A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Influence of Post and Resin Cement on Stress Distribution of Maxillary Central Incisors Restored with Direct Resin Composite

The current study evaluated the influence of two endodontic post systems and the elastic modulus and film thickness of resin cement on stress distribution in a maxillary central incisor (MCI) restored with direct resin composite using finite element analysis (FEA). A three-dimensional model of an MCI with a coronary fracture and supporting structures was performed. A static chewing pressure of 2.16 N/mm(2) was applied to two areas on the palatal surface of the composite restoration. Zirconia ceramic (ZC) and glass fiber (GF) posts were considered. The stress distribution was analyzed in the post, dentin and cement layer when ZC and GF posts were fixed to the root canals using resin cements of different elastic moduli (7.0 and 18.6 GPa) and different layer thicknesses (70 and 200 mu m). The different post materials presented a significant influence on stress distribution with lesser stress concentration when using the GF post. The higher elastic modulus cement created higher stress levels within itself. The cement thicknesses did not present significant changes.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Stress Analysis in Simulation Models With or Without Implant Threads Representation

Purpose: This study aimed to evaluate the influence of implants with or without threads representation on the outcome of a two-dimensional finite element (FE) analysis. Materials and Methods: Two-dimensional FE models that reproduced a frontal section of edentulous mandibular posterior bone were constructed using a standard crown/implant/screw system representation. To evaluate the effect of implant threads, two models were created: a model in which the implant threads were accurately simulated (precise model) and a model in which implants with a smooth surface (press-fit implant) were used (simplified model). An evaluation was performed on ANSYS software, in which a load of 133 N was applied at a 30-degree angulation and 2 mm off-axis from the long axis of the implant on the models, The Von Mises stresses were measured. Results: The precise model (1.45 MPa) showed higher maximum stress values than the simplified model (1.2 MPa). Whereas in the cortical bone, the stress values differed by about 36% (292.95 MPa for the precise model and 401.14 MPa for the simplified model), in trabecular bone (19.35 MPa and 20.35 MPa, respectively), the stress distribution and stress values were similar. Stress concentrations occurred around the implant neck and the implant apex. Conclusions: Considering implant and cortical bone analysis, remarkable differences in stress values were found between the models. Although the models showed different absolute stress values, the stress distribution was similar. INT J ORAL MAXILLOFAC IMPLANTS 2009;24:1040-1044

Effect of different mucosa thickness and resiliency on stress distribution of implant-retained overdentures-2D FEA

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparison of stress distribution between complete denture and implant-retained overdenture-2D FEA

The aim of this study was to compare the stress distribution induced by posterior functional loads on conventional complete dentures and implant-retained overdentures with different attachment systems using a two-dimentional Finite Element Analysis (FEA-2D). Three models representative of edentulous mandible were constructed on AutoCAD software; Group A (control), a model of edentulous mandible supporting a complete denture; Group B, a model of edentulous mandible supporting an overdenture over two splinted implants connected with the bar-clip system; Group C, a model of edentuluos mandible supporting an overdenture over two unsplinted impants with the O-ring system. Evaluation was conducted on Ansys software, with a vertical force of 100 N applied on the mandibular left first molar. When the stress was evaluated in supporting tissues, groups B (51.0 MPa) and C (52.6 MPa) demonstrated higher stress values than group A (10.1 MPa). Within the limits of this study, it may be conclued that the use of an attachment system increased stress values; furthermore, the use of splinted implants associated with the bar-clip attachment system favoured a lower stress distribution over the supporting tissue than the unsplinted implants with an O-ring abutment to retain the manibular overdenture.

Short Implant to Support Maxillary Restorations: Bone Stress Analysis Using Regular and Switching Platform

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of customized composite resin fibreglass posts on the mechanics of restored treated teeth

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of Implant Inclination Associated With Mandibular Class I Removable Partial Denture

The aim of this study was to use two-dimensional finite element method to evaluate the displacement and stress distribution transmitted by a distal extension removable partial denture (DERPD) associated with an implant placed at different inclinations (0, 5, 15, and 30 degrees) in the second molar region of the edentulous mandible ridge. Six hemimandibular models were created: model A, only with the presence of the natural tooth 33; model B, similar to model A, with the presence of a conventional DERPD replacing the missing teeth; model C, similar to the previous model, with a straight implant (0 degrees) in the distal region of the ridge, under the denture base; model D, similar to model C, with the implant angled at 5 degrees in the mesial direction; model E, similar to model C, with the implant angled at 15 degrees in the mesial direction; and model F, similar to ME, with the implant angled at 30 degrees in the mesial direction. The models were created with the use of the AutoCAD 2000 program (Autodesk, Inc, San Rafael, CA) and processed for finite element analysis by the ANSYS 8.0 program (Swanson Analysis Systems, Houston, PA). The force applied was vertical of 50 N on each cusp tip. The results showed that the introduction of the RPD overloaded the supporting structures of the RPD and that the introduction of the implant helped to relieve the stresses of the mucosa alveolar, cortical bone, and trabecular bone. The best stress distribution occurred in model D with the implant angled at 5 degrees. The use of an implant as a support decreased the displacement of alveolar mucosa for all inclinations simulated. The stress distribution transmitted by the DERPD to the supporting structures was improved by the use of straight or slightly inclined implants. According to the displacement analysis and von Mises stress, it could be expected that straight or slightly inclined implants do not represent biomechanical risks to use.

Regular and Platform Switching: Bone Stress Analysis Varying Implant Type

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of the influence of location of osseointegrated implants associated with mandibular removable partial dentures

Purpose: The aim of this research was to assess, by means of, the bi-dimensional finite element method, the best implant location in the alveolar edge, through stress distribution and support structure displacement of a distal extension removable partial denture associated with an osseointegrated implant of 10.0 x .75 mm, acting as abutment for the denture base.Methods and Materials: Five models in sagittal cut were used to represent: model A-hemi arch containing natural tooth 33 and the distal alveolar edge; model B-similar to model A, but with a conventional removable partial denture to replace the absent teeth; model C (MC)-similar to the previous one, with an implant in the distal region of the edge under the denture base; model D-similar to MC, with the implant in the central region of the edge; model E-similar to MC, with an implant in the mesial region of the edge. With the aid of the finite element program ANSYS 8.0, the models were loaded with strictly vertical forces of 50 N on each cusp tip. Displacement and von Mises Maps were plotted for visualization of results.Results: The introduction of implant diminished the tendency of intrusion of the removable partial denture in all situations. The maximum stress was observed on implant in all situations. Approximating implant in direction of support teeth was benefit for stress distribution.Conclusion: Model D presented the lowest value for maximum tendency to displacement when compared with those found in the other models; model E demonstrated better relief with regard to demand from the abutment tooth; locating the implant near of the abutment tooth influenced positively the distribution of stresses on the analyzed structures.

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.

Evaluation of Different Retention Systems on a Distal Extension Removable Partial Denture Associated With an Osseointegrated Implant

The aim of this study was to evaluate the biomechanical behavior of a mandibular distal extension removable partial denture (DERPD) associated with an implant and different retention system, by bidimensional finite element method. Five hemimandible models with a canine and external hexagon implant at second molar region associated with DERPD were simulated: model A, hemimandible with a canine and a DERPD; model B, hemimandible with a canine and implant with a healing abutment associated to a DERPD; model C, hemimandible with a canine and implant with an ERA attachment associated to a DERPD; model D, hemimandible with a canine and implant with an O'ring attachment associated to a DERPD; and model E, hemimandible with a canine and implant-supported prosthesis associated to a DERPD. Cusp tips were loaded with 50 N of axial or oblique force (45 degrees). Finite element analysis was performed in ANSYS 9.0. model E showed the higher displacement and overload in the supporting tissues; the patterns of stress distribution around the dental apex of models B, C, and D were similar. The association between a DERPD and an osseointegrated implant using the ERA or O'ring systems shows lower stress values. Oblique forces showed higher stress values and displacement. Oblique forces increased the displacement and stress levels in all models; model C displayed the best stress distribution in the supporting structures; healing abutment, ERA, and O'ring systems were viable with RPD, but DERPD association with a single implant-supported prosthesis was nonviable.