• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.221-238
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• 2016

One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non-cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.

• International Journal of Aeronautical and Space Sciences
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• v.1 no.2
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• pp.9-16
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• 2000

For aerodynamic design of missile bodies of non-circular cross-section, the combination of the slender body theory and the cross-flow analogy can hardly be applied owing to the lack of experimental data. An alternative is to utilize the Euler solution in the design stage. For enhanced accuracy, however, an adequate viscous correction is necessary to the Euler solution. In this work, such a procedure is examined to compensate the viscous effect by utilizing the concept of proportionality factor in cross-flow analogy. Predictions of aerodynamic coefficients combining the Euler solution and the viscous correction via proportionality factor are made for a missile body of elliptic cross-section. Results indicate that the present approach can be adopted in designing missile bodies of non-circular cross-sections.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.66-72
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• 1997

Circular-to-rectangular transition ducts are used as exhaust components of high performance fighter aircraft with vectored thrust nozzles. Three-dimensional incompressible Navier-Stokes solver is used to analyze the transition duct. Cross sections of transition duct are defined by superelliptic equation. The grid system is generated by Non-Uniform Rational B-Spline, after generating surface grid by blending the cross sections. Good agreement between the results of the computational simulation and the experimental data is observed.

• Steel and Composite Structures
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• v.18 no.3
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• pp.659-672
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• 2015

This research deals with the analytical solution of a curved beam with different shapes made of functionally graded materials (FGM's). It was assumed that modulus of elasticity is graded along the thickness direction of curved beam based on a power function. The beam was loaded under pure bending. Using the linear theory of elasticity, the general relation for radial distribution of radial and circumferential stresses of arbitrary cross section was derived. The effect of nonhomogeneity was considered on the radial distribution of circumferential stress. This behavior can be investigated for positive and negative values of nonhomogeneity index. The novelty of this study is application of the obtained results for different combination of material properties and cross sections. Achieved results indicate that employing different nonhomogeneity index and selection of various types of cross sections (rectangular, triangular or circular) can control the distribution of radial and circumferential stresses as designer want and propose new solutions by these options. Increasing the nonhomogeneity index for positive or negative values of nonhomogeneity index and for various cross sections presents different behaviors along the thickness direction. In order to validate the present research, the results of this research can be compared with previous result for reachable cross sections and non homogeneity index.

• Coupled systems mechanics
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• v.8 no.5
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• pp.377-391
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• 2019

The present paper is focused on analyzing the delamination of inhomogeneous multilayered rods of circular cross-section loaded in torsion. The rods are made of concentric longitudinal layers of individual thickness and material properties. A delamination crack is located arbitrary between layers. Thus, the internal and external crack arms have circular and ring-shaped cross-sections, respectively. The layers exhibit continuous material inhomogeneity in radial direction. Besides, the material has non-linear elastic behavior. The delamination is analyzed in terms of the strain energy release rate. General solution to the strain energy release rate is derived by considering the energy balance. The solution is applied to analyze the delamination of cantilever rod. For verification, the strain energy release rate is derived also by considering the complementary strain energy.

• Advances in materials Research
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• v.5 no.4
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• pp.299-318
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• 2016

Analytical investigations were performed of a longitudinal crack representing a cylindrical surface in circular shafts loaded in torsion with taking into account the non-linear material behavior. Both functionally graded and multilayered shafts were analyzed. It was assumed that the material is functionally graded in radial direction. The mechanical behavior of shafts was modeled by using non-linear constitutive relations between the shear stresses and shear strains. The fracture was studied in terms of the strain energy release rate. Within the framework of small strain approach, the strain energy release rate was derived in a function of the torsion moments in the cross-sections ahead and behind the crack front. The analytical approach developed was applied to study the fracture in a clamped circular shaft. In order to verify the solution derived, the strain energy release rate was determined also by considering the shaft complimentary strain energy. The effects were evaluated of material properties, crack location and material non-linearity on the fracture behavior. The results obtained can be applied for optimization of the shafts structure with respect to the fracture performance. It was shown that the approach developed in the present paper is very useful for studying the longitudinal fracture in circular shafts in torsion with considering the material non-linearity.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.41-54
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• 1999

For free vibration of non-symmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for in-plane free vibration behaviors of simply supported thin-walled curved beams with monosymmetric cross-sections is newly derived. Also, a finite element formulation using two noded curved beams element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the straight beam element and the ABAQUS's shell element.

• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.195-205
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• 2013

The buckling problem of linearly tapered micro-columns is investigated on the basis of modified strain gradient elasticity theory. Bernoulli-Euler beam theory is used to model the non-uniform micro column. Rayleigh-Ritz solution method is utilized to obtain the critical buckling loads of the tapered cantilever micro-columns for different taper ratios. Some comparative results for the cases of rectangular and circular cross-sections are presented in graphical and tabular form to show the differences between the results obtained by modified strain gradient elasticity theory and those achieved by modified couple stress and classical theories. From the results, it is observed that the differences between critical buckling loads achieved by classical and those predicted by non-classical theories are considerable for smaller values of the ratio of the micro-column thickness (or diameter) at its bottom end to the additional material length scale parameters and the differences also increase due to increasing of the taper ratio.

• Journal of Korean Dental Science
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• v.15 no.1
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• pp.51-60
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• 2022

Purpose: The aim of this study was to evaluate the bio-durability and bone regeneration capacity of the non-cross-linked collagen membrane in rabbit calvarial defect models. Materials and Methods: Four circular defects with 8 mm diameter were made in each of calvarium of 10 male rabbits. The following groups was randomly assigned to each defect - 1) Control, 2) membrane group containing non-cross-linked collagen membrane only (M), 3) bone graft group (B), 4) bone graft with membrane group (B+M). Animals were sacrificed and samples were harvested at 2 weeks (n=5) and 8 weeks (n=5). Histologic sections were prepared and histomorphometric analysis was performed. Result: Histologic results showed well adaptation of the non-cross-linked membrane on each defect and normal healing response at 2 weeks. At 8 weeks, the membranes were partially biodegraded. Histomorphometrically, B and B+M group showed the significantly greater total augmented area (B+M group, 10.44±1.49, P=0.016; B group, 9.13±0.53, P=0.032) and new bone formation (B+M group, 2.89±0.93, P=0.008; B group, 2.85±1.15, P=0.008) compared to control group. Collapsing of the central portion of the membrane, membrane group showed greater value in new bone formation at 8 weeks (1.78±0.68, P=0.032). Conclusion: Within the limitations of this study, the non-cross-linked collagen membrane fabricated using the improved decellularized method was shown to be effective for the regeneration of calvarial bone defects. In addition, prolonged barrier function might be provided using this collagen membrane.

• Smart Structures and Systems
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• v.20 no.4
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• pp.473-481
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• 2017

This study suggests a simple, convenient and non-destructive method for investigation of the Young's modulus detection in stepped shafts which only utilizes the first-order resonant frequency in flexural mode and dimensions of structures. The method is based on the impulse excitation technique (IET) to pick up the fundamental resonant frequencies. The standard Young's modulus detection formulas for rectangular and circular cross-sections are well investigated in literatures. However, the Young's modulus of stepped shafts can not be directly detected using the formula for a beam with rectangular or circular cross-section. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formula to detect Young's modulus of stepped shafts. The numerical simulation performed by finite element method (FEM) to obtain enough simulation data for RSM analysis. After analysis and calculation, the relationship of flexural resonant frequencies, dimensions of stepped shafts and Young's modulus is obtained. Numerical simulations and experimental investigations show that the IET method can be used to investigate Young's modulus in stepped shafts, and the FEM simulation and RSM based IET formula proposed in this paper is applicable to calculate the Young's modulus in stepped shaft. The method can be further developed to detect mechanical parameters of more complicated structures using the combination of FEM simulation and RSM.