• Steel and Composite Structures
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• 제29권3호
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Computers and Concrete
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• 제33권3호
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• pp.241-250
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• 2024

This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

• 대한조선학회논문집
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• 제31권1호
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• pp.142-154
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• 1994

본 논문에서는 정하중을 받는 보강 원통형 쉘의 확률론적 초기결함 민감도 해석을 수행하였다. Donnell의 쉘이론, Galerkin 근사법에 의거 좌굴하중 도출을 위한 다중모드 정식화를 수행하고 이에 random한 기하학적 초기결함의 확률장 이론 및 응답면 기법을 결합하였다. 계산된 확률론적 좌굴하중 결과로부터 신뢰도 지수-하중, 신뢰도 지수-안전계수의 관계를 구할 수 있고 이를 이용하면 요구되는 안전계수의 범위, 허용가능 초기결함의 범위 설정이 가능할 것이다.

• Structural Engineering and Mechanics
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• 제16권3호
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• pp.361-369
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• 2003

In this paper, the structural behavior of R/C cylindrical panel is analyzed by experimental results. To avoid the geometric imperfection, R/C shell specimens are made by use of a stiff steel mold. From experimental results, the load carrying behavior of R/C cylindrical panel is presented under an external lateral pressure. Even if R/C shell does not posses geometric imperfections, the inaccuracy of the reinforcement position strongly affects to the ultimate strength and the failure patterns of such shells. To explain these effects, FEM nonlinear analyses are done under the same conditions as those of experiments. The behavior of R/C cylindrical shells are well simulated under the consideration of both the geometric imperfection and several inaccuracies.

• Steel and Composite Structures
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• 제33권2호
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• pp.245-259
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• 2019

The present study aims to investigate the ultimate strength and geometric nonlinear behavior of composite plates containing initial imperfection subjected to combined end-shortening strain and lateral pressure loading by using a semi-analytical method. In this study, the first order shear deformation plate theory is considered with the assumption of large deflections. Regarding in-plane boundary conditions, two adjacent edges of the laminates are completely held while the two others can move straightly. The formulations are based on the concept of the principle of minimum potential energy and Newton-Raphson technique is employed to solve the nonlinear set of algebraic equations. In addition, Hashin failure criteria are selected to predict the failures. Further, two distinct models are assumed to reduce the mechanical properties of the failure location, complete ply degradation model, and ply region degradation model. Degrading the material properties is assumed to be instantaneous. Finally, laminates having a wide range of thicknesses and initial geometric imperfections with different intensities of pressure load are analyzed and discuss how the ultimate strength of the plates changes.

• Structural Engineering and Mechanics
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• 제87권1호
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• pp.85-94
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• 2023

In the present work, thermal buckling and post-buckling behaviors of imperfect graphene platelet reinforced metal foams (GPRMFs) doubly curved shells are examined. Material properties of GPRMFs doubly curved shells are presumed to be the function of the thickness. Reddy' shell theory incorporating geometric nonlinearity is utilized to derive the governing equations. Various types of the graphene platelets (GPLs) distribution patterns and doubly curved shell types are taken into account. The nonlinear equations are discretized for the case of simply supported boundary conditions. The thermal post-buckling response are presented to analyze the effects of GPLs distribution patterns, initial geometric imperfection, GPLs weight fraction, porosity coefficient, porosity distribution forms, doubly curved shell types. The results show that these factors have significant effects on the thermal post-buckling problems.

• Steel and Composite Structures
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• 제45권5호
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

• Structural Engineering and Mechanics
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• 제90권4호
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Composites Research
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• 제34권5호
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• pp.283-289
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• 2021

본 연구에서는 압축력을 받는 얇은 복합재 원통 구조에 대하여 기하학적 혹은 하중에 대한 초기 결함 모델을 이용하여 수치해석적으로 좌굴 Knockdown factor를 새롭게 도출하였다. 전역 좌굴이 발생하기 이전에 타원형상의 변형 형상을 갖는 복합재 원통 구조를 사용하였다. 복합재 원통 구조의 기하학적 초기 결함만 고려하기 위하여 Single Perturbation Load Approach를 이용하였으며, 기하학적 초기 결함과 더불어 하중 불균일을 함께 구현하기 위하여 Single Boundary Perturbation Approach를 사용하였다. 기하학적 초기 결함 모델의 좌굴 Knockdown factor는 NASA의 기존의 좌굴 Knockdown factor보다 약 84% 높게 도출되었으며, 좌굴 시험에 비하여서는 약 9% 낮게 도출되었다. 기하학적 초기 결함과 하중 불균일을 함께 고려하는 모델의 좌굴 Knockdown factor는 NASA의 좌굴 Knockdown factor에 비하여서는 약 75% 높게, 그리고 좌굴 시험보다 약 14% 낮게 계산되었다. 따라서, 본 연구의 좌굴 설계 기준은 고려된 초기 결함 모델과 상관없이 기존의 좌굴 설계 기준에 비하여 경량 설계의 제공이 가능함과 동시에 좌굴 시험 대비 적절히 보수적인 설계 기준을 제공할 수 있음을 확인하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.585-591
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• 2003

It has been widely known that geometrical or form errors of ball bearings such as ball size error, ball waviness, inner and outer race waviness due to inherent manufacturing imperfection are one of the major sources of uncontrollable non-repeatable run-out (NRRO) vibration in HDD spindle motor. NRRO in HDD is also known to be the primary cause of limiting the storage capacity of HDD. In this paper, We performed vibration analysis for NRRO a ball bearing being used in 3.5" HDD spindle motor. To theoretically estimate NRRO considering the geometrical errors of ball bearing components, a simple three degrees of freedom model was proposed and then vibration analysis for axial and radial NRRO was conducted utilizing the measured geometric imperfection of a bearing with both the waviness magnitude and phase taken into account. Effects of bearing preload and clearance on NRRO was also investigated as an effort to predict their optimum values minimizing bearing NRRO.