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 136
- Downloads 0
Sensitivity analysis of transient bioheat transfer with perfusion rate dependent on tissue injury. (Received in the final form January 18, 2010)
The sensitivity analysis of transient temperature field in the tissue domain with respect to its thermophysical parameters is discussed. In particular, the influence of tissue specific heat, thermal conductivity, perfusi...
Applying Artificial Neural Networks for analysis of geotechnical problems
The paper presents a discussion of some applications of Artificial Neural Networks (ANNs) in geoengineering using the analysis of the following six geotechnical problems, related mainly to prediction and classification p...
Regularization using truncated singular value decomposition for estimating the Fourier spectrum of a noised space distribution over an extended support
This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are...
Gaussian mixture model for time series-based structural damage detection
In this paper, a time series-based damage detection algorithm is proposed using Gaussian mixture model (GMM) and expectation maximization (EM) framework. The vibration time series from the structure are modelled as the a...
Improved GETMe by adaptive mesh smoothing
Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized soluti...