A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and to be in the form of minimizers in appropriate sets of admissible finite element functions for both methods...

In this paper, nonlinear implicit finite element analyses are used to explore parametric excitation of a bridge stay cable resulting from cyclic motion of the deck. “Parametric excitation” is excitation of a cable mode with deck motion at near twice the frequency of the excited mode. Third-mode parametric frequency response curves are consistently predicted when the finite element mesh is suffi...

This paper studies the post-local buckling behaviour of steel plates in concrete-filled thin-walled steel tubular columns under biaxial loading using the finite element method. Geometric and material nonlinear finite element analyses are undertaken to investigate the post-local buckling strengths of imperfect steel plates under stress gradients. Based on the results obtained from the nonlinear ...

A finite-element deformable surface-spine model is developed in this paper to register two surfaces by recovering the nonlinear deformation with respect to each other. The deformable surface-spine model is a dynamic model governed by Lagrangian motion equations. A 9 degree-of-freedom (dof) finite-element surface element and a $-dof spine element are developed to iteratively solve Lagrangian equ...

The interest for time Galerkin and corresponding space-time finite element methods has been linked during the last decade to the development of adaptivity of mesh selection for evolution PDE’s. Certain issues as, e.g., a posteriori estimates, estimates of optimal order and regularity, fully discrete schemes with mesh modification, etc., have been extensively considered in the framework of Conti...

Numerical modeling of machining processes is of significance in the parametric analysis and optimization of their performance. In this paper, a finite element-based model of abrasive waterjet (AWJ) cutting of a ductile material is presented with the help of an explicit, nonlinear finite element method. In this model, both solid-solid interaction and fluid-structure interaction are considered. T...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...

finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural introduction to finite element vibration analys...

We present a systematic method for developing low order nonlinear models from physically based, large scale finite element models of rapid thermal processing (RTP) systems. These low order models are extracted from transient results of a detailed finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are then used as basis functi...