Comments on Variational Method and Energy Method in Computational Mechanics

The Stochastic Perturbation Method for Computational Mechanics

Granular element method for computational particle mechanics

0045-7825/$ see front matter 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.cma.2012.06.012 ⇑ Corresponding author. E-mail address: [email protected] (J.E. Andrad This paper presents a method within the family of the discrete element method (DEM) capable of accurately capturing grain shape by using Non-Uniform Rational Basis-Splines (NURBS). The new method, called GEM, bypasses one of the ...

A Meshless Method for Computational Stochastic Mechanics

This paper presents a stochastic meshless method for probabilistic analysis of linear-elastic structures with spatially varying random material properties. Using Karhunen-Loève (K-L) expansion, the homogeneous random field representing material properties was discretized by a set of orthonormal eigenfunctions and uncorrelated random variables. Two numerical methods were developed for solving th...

Reduced Basis Method for Variational Inequalities in Contact Mechanics

We present an efficient model order reduction method [1] for parametrized elliptic variational inequalities of the first kind: find u ∈ K such that: a(u, v − u;μ) ≥ f(v − u;μ), ∀v ∈ K(μ) where K(μ) := {v ∈ H1(Ω)|Bv ≤ g(μ)}. Motivated by numerous engineering applications that involve contact between elastic body and rigid obstacle, e.g. the obstacle problem [2], we develop a primaldual reduced b...

NURBS-Based Isogeometric Analysis Method Application to Mixed-Mode Computational Fracture Mechanics

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...