Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Three-dimensional finite element thermal analysis of dental tissues irradiated with Er,Cr:YSGG laser

In the present study, a finite element model of a half-sectioned molar tooth was developed in order to understand the thermal behavior of dental hard tissues (both enamel and dentin) under laser irradiation. The model was validated by comparing it with an in vitro experiment where a sound molar tooth was irradiated by an Er,Cr:YSGG pulsed laser. The numerical tooth model was conceived to simulate the in vitro experiment, reproducing the dimensions and physical conditions of the typical molar sound tooth, considering laser energy absorption and calculating the heat transfer through the dental tissues in three dimensions. The numerical assay considered the same three laser energy densities at the same wavelength (2.79 mu m) used in the experiment. A thermographic camera was used to perform the in vitro experiment, in which an Er, Cr: YSGG laser (2.79 mu m) was used to irradiate tooth samples and the infrared images obtained were stored and analyzed. The temperature increments in both the finite element model and the in vitro experiment were compared. The distribution of temperature inside the tooth versus time plotted for two critical points showed a relatively good agreement between the results of the experiment and model. The three dimensional model allows one to understand how the heat propagates through the dentin and enamel and to relate the amount of energy applied, width of the laser pulses, and temperature inside the tooth. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2953526]

Aerodynamic study of three-dimensional larynx models using finite element methods

The airflow velocities and pressures are calculated from a three-dimensional model of the human larynx by using the finite element method. The laryngeal airflow is assumed to be incompressible, isothermal, steady, and created by fixed pressure drops. The influence of different laryngeal profiles (convergent, parallel, and divergent), glottal area, and dimensions of false vocal folds in the airflow are investigated. The results indicate that vertical and horizontal phase differences in the laryngeal tissue movements are influenced by the nonlinear pressure distribution across the glottal channel, and the glottal entrance shape influences the air pressure distribution inside the glottis. Additionally, the false vocal folds increase the glottal duct pressure drop by creating a new constricted channel in the larynx, and alter the airflow vortexes formed after the true vocal folds. (C) 2007 Elsevier Ltd. All rights reserved.

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Three-Dimensional Stress Distribution in the Human Periodontal Ligament in Masticatory, Parafunctional, and Trauma Loads: Finite Element Analysis

Background: The presence of the periodontal ligament (PDL) makes it possible to absorb and distribute loads produced during masticatory function and other tooth contacts into the alveolar process via the alveolar bone proper. However, several factors affect the integrity of periodontal structures causing the destruction of the connective matrix and cells, the loss of fibrous attachment, and the resorption of alveolar bone. Methods: The purpose of this study was to evaluate the stress distribution by finite element analysis in a PDL in three-dimensional models of the upper central incisor under three different load conditions: 100 N occlusal loading at 45 degrees (model 1: masticatory load); 500 N at the incisal edge at 45 degrees (model 2: parafunctional habit); and 800 N at the buccal surface at 90 degrees (model 3: trauma case). The models were built from computed tomography scans. Results: The stress distribution was quite different among the models. The most significant values (harmful) of tensile and compressive stresses were observed in models 2 and 3, with similarly distinct patterns of stress distributions along the PDL. Tensile stresses were observed along the internal and external aspects of the PDL, mostly at the cervical and middle thirds. Conclusions: The stress generation in these models may affect the integrity of periodontal structures. A better understanding of the biomechanical behavior of the PDL under physiologic and traumatic loading conditions might enhance the understanding of the biologic reaction of the PDL in health and disease. J Periodontol 2009;80:1859-1867.

Three Dimensional Finite Element Analyses of Oral Structures by Computerized Tomography

Our aim was to document the benefits of three dimensional finite element model generations from computed tomography data as well as the realistic creation of all oral structures in a patient. The stresses resulting from the applied load in our study did not exceed the structure limitations, suggesting a clinically acceptable physiological condition.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Influence of Cusp Inclination on Stress Distribution in Implant-Supported Prostheses. A Three-Dimensional Finite Element Analysis

Purpose: The aim of this study was to assess the influence of cusp inclination on stress distribution in implant-supported prostheses by 3D finite element method.Materials and Methods: Three-dimensional models were created to simulate a mandibular bone section with an implant (3.75 mm diameter x 10 mm length) and crown by means of a 3D scanner and 3D CAD software. A screw-retained single crown was simulated using three cusp inclinations (10 degrees, 20 degrees, 30 degrees). The 3D models (model 10d, model 20d, and model 30d) were transferred to the finite element program NeiNastran 9.0 to generate a mesh and perform the stress analysis. An oblique load of 200 N was applied on the internal vestibular face of the metal ceramic crown.Results: The results were visualized by means of von Mises stress maps. Maximum stress concentration was located at the point of application. The implant showed higher stress values in model 30d (160.68 MPa). Cortical bone showed higher stress values in model 10d (28.23 MPa).Conclusion: Stresses on the implant and implant/abutment interface increased with increasing cusp inclination, and stresses on the cortical bone decreased with increasing cusp inclination.

Passivity Versus Unilateral Angular Misfit: Evaluation of Stress Distribution on Implant-Supported Single Crowns: Three-Dimensional Finite Element Analysis

The aim of this study was to evaluate the effect of unilateral angular misfit of 100 Km on stress distribution of implant-supported single crowns with ceramic veneering and gold framework by three-dimensional finite element analysis. Two three-dimensional models representing a maxillary section of premolar region were constructed: group 1 (control)-crown completely adapted to the implant and group 2-crown with unilateral angular misfit of 100 Km. A vertical force of 100 N was applied on 2 centric points of the crown. The von Mises stress was used as an analysis criterion. The stress values and distribution in the main maps (204.4 MPa for group 1 and 205.0 MPa for group 2) and in the other structures (aesthetic veneering, framework, retention screw, implant, and bone tissue) were similar for both groups. The highest stress values were observed between the first and second threads of the retention screw. Considering the bone tissue, the highest stress values were exhibited in the peri-implant cortical bone. The unilateral angular misfit of 100 Km did not influence the stress distribution on the implant-supported prosthesis under static loading.

Platform Switching: Biomechanical Evaluation Using Three-Dimensional Finite Element Analysis

Purpose: The objective of this study was to evaluate, using three-dimensional finite element analysis (3D FEA), the stress distribution in peri-implant bone tissue, implants, and prosthetic components of implant-supported single crowns with the use of the platform-switching concept. Materials and Methods: Three 3D finite element models were created to replicate an external-hexagonal implant system with peri-implant bone tissue in which three different implant-abutment configurations were represented. In the regular platform (RP) group, a regular 4.1-mm-diameter abutment (UCLA) was connected to regular 4.1-mm-diameter implant. The platform-switching (PS) group was simulated by the connection of a wide implant (5.0 mm diameter) to a regular 4.1-mm-diameter UCLA abutment. In the wide-platform (WP) group, a 5.0-mm-diameter UCLA abutment was connected to a 5.0-mm-diameter implant. An occlusal load of 100 N was applied either axially or obliquely on the models using ANSYS software. Results: Both the increase in implant diameter and the use of platform switching played roles in stress reduction. The PS group presented lower stress values than the RP and WP groups for bone and implant. In the peri-implant area, cortical bone exhibited a higher stress concentration than the trabecular bone in all models and both loading situations. Under oblique loading, higher intensity and greater distribution of stress were observed than under axial loading. Platform switching reduced von Mises (17.5% and 9.3% for axial and oblique loads, respectively), minimum (compressive) (19.4% for axial load and 21.9% for oblique load), and maximum (tensile) principal stress values (46.6% for axial load and 26.7% for oblique load) in the peri-implant bone tissue. Conclusion: Platform switching led to improved biomechanical stress distribution in peri-implant bone tissue. Oblique loads resulted in higher stress concentrations than axial loads for all models. Wide-diameter implants had a large influence in reducing stress values in the implant system. INT J ORAL MAXILLOFAC IMPLANTS 2011;26:482-491

Effect of Metal-Ceramic or All-Ceramic Superstructure Materials on Stress Distribution in a Single Implant-Supported Prosthesis: Three-Dimensional Finite Element Analysis

Purpose: This three-dimensional finite element analysis study evaluated the effect of different material combinations on stress distribution within metal-ceramic and all-ceramic single implant-supported prostheses. Materials and Methods: Three-dimensional finite element models reproducing a segment of the maxilla with a missing left first premolar were created. Five groups were established to represent different superstructure materials: GP, porcelain fused to gold alloy; GR, modified composite resin fused to gold alloy; TP, porcelain fused to titanium; TR, modified composite resin fused to titanium; and ZP, porcelain fused to zirconia. A 100-N vertical force was applied to the contact points of the crowns. All models were fixed in the superior region of bone tissue and in the mesial and distal faces of the maxilla section. Stress maps were generated by processing with finite element software. Results: Stress distribution and stress values of supporting bone were similar for the GP, GR, TP, and ZP models (1,574.3 MPa, 1,574.3 MPa, 1,574.3 MPa, and 1,574.2 MPa, respectively) and different for the TR model (1,838.3 MPa). The ZP model transferred less stress to the retention screw (785 MPa) than the other groups (939 MPa for GP, 961 MPa for GR, 1,010 MPa for TP, and 1,037 MPa for TR). Conclusion: The use of different materials to fabricate a superstructure for a single implant-supported prosthesis did not affect the stress distribution in the supporting bone. The retention screw received less stress when a combination of porcelain and zirconia was used. Int J Oral Maxillofac Implants 2011;26:1202-1209

Three-Dimensional Finite Element Analysis of Vertical and Angular Misfit in Implant-Supported Fixed Prostheses

Purpose: Three-dimensional finite element analysis was used to evaluate the effect of vertical and angular misfit in three-piece implant-supported screw-retained fixed prostheses on the biomechanical response in the peri-implant bone, implants, and prosthetic components. Materials and Methods: Four three-dimensional models were fabricated to represent a right posterior mandibular section with one implant in the region of the second premolar (2PM) and another in the region of the second molar (2M). The implants were splinted by a three-piece implant-supported metal-ceramic prosthesis and differed according to the type of misfit, as represented by four different models: Control = prosthesis with complete fit to the implants; UAM (unilateral angular misfit) = prosthesis presenting unilateral angular misfit of 100 pm in the mesial region of the 2M; UVM (unilateral vertical misfit) = prosthesis presenting unilateral vertical misfit of 100 pm in the mesial region of the 2M; and TVM (total vertical misfit) = prosthesis presenting total vertical misfit of 100 pm in the platform of the framework in the 2M. A vertical load of 400 N was distributed and applied on 12 centric points by the software Ansys, ie, a vertical load of 150 N was applied to each molar in the prosthesis and a vertical load of 100 N was applied at the 2PM. Results: The stress values and distribution in peri-implant bone tissue were similar for all groups. The models with misfit exhibited different distribution patterns and increased stress magnitude in comparison to the control. The highest stress values in group UAM were observed in the implant body and retention screw. The groups UVM and TVM exhibited high stress values in the platform of the framework and the implant hexagon, respectively. Conclusions: The three types of misfit influenced the magnitude and distribution of stresses. The influence of misfit on peri-implant bone tissue was modest. Each type of misfit increased the stress values in different regions of the system. INT J ORAL MAXILLOFAC IMPLANTS 2011;26:788-796