• Steel and Composite Structures
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• v.47 no.3
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• pp.365-374
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• 2023

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

• Structural Engineering and Mechanics
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• v.8 no.1
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• pp.19-26
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• 1999

Superior performance of field consistent eight-node hexahedron element in static bending problems has already been demonstrated in literature. In this paper, its performance in free vibration is investigated. Free vibration frequencies of typical test problems have been computed using this element. The results establish its superior performance in free vibration, particularly in thin plate application and near incompressibility regimes, demonstrating that shear locking, Poisson's stiffening and volumetric locking have been eliminated.

• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.575-593
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• 2002

Based on the Mindlin plate theory, a refined discrete 15-DOF triangular laminated composite plate finite element RDTMLC with the re-constitution of the shear strain is proposed. For constituting the element displacement function, the exact displacement function of the Timoshenko's laminated composite beam as the displacement on the element boundary is used to derive the element displacements. The proposed element can be used for the analysis of both moderately thick and thin laminated composite plate, and the convergence for the very thin situation can be ensured theoretically. Numerical examples presented show that the present model indeed possesses the properties of higher accuracy for anisotropic laminated composite plates and is free of locking even for extremely thin laminated plates.

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

• Architectural research
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• v.18 no.3
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• pp.113-120
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• 2016

The stability and resistance of the plates under in-plane loading is crucial in the design of structures. For the assessment of structural stability, it is necessarily required to have accurate finite element technologies. Therefore, the enhanced 9-node plate (Q9-ANS) element is introduced for the linear buckling analysis of plate where the critical buckling load has to be determined. The Q9-ANS is developed with the Reissner-Mindlin (RM) assumptions which consider transverse shear deformation of the plate. Assumed shear strain is used to alleviate the shear locking phenomenon. Numerical examples are carried out to verify the performance of the Q9-ANS element in calculation of critical buckling load of the plates.

• Clinics in Shoulder and Elbow
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• v.12 no.1
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• pp.44-52
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• 2009

Purpose: We assessed the radiographic and clinical results of one surgeon's experience treating proximal humerus fractures with a locked proximal humeral plate. Materials and Methods: Twenty patients with unstable proximal humerus fractures were treated with a locking compression plate between February 2005 and September 2007. The average age of the patients was 60.6 years, and the average postoperative follow-up period was 22.3 months. The clinical results were evaluated using the Constant and DASH scores. The radiologic results were evaluated by the Paavolainen method, which measures the neck shaft angle and humeral head height. Results: At the last follow-up examination, the mean Constant score was 75.3 and 15 cases (75%) had excellent or good results; the mean DASH score was 16.4. The mean neck shaft angle was $137.1^{\circ}$, and 19 cases (95%) had good results by the Paavolainen method. There was one delayed union, malunion, and screw loosening. Conclusion: The patients treated with a locking compression plate had relatively good clinical and radiologic results, and a low complication rate. Moreover, the patients could exercise earlier due to good reduction and initial stability. Treatment of unstable proximal humerus fractures with a locking compression plate is a reliable method.

• Journal of Trauma and Injury
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• v.26 no.4
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• pp.286-290
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• 2013

Purpose: To report the postoperative Clinical and Radiological outcomes following distal femoral fractures in elderly patients compared with young patients. Methods: From March, 1996 to March, 2012, 83 patients who received surgical treatment for fractures of the distal femur were enrolled in this retrospective study. Ages more than 65 was named group A. Group A was 49 cases and mean age is 72.5 year(65~91year). Group B was 49 cases and mean age is 45.7 year(16~61 year). Surgical methods are retrograde IM nail, locking compression plate, cannulated screw and postoperative rehabilitation is no difference between two groups. Clinical results were evaluated using Neer scores, radiographic results and the presence of clinical complications. Results: The mean union period was 18.4(12-40) weeks in group A and 17(10-24) weeks in group B. Neer functional scores are no significant statistical difference between two groups. There are 5 cases metal breakage in group A and 1case in group B. There are 3 cases nonunion in group A and 1 case in group B. Conclusion: In the case of fractures of the distal femur in elderly patients, locking plate using minimally invasive percutaneous periosteal osteosynthesis (MIPPO) technique may be one of the most effective methods and preoperative bone stock evaluation in important.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.728-732
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• 2004

In the FE analysis of sheet metal forming, efficient results can be obtained by using shell elements rather than using solid elements. However, shell elements have some limitations to describe three-dimensional material laws. In the recent years, solid-shell element, which has only translational degree of freedom like solid element, has been presented. The assumed nature strain (ANS) and enhanced assumed strain (EAS) methods can be used to remove several solid-shell locking problems. In this paper, ANS method was used for diminish transverse shear locking and EAS method for thickness locking. Using the element, the steel pipe making process from flat plate analyzed effectively, which is including bending and welding.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.205-229
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• 2012

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations ${\theta}_x$ and ${\theta}_y$ are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

• Journal of Trauma and Injury
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• v.26 no.3
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• pp.163-169
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• 2013

Purpose: This study was conducted to confirm the anatomic conformity of the new periarticular locking plates designed by Zimmer on Korean adult bones and to identify the structures at risk during the application of these implants. Methods: The study was performed on the humerus, radius, and tibia of 10 adult cadavers(6 males and 4 females) procured from the cadaveric lab of our hospital. Anteroposterior (AP) and lateral X-rays were taken to confirm that the cadavers were free of any unusual lesions or anatomic variations. We used the 3.5-mm proximal humerus plate, 2.7-mm distal radius plate, 3.5- and 5.0-mm proximal tibia plates, and 3.5-mm distal tibia plate developed by Zimmer, Inc. (Zimmer periarticular locking plate). The longest plate from each group was used to confirm anatomical conformity. Standard approaches were used for each area, and soft tissue was retracted in order to pass the plate beneath the muscle. The position of the plate was confirmed using standard AP and lateral view X-rays. After this procedure had been completed, the region was dissected along the length of the implant to determine the conformity of the implant to bone and the penetrations of screws into the articular surface or violations of any vital structures, such as nerves, blood vessels, or tendons. Results: Excellent anatomical conformity was observed with Zimmer periarticular locking plates for Korean adults. The tibial nerve and the posterior tibial artery were found to be structures at risk when applying a distal tibial plate. Conclusion: Additional posterolateral fixation is recommended when dealing with cases of tibial plateau fracture when the fracture line extends to the posterolateral cortex. We recommend taking proper views using 10~15 degrees of internal rotation to ensure correct screw length and, thus, avoid penetration of vital structures and tendons.