• Structural Engineering and Mechanics
• /
• 제70권5호
• /
• pp.525-534
• /
• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Structural Engineering and Mechanics
• /
• 제68권2호
• /
• pp.171-182
• /
• 2018

For the first time, nonlocal damped vibration and buckling analyses of arbitrary tapered bidirectional functionally graded solid circular nano-plate (BDFGSCNP) are presented by employing modified spectral Ritz method. The energy method based on Love-Kirchhoff plate theory assumptions is applied to derive neutral equilibrium equation. The Eringen's nonlocal continuum theory is taken into account to capture small-scale effects. The characteristic equations and corresponding first mode shapes are calculated by using a novel modified basis in spectral Ritz method. The modified basis is in terms of orthogonal shifted Chebyshev polynomials of the first kind to avoid employing adhesive functions in the spectral Ritz method. The fast convergence and compatibility with various conditions are advantages of the modified spectral Ritz method. A more accurate multivariable function is used to model two-directional variations of elasticity modulus and mass density. The effects of nanoscale, in-plane pre-load, distributed dashpot, arbitrary tapering, pinned and clamped boundary conditions on natural frequencies and buckling loads are investigated. Observing an excellent agreement between results of current work and outcomes of previously published works in literature, indicates the results' accuracy in current work.

• Structural Engineering and Mechanics
• /
• 제54권1호
• /
• pp.87-103
• /
• 2015

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake's length and thickness on the critical buckling load.

• 한국복합재료학회:학술대회논문집
• /
• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
• /
• pp.211-214
• /
• 2000

Filament wound pressure vessels have been studied for the efficient design tool to consider the variation of fiber angles through-the thickness direction. Filament winding patterns were simulated from semi-geodesic fiber path equation to calculate fiber path on arbitrary surface. Finite element analyses were performed considering fiber angle variation in longitudinal and thickness directions by ABAQUS. For the finite element modeling of the pressure tank, the 3-dimensional layered solid element was utilized. From the stress results of pressure tanks, maximum stress criterion in transverse direction was applied to modify material properties for failed region. In the end of each load increment, resultant layer stresses were compared with a failure criterion and properties were reduced to 1/10 for a failed layer. Results of progressive failure analysis were compared with two experimental data.

• Coupled systems mechanics
• /
• 제9권4호
• /
• pp.381-396
• /
• 2020

Analytical investigation of the fracture of inhomogeneous beam with two parallel lengthwise cracks is performed. The thickness of the beam varies continuously along the beam length. The beam is loaded in three-point bending. Two beam configurations with different lengths of the cracks are analyzed. The two cracks are located arbitrary along the thickness of the beam. Solutions to the strain energy release rate are derived assuming that the material has non-linear elastic mechanical behavior. Besides, the beam exhibits continuous material inhomogeneity along its thickness. The balance of the energy is analyzed in order to derive the strain energy release rate. Verifications of the solutions are carried-out by considering the complementary strain energy stored in the beam configurations. The influence of the continuous variation of the thickness along the beam length on the lengthwise fracture behavior is investigated. The dependence of the lengthwise fracture on the lengths of the two parallel cracks is also studied.

• Steel and Composite Structures
• /
• 제34권3호
• /
• pp.361-376
• /
• 2020

This paper presents a free vibration analysis of shell panels made of functionally graded material (FGM) in the form of the ordinary and sandwich FGM and laminated shells using the isogeometric B3-spline finite strip method (IG-SFSM). B3-spline and Lagrangian interpolation are employed along the longitudinal and transverse directions respectively in this type of finite strip. The introduced finite strip formulation is based on the degenerated shell method, which provides variable thickness, arbitrary geometries, and analysis of thin or thick shells. Validity of the obtained natural frequencies by IG-SFSM is checked by comparison with results extracted from references for similar cases in different examples. These examples incorporate several geometries, materials, boundary conditions, and continuous thickness variation. A comparison of these two kinds of results and their proximity showed that the introduced IG-SFSM is a reliable tool which can be used in analysis of shells with the aforementioned properties.

• Composites Research
• /
• 제13권2호
• /
• pp.51-60
• /
• 2000

본 논문에서는 두께 방향의 와인딩 각도 변화를 고려한 필라멘트 와인딩 된 압력탱크의 해석을 수행하였다. 두께방향의 와인딩 각도를 고려하기 위하여 임의의 맨드릴 표면에 대한 필라멘트 와인딩 궤적을 찾아낼 수 있는 semi-geodesic path식을 도입하였다. 필라멘트 와인딩 된 압력탱크의 유한요소 모델링을 위하여 3차원 적층고체요소를 사용하였으며, 상용프로그램ABAQUS를 이용하여 유한요소해석을 수행하였다. 해석에서는 모재 파손에 의한 강성저하를 모사하기 위하여 재료 비선형성을 고려하였으며, 이를 위하여 각 하중 증분 후에 섬유 수직방향 응력을 모재의 인장강도와 비교하는 최대응력파손이론을 도입하였고, 파손이 일어난 층에 대해서 모재 방향의 재료 상수를 1/10로 저하시켰다. 그리고, 점진적 파손해석을 수행한 결과를 문헌에 주어진 실험데이터와 비교하였다.

• Steel and Composite Structures
• /
• 제34권5호
• /
• pp.657-670
• /
• 2020

In this paper, vibration analysis of functionally graded nanoshell is studied based on the sinusoidal higher-order shear and normal deformation theory to account thickness stretching effect. To account size-dependency, Eringen nonlocal elasticity theory is used. For more accurate modeling the problem and corresponding numerical results, sinusoidal higher-order shear and normal deformation theory including out of plane normal strain is employed in this paper. The radial displacement is decomposed into three terms to show variation along the thickness direction. Governing differential equations of motion are derived using Hamilton's principle. It is assumed that the cylindrical shell is made of an arbitrary composition of metal and ceramic in which the local material properties are measured based on power law distribution. To justify trueness and necessity of this work, a comprehensive comparison with some lower order and lower dimension works and also some 3D works is presented. After presentation of comparative study, full numerical results are presented in terms of significant parameters of the problem such as small scale parameter, length to radius ratio, thickness to radius ratio, and number of modes.

• 한국구조물진단유지관리공학회 논문집
• /
• 제8권2호
• /
• pp.147-158
• /
• 2004

많은 장점을 가진 복합재료를 사용한 보강판에 대하여 지금까지 많은 연구자들이 변위법에 근거한 등매개변수 평판 요소와 보요소를 결합한 유한요소법을 사용하여왔다. 이러한 유한요소법은 보요소를 평판 요소의 절점에 대한 강성으로 치환하기 때문에 보강재에 대한 국부적인 거동을 파악할 수 없으며 복합적층 구조인 경우 그 적용성이 제한적이다. 따라서, 본 연구에서는 복합재료 보강판의 해석에 있어 보강재 및 판에 대하여 3차원 쉘요소를 사용하여 거동을 분석하고자 한다. 본 연구에서는 Reissner-Mindlin의 1차 전단변형이론을 사용하였다. 그러나 Reissner-Mindlin이론에 의한 등매개변수 평판 휨 요소는 판의 두께가 얇아지는 경우 일반적으로 전단잠김현상과 가상의 제로에너지 모드가 발생하는데 이를 제거하기 위해 대체전단변형률장을 사용하였다. 폭-두께비, 형상비 뿐만아니라 경사판의 경사각 변화에 따른 임의방향 보강재를 갖는 단순지지된 복합적층 구형 및 경사판에 대한 처짐분포를 비교 분석하였다.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2008년도 춘계학술대회논문집
• /
• pp.300-303
• /
• 2008

In the present study, the simple form of the heat transfer equation were suggested to estimate the temperature variation inside the oil pipe in order to determine the thickness of the insulating materials to retain the working oils below the critical temperature. The conservation of the thermal energy at arbitrary time were modeled to one dimensional unsteady equation with the empirical formula or data. The calculating results for non-insulation case showed that the temperature were very sensitive to the thermal convection by the velocity of the external wind. For insulation case, the insulation material which has higher density and specific heat, lower thermal conductivity should be chosen with more brighter coloring outside the pipe in order to retain the working oils below the critical temperature.