• Structural Engineering and Mechanics
• /
• v.65 no.3
• /
• pp.213-222
• /
• 2018

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Journal of Korean Neurosurgical Society
• /
• v.45 no.4
• /
• pp.213-218
• /
• 2009

Objective : This study is a retrospective clinical study over more than 4 years of follow up to understand the mechanism of load sharing across the graft-bone interface in the static locking plate (SLP) fixation compared with non-locking plate (NLP). Methods : Orion locking plates and Top non-locking plates were used for SLP fixation in 29 patients and NLP fixation in 24 patients, respectively. Successful interbody fusion was estimated by dynamic X-ray films. The checking parameters were as follows : screw angle (SA) between upper and lower screw, anterior and posterior height of fusion segment between upper and lower endplate (AH & PH), and upper and lower distance from vertebral endplate to the end of plate (UD & LD). Each follow-up value of AH and PH were compared to initial values. Contributions of upper and lower collapse to whole segment collapse were estimated. Results : Successful intervertebral bone fusion rate was 100% in the SLP group and 92% in the NLP group. The follow-up mean value of SA in SLP group was not significantly changed compared with initial value, but follow-up mean value of SA in NLP group decreased more than those in SLP group (p=0.0067). Statistical analysis did not show a significant difference in the change in AH and PH between SLP and NLP groups (p>0.05). Follow-up AH of NLP group showed more collapse than PH of same group (p=0.04). The upper portion of the vertebral body collapsed more than the lower portion in the SLP fixation (p=0.00058). Conclusion : The fused segments with SLP had successful bone fusion without change in initial screw angle, which was not observed in NLP fixation. It suggests that there was enough load sharing across bone-graft interface in SLP fixation.

• Clinics in Shoulder and Elbow
• /
• v.20 no.4
• /
• pp.217-221
• /
• 2017

Background: The purpose of this study was to evaluate the clinical and radiographic outcomes of internal fixation with locking T-plates for osteoporotic fractures of the proximal humerus in patients aged 65 years and older. Methods: From January 2007 through to December 2015, we recruited 47 patients aged 65 years and older with osteoporotic fractures of the proximal humerus. All fractures had been treated using open reduction and internal fixation with a locking T-plate. We classified the fractures in accordance to the Neer classification system; At the final follow-up, the indicators of clinical outcome-the range of motion of the shoulder (flexion, internal rotation, and external rotation) and the presence of postoperative complications-and the indicators of radiographic outcome-the time-to-union and the neck-shaft angle of the proximal humerus-were evaluated. The Paavolainen method was used to grade the level of radiological outcome in the patients. Results: The mean flexion was $155.0^{\circ}$ (range, $90^{\circ}-180^{\circ}$), the mean internal rotation was T8 (range, T6-L2), and the mean external rotation was $66.8^{\circ}$ (range, $30^{\circ}-80^{\circ}$). Postoperative complications, such as plate impingement, screw loosening, and varus malunion were observed in five patient. We found that all patients achieved bone union, and the mean time-to-union was 13.5 weeks of the treatment. The mean neck-shaft angle was $131.4^{\circ}$ at the 6-month follow-up. According to the Paavolainen method, "good" and "fair" radiographic results each accounted for 38 and 9 of the total patients, respectively. Conclusions: We concluded that locking T-plate fixation leads to satisfactory clinical and radiological outcomes in elderly patients with proximal humeral fractures by providing a larger surface area of contact with the fracture and a more rigid fixation.

• Clinics in Shoulder and Elbow
• /
• v.17 no.1
• /
• pp.2-9
• /
• 2014

Background: Indirect reduction technique offers a valid option in the treatment of proximal humerus fracture. The purpose of this study is to evaluate the functional outcome and the complication rate after indirect reduction and internal fixation of unstable proximal humeral fractures with use of a locking plate. Methods: Twenty four patients with acute proximal humerus fracture were managed with indirect reduction and internal fixation with a locking plate. The mean follow-up period was 15.5 months. Results: The anatomical reduction of the medial cortex buttress was seen in 16 patients (66%) of the Group A and the non-anatomical reduction was seen in 8 patients (33%) of the Group B. Mean union time was $3.2{\pm}1.9$ months; it was $2.2{\pm}0.6$ months in the Group A and $5.3{\pm}2.2$ months in the Group B (p < 0.05). In our series, there were 6 cases of complications and these include 2 cases of varus malunion, 2 cases of shoulder stiffness, 1 case of heterotrophic ossification, 2 cases of screw perforation and 1 case of impingement. Conclusions: We conclude from our studies that indirect reduction and internal fixation using locking plate for acute proximal humerus fracture can give good results with bony union and predictable good overall functional outcome. If the medial cortex buttress is well maintained, a better anatomical reduction would be achieved, the union would be prompted, the pain would be further reduced and the range of the motion would be recovered more promptly.

• Clinics in Shoulder and Elbow
• /
• v.21 no.4
• /
• pp.227-233
• /
• 2018

Background: The purpose of this study was to compare the radiologic results of patients who underwent surgery with a hook plate and a locking plate in distal clavicle fractures. Methods: Sixty patients underwent surgical treatment for Neer type IIa, IIb, III, and V distal clavicle fracture. Twenty-eight patients underwent fracture fixation with a hook plate and 32 with a locking plate. Coracoclavicular distance was measured on standard anteroposterior radiographs before and after the surgery, and union was confirmed by radiograph or computed tomography taken at 6 months postoperatively. Other radiologic complications like osteolysis was also checked. Results: Bony union was confirmed in 59 patients out of 60 patients, and 1 patient in the hook plate group showed delayed union. Coracoclavicular distance was decreased more in the hook plate group after surgery (p<0.01). After 6 weeks of the hook plate removal, the coracoclavicular distance was increased a little compared to before metal removal, but there was no difference compared to the contralateral shoulder. Eleven out of 28 patients (39.3%) showed osteolysis on the acromial undersurface in the hook plate group. Conclusions: Both the hook plate group and the locking plate group showed satisfactory radiologic results in distal clavicle fractures. Both hook plate and locking plate could be a good treatment option if it is used in proper indication in distal clavicle fracture with acromioclavicular subluxation or dislocation.

• Structural Engineering and Mechanics
• /
• v.57 no.3
• /
• pp.473-506
• /
• 2016

The aim of this work is the development of a 2D quadrilateral isoparametric finite element model, based on a layerwise approach, for the bending analysis of sandwich plates. The face sheets and the core are modeled individually using, respectively, the first order shear deformation theory and the third-order plate theory. The displacement continuity condition at the interfaces 'face sheets-core' is satisfied. The assumed natural strains method is introduced to avoid an eventual shear locking phenomenon. The developed element is a four-nodded isoparametric element with fifty two degrees-of-freedom (52 DOF). Each face sheet has only two rotational DOF per node and the core has nine DOF per node: six rotational degrees and three translation components which are common for the all sandwich layers. The performance of the proposed element model is assessed by six examples, considering symmetric/unsymmetric composite sandwich plates with different aspect ratios, loadings and boundary conditions. The numerical results obtained are compared with the analytical solutions and the numerical results obtained by other authors. The results indicate that the proposed element model is promising in terms of the accuracy and the convergence speed for both thin and thick plates.

• Steel and Composite Structures
• /
• v.42 no.1
• /
• pp.23-32
• /
• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Clinics in Shoulder and Elbow
• /
• v.20 no.1
• /
• pp.37-41
• /
• 2017

Background: Increased frequency of comminuted clavicle mid-shaft fractures and importance of functional satisfaction through early joint exercise has resulted in higher emphasis on surgical treatments. This study aimed to evaluate the clinical radiological results of treatment of clavicle mid-shaft fractures by open reduction and internal fixation using a plate with a small incision. Methods: The subjects of this study were 80 clavicle mid-shaft fracture cases treated with internal fixation using a plate from October 2010 to July 2014. Clavicle mid-shaft fractures were internally fixated using anatomical plates or locking compression plates. Achievement of bone union, union period, and clavicle length shortening were evaluated radiologically, and clinical assessment was done by using Constant and University of California at Los Angeles (UCLA) scores. Results: All 80 cases were confirmed to have achieved bone union through radiographs with an average union period of 10.9 weeks (range: 7-18 weeks). The average clavicle length of shortening in the affected side was 1.8 mm (range: 0-17 mm). The average UCLA score and Constant score were 33.6 (range: 25-35) and 92.5 (range: 65-100), respectively. Regarding complications, four cases reported skin irritation by metal plates, and one case reported a screw insertion site fracture due to minor trauma history. Conclusions: We were able to induce successful bone union and obtain clinically satisfactory results in displaced mid-shaft fractures of the clavicle without major complications such as nonunion through treatment of internal fixation using a plate.

• Structural Engineering and Mechanics
• /
• v.18 no.1
• /
• pp.79-90
• /
• 2004

A high precision shear deformable triangular element has been proposed for bending analysis of triangular plate. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has thirty-five degrees of freedom, which has been reduced to thirty by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different boundary conditions, side ratios (b/a) and thickness ratios (h/a = 0.001, 0.1 and 0.2) have been analyzed using the proposed shear locking free element. Concentrated and uniformly distributed transverse loads have been used for the analysis. The formulation is made based on first order shear deformation theory. For validation of the present element and formulation few results of thin triangular plate have been compared with the analytical solutions. Results for thick plate have been presented as new results.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.7 no.2
• /
• pp.324-345
• /
• 2015

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature.