• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Clinics in Shoulder and Elbow
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• v.17 no.3
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• pp.114-119
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• 2014

Background: To evaluate clinical and radiological outcome using AO hook locking plate in acute acromioclavicular joint injuries. Methods: This study was based on patients with Rockwood type 3 or 5 acromioclavicular joint injuries who received surgery with AO hook locking plate from June 2008 until June 2009. Among the 22 patients, 19 of them were male and 3 were female, the mean age was $44.4{\pm}15.57$ years (20-72 years) and follow-up period was $15.5{\pm}3.90$ months (12-23 months). Preoperatively, postoperatively, and at the final follow-up after the plate removal, both coracoclavicular distances were measured from the anteroposterior radiograph. Also, the Shoulder Rating Scale of the University of California at Los Angeles scores (UCLA scores), the American Shoulder and Elbow Surgeons scores (ASES scores), Constant scores, and the Korean Shoulder Society scores (KSS scores) were measured at the final followup to evaluate the function of the shoulder joint. Results: At the time of injury, the mean coracoclavicular distance of the injured side was $17.69{\pm}4.23mm$ (9.57-27.82 mm) and the unaffected side was $7.55{\pm}2.20mm$ (3.24-13.05 mm). The mean coracoclavicular distance measured postoperatively and at the final follow-up was $6.87{\pm}2.34mm$ (4.07-14.13 mm) and $8.47{\pm}2.96mm$ (4.37-17.48 mm), respectively. The mean UCLA, ASES, Constant, and KSS scores measured in the final follow-up were $33.5{\pm}1.30$ (31-35), $90.8{\pm}8.36$ (72-100), $78.6{\pm}8.80$ (62-100), and $94.4{\pm}5.08$ (84-100) each. Conclusions: From this short-term research, the surgical treatment using AO hook locking plates in acute acromioclavicular joint injuries is clinically and radiographically satisfying and considered as a useful treatment method.

• Clinics in Shoulder and Elbow
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• v.15 no.2
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• pp.117-122
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• 2012

Purpose: To assess the effectiveness of internal fixation using a precontoured locking compression plate for the treatment of the displaced clavicle fracture by analyzing both radiological and clinical outcomes. Materials and Methods: We reviewed 34 cases of displaced clavicle shaft fracture treated by internal fixation using precontoured locking compression plates between May 2009 and February 2010. Radiological outcomes were analized on the basis of bone union and the differences between the time for bone union depending on sex and age. Clinical outcomes were analyzed on the basis of quick DASH Scores and the differences in the range of motion of the affected shoulder compared to the contralateral shoulder. Results: In the radiological evaluation, all fractures showed bone union, and the average time for bone union was 12.3 weeks, without delayed unions. Time for bone union did not differ significantly with respect to sex and age (p=0.87). In the clinical evaluation, the average final quick DASH Score was 23.5 (range, 12~42). At final follow up, the range of motion after bone union in the affected shoulder was not significantly different from that of the contralateral shoulder (p=0.69). Conclusion: The internal fixation achieved using precontoured locking compression plate in displaced clavicle shaft fracture showed effective bone union and can be considered as a reliable method with fine clinical results showing early range of motion at the shoulder joint.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.7
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• pp.2661-2669
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• 2010

In this study, a finite element formulation based first-order shear deformation theory is developed for non-linear behaviors of laminated composite plates containing matrix cracking. The multi-directional stiffness degradation is developed for adopting the stiffness variation induced from matrix cracking, which is proposed by Duan and Yao. The matrix cracking can be expressed in terms of the variation of material properties, such as Young's modulus, shear modulus and Possion ratio of plates, and sequently it is possible to predict the variation of the local stiffness. Using the assumed natural strain method, the present shell element generates neither membrane nor shear locking behavior. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear or geometrical nonlinear analysis of laminated composite plates. The results of laminated composite plates with matrix cracking may be the benchmark test for the non-linear analysis of damaged laminated composite plates.

• The Academic Congress of Korean Shoulder and Elbow Society
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• 2009.03a
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• pp.196-196
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• 2009

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.39-44
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• 1992

This paper is concerned with formulations of the hierarchical $C^{o}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method we proposed to verify the superior convergence and algorithmic efficiency with the help of the clamped L-shaped plate problems.s.

• Structural Engineering and Mechanics
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• v.9 no.1
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• pp.99-110
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• 2000

The objective of this paper is to extend the use of the improved degenerated shell element to the linear and the large displacement analysis of plates and shells with laminated composites. In the formulation of the element stiffness, the combined use of three different techniques was made. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. The total Lagrangian approach has been utilized for the definition of the deformation and the solution to the nonlinear equilibrium equations is obtained by the Newton-Raphson method. The applicability and accuracy of this improved degenerated shell element in the analysis of laminated composite plates and shells are demonstrated by solving several numerical examples.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.2284-2291
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• 2010

In this paper, we investigate the vibration analysis of plates, using an 8-node shell element that accounts for the transverse shear strains and rotary inertia. The forced vibration analysis of plates subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve an 8-node shell element for forced vibration analysis, the new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory which allows the shear deformation without shear correction factor and rotary inertia effect to be considered is adopted for development of 8-node assumed strain shell element. In order to validate the finite element numerical solutions, the reference solutions of plates are presented. Results of the present theory show good agreement with the reference solution. In addition the effect of damping is investigated on the forced vibration analysis of plates.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.