Milestones of Direct Variational Calculus and its Analysis from the 17th Century until today and beyond- Mathematics meets Mechanics- with restriction to linear elasticity
Journal Title: Computer Assisted Methods in Engineering and Science - Year 2012, Vol 19, Issue 1
Abstract
This treatise collects and reflects the major developments of direct (discrete) variational calculus since the end of the 17th century until about 1990, with restriction to classical linear elastome- chanics, such as 1D-beam theory, 2D-plane stress analysis and 3D-problems, governed by the 2nd order elliptic Lam´e-Navier partial differential equations.The extension of the historical review to non-linear elasticity, or even more, to inelastic defor-mations would need an equal number of pages and, therefore, should be published separately.A comprehensive treatment of modern computational methods in mechanics can be found in the Encyclopedia of Computational Mechanics [83].
Authors and Affiliations
Erwin Stein
Keywords
Related Articles
- EP ID EP73920
- DOI -
- Views 140
- Downloads 0
Computational challenges in the simulation of nonlinear electroelasticity
Nonlinear electroelasticity is not a new problem, its theory involving nonlinear deformation and nonlinear material behavior has been well established. However, the numerical simulation of nonlinear electroelasticity is...
Method of fundamental solutions and random numbers for the torsion of bars with multiply connected cross sections
The torsion of bars with multiply connected cross section by means of the method of fundamental solutions (MFS) is considered. Random numbers were used to determine the minimal errors for MFS. Five cases of cross section...
Inverse problem in anomalous diffusion with uncertainty propagation
Recently, Bevilacqua, Galeão and co-workers have developed a new analytical formulation for the simulation of diffusion with retention phenomena. This new formulation aims at the reduction of all diffusion processes with...
Solution of 2D non-homogenous wave equation by using polywave functions. (Received in the final form February 9, 2010)
The paper presents a specific technique of solving the non-homogenous wave equation with the use of Trefftz functions for the wave equation. The solution was presented as a sum of a general integral and a particular inte...
Identification of aerodynamic coefficients of a projectile and reconstruction of its trajectory from partial flight data
Several optimization techniques are proposed both to identify the aerodynamic coefficients and to reconstruct the trajectory of a fin-stabilized projectile from partial flight data. A reduced ballistic model is used inst...