Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Finite element aided design evolution of composite leaf spring

This paper shows the process of the virtual production development of the mechanical connection between the top leaf of a dual composite leaf spring system to a shackle using finite element methods. The commercial FEA package MSC/MARC has been used for the analysis. In the original design the joint was based on a closed eye-end. Full scale testing results showed that this configuration achieved the vertical proof load of 150 kN and 1 million cycles of fatigue load. However, a problem with delamination occurred at the interface between the fibres going around the eye and the main leaf body. To overcome this problem, a second design was tried using transverse bandages of woven glass fibre reinforced tape to wrap the section that is prone to delaminate. In this case, the maximum interlaminar shear stress was reduced by a certain amount but it was still higher than the material’s shear strength. Based on the fact that, even with delamination, the top leaf spring still sustained the maximum static and fatigue loads required, the third design was proposed with an open eye-end, eliminating altogether the interface where the maximum shear stress occurs. The maximum shear stress predicted by FEA is reduced significantly and a safety factor of around 2 has been obtained. Thus, a successful and safe design has been achieved.

An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data, the arbitrary refractive index profile is modeled by a. nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO3 waveguides are computed by the finite element method.

MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for Ex (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for Ex modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

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.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

A 2-D Delaunay refinement algorithm using an initial prerefinement from the boundary mesh

An improvement to the quality bidimensional Delaunay mesh generation algorithm, which combines the mesh refinement algorithms strategy of Ruppert and Shewchuk is proposed in this research. The developed technique uses diametral lenses criterion, introduced by L. P. Chew, with the purpose of eliminating the extremely obtuse triangles in the boundary mesh. This method splits the boundary segment and obtains an initial prerefinement, and thus reducing the number of necessary iterations to generate a high quality sequential triangulation. Moreover, it decreases the intensity of the communication and synchronization between subdomains in parallel mesh refinement.

A 2-D delaunay refinement algorithm using an initial prerefinement from the boundary mesh

An improvement to the quality bidimensional Delaunay mesh generation algorithm, which combines the mesh refinement algorithms strategy of Ruppert and Shewchuk is proposed in this research. The developed technique uses diametral lenses criterion, introduced by L. P. Chew, with the purpose of eliminating the extremely obtuse triangles in the boundary mesh. This method splits the boundary segment and obtains an initial prerefinement, and thus reducing the number of necessary iterations to generate a high quality sequential triangulation. Moreover, it decreases the intensity of the communication and synchronization between subdomains in parallel mesh refinement. © 2008 IEEE.

High-field magnetic resonance imaging with reduced field/tissue RF artefacts - A modeling study using hybrid MoM/FEM and FDTD technique

Due to complex field/tissue interactions, high-field magnetic resonance (MR) images suffer significant image distortions that result in compromised diagnostic quality. A new method that attempts to remove these distortions is proposed in this paper and is based on the use of transceiver-phased arrays. The proposed system uses, in the examples presented herein, a shielded four-element transceive-phased array head coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both the images together, the image distortion can be reduced several fold. A combined hybrid method of moments (MoM)/finite element method (FEM) and finite-difference time-domain (FDTD) technique is proposed and used to elucidate the concept of the new method and to accurately evaluate the electromagnetic field (EMF) in a human head model. In addition, the proposed method is used in conjunction with the generalized auto-calibrating partially parallel acquisitions (GRAPPA) reconstruction technique to enable rapid imaging of the two scans. Simulation results reported herein for 11-T (470-MHz) brain imaging applications show that the new method with GRAPPA reconstruction theoretically results in improved image quality and that the proposed combined hybrid MoM/FEM and FDTD technique is. suitable for high-field magnetic resonance imaging (MRI) numerical analysis.

Methods Used for Assessing Stresses in Buccomaxillary Prostheses: Photoelasticity, Finite Element Technique, and Extensometry

The authors describe a literature revision on assessing stresses in buccomaxillary prostheses photoelasticity, finite element technique, and extensometry. They describe the techniques and the importance for use of each method in buccomaxillary prostheses with implants and the need of accomplishing more studies in this scarce literary area.

Finite element evaluation of three methods of stable fixation of condyle base fractures

The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.

Computer graphics applied to anatomy: a study of two bio-cad modeling methods on finite element analysis of human edentulous hemi-mandible

Modeling is a step to perform a finite element analysis. Different methods of model construction are reported in literature, as the Bio-CAD modeling. The purpose of this study was to perform a model evaluation and application using two methods of Bio-CAD modeling from human edentulous hemi-mandible on the finite element analysis. From CT scans of dried human skull was reconstructed a stereolithographic model. Two methods of modeling were performed: STL conversion approach (Model 1) associated to STL simplification and reverse engineering approach (Model 2). For finite element analysis was used the action of lateral pterygoid muscle as loading condition to assess total displacement (D), equivalent von-Mises stress (VM) and maximum principal stress (MP). Two models presented differences on the geometry regarding surface number (1834 (model 1); 282 (model 2)). Were observed differences in finite element mesh regarding element number (30428 nodes/16683 elements (model 1); 15801 nodes/8410 elements (model 2). D, VM and MP stress areas presented similar distribution in two models. The values were different regarding maximum and minimum values of D (ranging 0-0.511 mm (model 1) and 0-0.544 mm (model 2), VM stress (6.36E-04-11.4 MPa (model 1) and 2.15E-04-14.7 MPa (model 2) and MP stress (-1.43-9.14 MPa (model 1) and -1.2-11.6 MPa (model 2). From two methods of Bio-CAD modeling, the reverse engineering presented better anatomical representation compared to the STL conversion approach. The models presented differences in the finite element mesh, total displacement and stress distribution.