchez ◽  
Bernardo Cockburn ◽  
Ngoc-Cuong Nguyen ◽  
Jaime Peraire
1991 ◽  
Vol 113 (1) ◽  
pp. 118-121 ◽  
Author(s):  
M. E. Ingrim ◽  
G. Y. Masada

To illustrate the use of the extended bond graph notation, a reticulation is developed for a conjugate variable approximation of the traction problem in linear elastodynamics. This reticulation is general in the sense that all vector and tensor quantities are expressed using direct notation; that is, no specific coordinate system is chosen a priori. In addition, the only limitation placed upon the elasticity tensor C(X) is that it be symmetric. This allows homogeneous and inhomogeneous isotropic, orthotropic, etc., linearly elastic bodies to be modeled using these results. The conjugate approximations used here are entirely compatible with Galerkin based finite element methods. Consequently, this extended bond graph reticulation allows well-developed approximation techniques in solid mechanics to be directly incorporated into bond graph based system models.


2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.


1983 ◽  
Author(s):  
W. HABASHI ◽  
M. HAFEZ ◽  
P. KOTIUGA

Sign in / Sign up

Export Citation Format

Share Document