and this problem can be solved analytically: u (x) = x − sinhx/sinh1. The purpose of starting with this problem is to demonstrate the fundamental concepts and pitfalls in FEM in a situation where we know the correct answer, so that we will know where our approximation is good and where it is poor. In cases of practical interest we will look at ODEs and PDEs that are too complex to be solved ana...

Finite element methods are based on the variational formulation of partial differential equations which only need to compute the gradient of a function. Although unknowns are still associated to nodes, the function composed by piece-wise polynomials on each element and thus the gradient can be computed element-wise. Finite element spaces can thus be constructed on general triangulations and thi...

the effect of boundary conditions on the solution of the inverse problem of identifying the geometry and location of a cavity inside an elastic solid body using displacement measurements obtained from a tension test is investigated. the boundary elements method (bem) coupled with the genetic algorithm (ga) and the conjugate gradient method (cgm) are implemented in this identification problem. a...

this paper presents an overview of model updating and particularly its application for updating of frame model. in this article a mathematical model of the frame was produced with finite element method. the frame was subjected to hammer modal testing. then the results of the modal testing were compared with those predicted with the model. this comparison revealed discrepancies between these two...

The Stochastic Finite Element Method has seen a number of incarnations over the past few years, ranging from perturbation-based methods, and Neumann-expansion based methods, to methods for evaluating bounds on the response variability, and more recent functional expansions combined with error minimization techniques. Of these, only the last class of methods provides an explicit expression to th...