| Abstract|| |
Background: The U-shaped maxillary major connector is considered to be the least-desirable design by many prosthodontists as it lacks rigidity, which is a primary requisite for a major connector.
Aims and Objectives: Design modifications in the U-shaped palatal major connector are desired because it lacks rigidity. The study also aimed to determine the best design when a U-shaped palatal major connector is indicated for clinical use.
Materials and Methods: The normal design and the design-modified models (modification 1, 2, 3, 4) were loaded at the functional cusps of the premolars and the molars with a magnitude of 200 N, 250 N and 300 N at angulations of 60 o and 90 o on both sides of the maxillary arch. Results for each loading were obtained as stress distribution colored images and numerical values were recorded. A three-dimensional finite element analysis study of the design-modified models was performed using two finite element softwares, namely PRO-E and IDEAS.
Results: The least stress value of 7.86 Megapascals (MPa) at 200 N, 60 o was recorded for the double-thickness design, followed by design 1, which was 8.03 MPa. The least stress value for the palatal mucosa and ligament was provided by design modification 1 (0.5 mm-thick U-shaped connector, 9 mm anteroposteiorly, 14.6 mm laterally), which was 9.78 MPa and 2.98 MPa, respectively.
Conclusion: The double-thickness group exhibited the least internal stress for the U-shaped major connector. However, it delivered the greatest stress to the palatal mucosa and the periodontal ligaments.
Keywords: 3D finite element, stress, U-shaped major connector
|How to cite this article:|
Ramakrishnan H, Singh RG. Three-dimensional finite element analysis of the stress distribution pattern in the design modifications of U-shaped palatal major connector. Indian J Dent Res 2010;21:506-11
The major connector functions to unite the various components of the prosthesis into a single unit. The major connector distributes the forces placed on the cast partial denture to all the supporting structures. It should be rigid, provide vertical support, protect the soft tissues, provide a means of obtaining indirect retention where indicated, provide an opportunity of positioning denture bases where needed and maintain patient comfort. 
|How to cite this URL:|
Ramakrishnan H, Singh RG. Three-dimensional finite element analysis of the stress distribution pattern in the design modifications of U-shaped palatal major connector. Indian J Dent Res [serial online] 2010 [cited 2020 Aug 15];21:506-11. Available from: http://www.ijdr.in/text.asp?2010/21/4/506/74219
Among the various designs of maxillary major connector, the U-shape is given less importance because it has less rigidity and exhibits flexion. , This study aims at design modifications for improvement in rigidity and identification of the best possible design for clinical use.
| Materials and Methods|| |
In this study, a typical long-span (missing 13 to 23) Kennedy Class IV situation with the U-shaped major connector cast partial denture in place was simulated three dimensionally using the PRO-ENGINEER software. Additionally, natural teeth (premolars and molars), alveolar bone, periodontal ligament, palatal mucosa and the hard palate were also modeled three dimensionally. All vital tissues were assumed to be isotropic, elastic and homogenous. The thickness of the periodontal ligament used in this study was 0.2 mm and the thickness of the palatal mucosa was 3 mm [Figure 1]. Another software named ANSYS was used for analyzing stress and for interpretation in megapascals.
The design modifications used in this FEA three-dimensional study were a palatal extension measuring 9 mm anteroposteriorly from the center of the normal U-shape and 14.6 mm laterally (design 1, [Figure 2]), medial extensions of the medial borders of the U-shape connector by 3 mm from either sides, thereby creating a wide U-shape connector (design 2, [Figure 3]), addition of a posterior strap measuring 4 mm in width (design 3, [Figure 4]) and a double thickness of 1 mm (design 4, [Figure 5]).
|Figure 2: Design modification 1 (0.5-mm thick, 9 mm anteroposteiorly, 14.6 mm laterally)|
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A typical PRO-E analysis has three distinct steps, such as:
Pre-processing involves generation of points along the X, Y and Z axes on a computer screen, which are subsequently connected to obtain a line diagram on the tooth. Joining of the lines create areas, and from these areas volumes were created. The smaller volumes were further joined to form an object.
- Preprocessing and modeling.
- Processing and meshing.
- Postprocessing and analysis.
Modeling involves assembling the teeth (maxillary premolars and molars with the rest seat preparation) on the right and left sides of a computer screen joined by the hard palate, with the cast partial denture in place. The thickness of the major connector in all designs except design 4 (double thickness, [Figure 5]) was standardized to exactly 0.5 mm. The surface of each root of the tooth was made to be offset equal to the thickness of periodontal ligaments. Roots of each tooth were modeled for alveolar bone.
The preprocessed model was subjected to processing by way of conversion of geometric data into a graphical data by the finite element software. This graphical data was divided into smaller, equal parts called elements. This step is called meshing. Elements can be of various shapes, like triangle, quadrilateral, tetrahedral. Accurate results can be obtained by selecting a particular shape of the element that suites the three-dimensional model. The material properties were then incorporated to the model after meshing. Values of enamel, dentin, pulp, cementum, alveolar bone, cobalt-chromium alloy, periodontal ligament and palatal tissue were used. Values were that of Young's modulus, which is the measure of stiffness or rigidity of the material under test, i.e. elastic stress divided by elastic strain, measured in megapascal. Poisson's ratio is lateral strain divided by longitudinal strain.
Postprocessing and analysis is the third and final stage. Analysis was performed with three magnitudes of forces, 200 N, 250 N and 300 N, with two different angulations of 90 o and 60 o . Equal amounts of forces were applied on the functional cusps of the maxillary premolars and molars simultaneously on both sides of the maxillary arch to simulate the maximal biting stresses at the intercuspal position of the teeth.
Finite element analysis, being a numerical and simulative study, has definitive advantages over other experimental studies like strain gauge and photoelastic study. The exact stress distribution pattern can be determined and visualized in finite element analysis. The models used in this study were simulations of natural maxillary premolars and molars, hard palate and alveolar bone. In photoelastic study, the models are magnified, which is a limitation. In a photoelastic study of a split major connector, Reitz  found that there was flexibility in the connector in the tissue ward direction and results demonstrated that the split connector reduced the stress delivered to the distal extension abutment.
The use of three-dimensional models is valuable in terms of element numbers and simulation quality and is more realistic. Effects of material properties and load variables can be primarily and effectively determined by the use of three-dimensional analysis.
Young's modulus and Poisson's ratio of a cobalt-chrome alloy for Removable partial denture (RPD) was used in this study. These values were used by researchers like Sato and Tsuga ,, in their studies. The cobalt-chrome alloy is said to have superior material properties than other alloys like nickel-chrome and titanium alloy, which are also used in fabrication of the cast partial denture [Table 1].
The values that have been used for periodontal ligament in various FEA studies range from 0.07 to 1,750 MPa.  Two independent studies (Middleton et al. and Rees and Jacobson) have correlated finite element models with clinical tooth displacement studies, and have suggested that an elastic modulus of 50 MPa and a Poisson's ratio of 0.49 for the ligament give good correlation between finite element models and clinical studies [Table 1]. Thus, these values were used for the ligament in this study. The palatal mucosa was modeled to a thickness of 3 mm and the hard palate, alveolar bone was also modeled with the aid of dentulous skull. The properties of these were added to the three-dimensional model during analysis.
The results were interpreted after the models were subjected to stress analysis. Constraints (locking of the entire three-dimensional model used in the software to create oral simulation) were applied throughout the perimeter and base of the three-dimensional model at the time of the analysis.
| Results|| |
The simulated three-dimensional models were loaded at the functional cusps of the premolars and the molars with a magnitude of 200 N, 250 N and 300 N and at angulations of 60 o and 90 o . Results for each loading were obtained as stress distribution colored images [Figure 6], and the numerical values were recorded.
The stress distribution pattern obtained for the normal U-design and the design modifications were subsequently tabulated. [Table 2], [Table 3] and [Table 4] show the numerical values of stress distribution in the normal and the design modifications of U-shaped connector in the palatal mucosa and in the ligaments of the premolars and molars. All the values are expressed in megapascals.
[Table 2] shows the stresses in various designs of the U-shaped palatal major connector and normal design. At a constant angulation of 60 o , when the magnitude of force was gradually increased, there was a corresponding increase in the stresses in all the designs of the U-shaped palatal major connector, which ranged from 7.86 MPa to 14.6 MPa. Also, at a constant angulation of 90 o , there was a corresponding increase in stresses in all the designs of the U-shaped connector, when the forces were gradually increased. This ranged from 8.21 MPa to 15.3 MPa. Again, when the amount of force was kept constant and the angulation was increased from 60 o to 90 o , there was an increase in stresses in the designs of the U-shaped connector. The least stress values for the three different forces at 60 o and 90 o were obtained for the double-thickness group (design 4), which were 7.86 MPa and 8.21 MPa, respectively, followed by design 1, which had values of 8.03 MPa and 8.98 MPa, respectively. This was followed by design 2, with values of 8.93 MPa and 9.14 MPa, respectively. The highest stress values were obtained for design modification 3 at all three different forces at 60 o and 90 o , which were 14.6 MPa and 15.3 MPa, respectively.
[Table 3] shows stresses occurring in the palatal mucosa. At a constant angulation of 60 o or 90 o , when the forces were gradually increased, there was a corresponding increase in the stresses delivered to the palatal mucosa, which ranged from 9.78 MPa to 24.4 MPa. It should be noted that the stress delivered to the palatal mucosa at 60 o was greater than that at 90 0 for the same magnitude of force. This shows that the lateral force delivers greater stress to the palatal mucosa in all design modifications. The least stress was delivered to the palatal mucosa by design modification 1 at three different forces at 60 o and 90 o , which were 10.84 MPa and 9.78 MPa, respectively, followed by design modification 2, with values of 14.9 MPa and 10.4 MPa, respectively. The double-thickness group delivered the highest stress to the palatal mucosa at 60 o and 90 o under the three magnitudes of forces, which were 24.4 MPa and 21.7 MPa, respectively, followed by design modification 3, where the values were 24.3 MPa and 20.4 MPa, respectively.
[Table 4] shows stresses delivered to the periodontal ligaments of the premolars and the molars. There was a gradual rise in stresses around the ligaments of both the premolars and the molars as the magnitude of force increased in all designs at 60 o and 90 o . This ranged from 2.98 MPa to 8.82 MPa. Also, stresses delivered to the ligaments at an angulation of 60 o were greater than those at 90 o for the same magnitude of force. This is in line with the fact that periodontal ligament fibers would tolerate vertical functional forces better than the destructive lateral forces.  The least stress was delivered to the periodontal ligaments of the premolars and the molars by design modification 1, at 60 o and 90 o , under the three magnitudes of forces, which were 2.98 MPa, 2.75 MPa and 4.94 MPa, and 4.32 MPa, respectively, followed by design modification 2, with values of 3.08 MPa, 2.88 MPa and 5.13 MPa, and 4.79 MPa, respectively. The greatest stress delivered to the ligaments of the premolars and the molars at the three magnitudes of forces at 60 o and 90 o was by the double-thickness group, which was 6.32 MPa 5.01 MPa and 8.82 MPa, and 8.54 MPa, followed by design modification 3, with values of 5.41 MPa, 4.38 MPa and 8.24 MPa, and 8.10 MPa, respectively.
| Discussion|| |
Rigidity is a necessary pre-requisite for a major connector so that it can transmit masticatory forces from one side of the arch to another. A U-shaped connector lacks the rigidity of other maxillary major connector designs. It has less resistance to flexing and movement can occur at the open ends. To improve its rigidity and stiffness, design modifications were made.
The preferred RPD design should resist and transfer crossarch destructive horizontal forces while exhibiting minimal or negligible flexibility with vertical masticatory forces. In this way, abutments are protected during mastication and the forces are absorbed by the supporting tissues. Karies  demonstrated that modifying the mandibular major connector to reduce its rigidity increased the horizontal stress on the abutment teeth. Flexible major connectors were unable to distribute stresses and therefore placed more stress on the individual abutments.
The maxillary major connector, in contrast to the mandibular major connector, can be designed to take advantage of the structure of the palate using various slopes, namely the anterior slope or the sagittal slope, palatal vault and lateral or vertical slopes of the palate. This is the L-bar principle used in rigid engineering structure, which states that forces transmitted on more than one plane are counteracted more easily and greater rigidity can be obtained.
In this study, the L-bar principle has been used on all design modifications where designs extend in more than one plane of the palate. Designs 1 and 2 extend in three planes of the palate while designs 3 and 4 extend in two planes only.
All the three-dimensional models, with the normal design and the design modifications, were loaded over functional cusps of the premolars and the molars with three different magnitudes of forces at two different angulations, namely 200 N, 250 N and 300 N at 60 o and 90 o . These forces simulate the maximal biting forces at the intercuspal region, as described by Ferrario.  A similar amount of force was used by Beata et al.  in their FEA analysis in mandibular molars during clenching. Following application of forces, the corresponding stresses generated in the three components, namely major connector - normal and design modifications, palatal mucosa and periodontal ligaments of premolars and molars were recorded in [Table 2], [Table 3] and [Table 4].
A comparison between design modification 1 and normal design showed that stresses induced in the design-modified connector (component 1), palatal mucosa (component 2) and ligaments around the premolars and molars (component 3) were much lower in the design modification 1. This can be explained by fact that design modification 1 extends in three planes whereas normal design extends in two planes, making the former more rigid. A comparison between design modification 2 and normal design showed that there was a small decrease in stress values of all the three components in design modification 2. This can be explained by the fact that both extend in two planes and that the 3 mm metal extension had caused a slight decrease in the stress values for design modification 2.
A comparison between design modification 3 and normal design showed that there was a gradual increase in the stress values in all three components for design modification 3. A comparison between design modification 4 (double thickness) and normal design showed the least stress values for the design modified, but the stress values for palatal mucosa and the periodontal ligament showed an appreciable increase. The lowest stress value for design modification 4 was 7.86 MPa and the highest values of stresses delivered to the palatal mucosa and ligament by design modification 4 were 24.4 MPa and 8.82 MPa, respectively.
Therefore, the lowest stress value among the design modifications was provided by design modification 4 (double-thickness group), which stood at 7.86 MPa, and the lowest stress values for the palatal mucosa and ligament was provided by design modification 1, which stood at 9.78 MPa and 2.98 MPa, respectively.
Lawrence et al.  concluded that when a U-shaped connector is used, the thickness of the framework should be increased by using two layers of pattern wax if maximal rigidity and resistance to flexion are desired, while other design modifications similar to the one used in this study showed a moderate improvement in rigidity. Only the U-shaped framework and a pair of testing and mounting brackets were used in the test, but this FEA study is a clinical simulative study because a long span typical Kennedy Class IV cast partial denture with surrounding teeth, palate, ligament and bone are modeled for analysis.
The thickness of the major connector denture in all designs except the thick one was standardized to exactly 0.5 mm in the present study. This standardization is very difficult to achieve in an in vitro study as the variation in thickness within the denture can arise following trimming procedures.
In studies by Ben et al., , rigidity tests were performed on the maxillary major connectors of different designs using both the Instron Testing Machine and a specialized steel wire and weight apparatus system. Designs used were palatal strap, anteroposterior palatal bar, anteroposterior palatal bar on different planes and the U-shaped palatal bar. It was concluded that for maximum stiffness, the maxillary major connector must cross the maxilla opposite the edentulous ridge anteriorly and posteriorly in different planes. They showed that the anteroposterior palatal bar in different planes is a good design for obtaining maximum stiffness and that the U-shape is less desirable. In this study, as mentioned earlier, design modifications of the U-shaped palatal major connector extend in more than one plane.
| Conclusions|| |
Within the limitations of this three-dimensional FEA study, the following inferences were made:
- Different angulations and different magnitude of forces induced different stress patterns in the U-shaped major connector designs, palatal mucosa and periodontal ligaments.
- Increase in magnitude of forces at both the angulations increases the stress values for the U-shaped major connector designs, palatal mucosa and ligaments.
- Lateral forces generate greater stress than the vertical forces in the palatal mucosa and the periodontal ligaments.
- The double-thickness group exhibits the least stress in the U-shaped connector design followed by design modifications 1. However, it delivers the greatest stress to the palatal mucosa and the periodontal ligaments.
- Design modifications 1 delivered the least stress to the palatal mucosa and ligaments.
| Clinical Interpretation and Scope|| |
The double-thickness group exhibited the least internal stress under loading, and it is the most rigid one. Therefore, it can be considered for use in clinical situations of Kennedy class IV. But, its use may produce slight alterations in the phonetic abilities of the patient because there is an increase in the weight of the cast partial denture. It also delivers greater stress to the underlying palatal mucosa and periodontal ligament when compared with other designs. This may produce areas of stress concentration in the palatal mucosa and ligament. Therefore, recalling patients for visits on a half-yearly basis would be helpful in assessing the soft tissue alterations, if any.
On the other hand, design modification 1 can also be considered for Kennedy class IV situations as it exhibits the second-best, least internal stress under loading and, also, is reasonably rigid as it extends in three planes of the hard palate.
This study used values of the cobalt-chrome alloy. Values of commercially pure titanium, super elastic titanium alloy can also be used for further studies.
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Department of Prosthodontics and Implantology, Meenakshi Ammal Dental College and Hospital, Chennai
Source of Support: None, Conflict of Interest: None
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2], [Table 3], [Table 4]