Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Hydrodynamic analysis of particle collection efficiency: comparing downflow and upflow filtration

Models of the filtration phenomenon describe the mass balance in bed filtration in terms of particle removal mechanisms, and allow for the determination of global particle removal efficiencies. These models are defined in terms of the geometry and characteristic elements of granule collectors, particles and fluid, and also the composition of the balance of forces that act in the particle collector system. This work analyzes particles collection efficiency comparing downflow and upflow direct filtration, taking into account the contribution of the gravitational factor of the settling removal efficiency in future proposal of initial collection efficiency models for upflow filtration. A qualitative analysis is also made of the proposal for the collection efficiency models for particle removal in direct downflow and upflow filtration using a Computational Fluid Dynamics (CFD) tool. This analysis showed a strong influence of gravitational factor in initial collection efficiency (t = 0) of particles, as well as the reasons of their values to be smaller for upflow filtration in comparison with the downflow filtration.