• 한국기계가공학회지
• /
• 제19권7호
• /
• pp.35-40
• /
• 2020

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.

• Structural Engineering and Mechanics
• /
• 제19권6호
• /
• pp.707-720
• /
• 2005

The bending stress formula that taking into account the transverse deformation is developed for plane-curved, untwisted isotropic beams subjected to loadings that result in deformations in the plane of curvature. In order to account the transverse Poisson contraction effect, a new constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved plate is derived in a $6{\times}6$ matrix form. This constitutive relation will provide the fundamental basis to the analyses of curved structures composing of isotropic or anisotropic materials. Then, the bending stress formula of a curved isotropic beam can be deduced from this newly developed curved plate theory. The stress predictions by the present analysis are compared to those by the analysis that neglected the Poisson contraction effect. The results show that the Poisson effect becomes more significant as the Poisson ratio and the curvature are getting larger.

• International Journal of Aeronautical and Space Sciences
• /
• 제9권2호
• /
• pp.41-47
• /
• 2008

The nonlinear structural analyses of high-aspect-ratio structures were performed. For the high-aspect-ratio structures, it is important to understand geometric nonlinearity due to large deflections. To consider geometric nonlinearity, finite element analyses based on the large deflection beam theory were introduced. Comparing experimental data and the present nonlinear analysis results, the current results were proved to be very accurate for the static and dynamic behaviors for both isotropic and anisotropic beams.

• 한국광학회지
• /
• 제15권3호
• /
• pp.200-213
• /
• 2004

등방성 빔 단면과 비등방성 공간 부분 코히어런스 특성을 갖는 가우시안 셀 모델 빔의 구현에 대하여 연구하였다. He-Ne 레이저의 가우시안 빔이 회전하는 홀로그래픽 확산판을 통과하면서 생성된 확산광을 등방성 빔 단면과 비등방성 공간 코히어런스 특성을 갖는 가우시안 셀 모델 빔으로 만드는 광학계를 제안하였다. 광학계의 해석적 설계 방정식을 유도하였고 이를 사용한 설계 예를 제시하였다.

• Advances in nano research
• /
• 제16권5호
• /
• pp.445-458
• /
• 2024

The objective of this paper is to present free vibration and static stability analyses of rotating composite beams reinforced with carbon nanotubes (CNTs) under uniform thermal loads. Beam structural equations and CNT-reinforced composite (CNTRC) beam formulations are derived based on Timoshenko beam theory (TBT). The temperature-dependent properties of the beam material, such as the elastic modulus, shear modulus, and material density, are assumed to vary over the thickness according to the rule of mixture. The beam material is modeled as a mixture of single-walled carbon nanotubes (SWCNTs) in an isotropic matrix. The SWCNTs are aligned and distributed in the isotropic matrix with different patterns of reinforcement, namely the UD (uniform), FG-O, FG-V, FG- Λ and FG-X distributions, where FG-V and FG- Λ are asymmetric patterns. Numerical examples are presented to illustrate the effects of several essential parameters, including the rotational speed, hub radius, effective material properties, slenderness ratio, boundary conditions, thermal force, and moments due to temperature variation. To the best of the authors' knowledge, this study represents the first attempt at the finite element modeling of rotating CNTRC Timoshenko beams under a thermal environment. The results are presented in tables and figures for both symmetric and asymmetric distribution patterns, and can be used as benchmarks for further validation.

• Structural Engineering and Mechanics
• /
• 제67권3호
• /
• pp.291-300
• /
• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

• Advances in nano research
• /
• 제13권4호
• /
• pp.351-368
• /
• 2022

Recently, promising structural technologies like multi-function, ultra-load bearing capacity and tailored structures have been put up for discussions. Finite Element (FE) modelling is probably the best-known option capable of treating these superior properties and multi-domain behavior structures. However, advanced materials such as Functionally Graded Material (FGM) and nanocomposites suffer from problems resulting from variable material properties, reinforcement aggregation and mesh generation. Motivated by these factors, this research proposes a unified shape function for FGM, nanocomposites, graded nanocomposites, in addition to traditional isotropic and orthotropic structural materials. It depends not only on element length but also on the beam's material properties and geometric characteristics. The systematic mathematical theory and FE formulations are based on the Timoshenko beam theory for beam structure. Furthermore, the introduced element achieves C1 degree of continuity. The model is proved to be convergent and free-off shear locking. Moreover, numerical results for static and free vibration analysis support the model accuracy and capabilities by validation with different references. The proposed technique overcomes the issue of continuous properties modelling of these promising materials without discarding older ones. Therefore, introduced benchmark improvements on the FE old concept could be extended to help the development of new software features to confront the rapid progress of structural materials.

• 비파괴검사학회지
• /
• 제26권3호
• /
• pp.198-205
• /
• 2006

The necessity of nondestructively inspecting austenitic steels, fiber-reinforced composites, and other inherently anisotropic materials has stimulated considerable interest in developing beam models for anisotropic media. The properties of slowness surface playa key role in the beam models based on the paraxial approximation. In this paper, we apply a modular multi-Gaussian beam (MMGB) model to study the effects of material anisotropy on ultrasonic beam profile. It is shown that the anisotropic effects of beam skew and excess beam divergence enter into the MMGB model through parameters defining the slope and curvature of the slowness surface. The overall beam profile is found when the quasilongitudinal(qL) beam propagates in the symmetry plane of transversely isotropic austenitic steels. Simulation results are presented to illustrate the effects of these parameters on ultrasonic beam diffraction and beam skew. The MMGB calculations are also checked by comparing the anisotropy factor and beam skew angle with other analytical solutions.

• 한국기계가공학회지
• /
• 제10권1호
• /
• pp.38-46
• /
• 2011

A study was performed to investigate the dynamic behaviors of fiber-reinforced composite materials subjected to transversely low-velocity impact. For this purpose, the simulation of modified beam finite element based on higher order beam theory for two(isotropic and anisotropic) materials is carried out according to the changes of material property, stacking sequence, geometric dimension and impact velocity of steel ball, etc. Main composite materials for simulation are composed of $[0^{\circ}/90^{\circ}/0^{\circ}/-90^{\circ}/0^{\circ}]_{2s}$, $[0^{\circ}/90^{\circ}/0^{\circ}/-90^{\circ}/0^{\circ}]_s$ and $[0^{\circ}/45^{\circ}/0^{\circ}/-45^{\circ}/0^{\circ}]_{2s}$, $[0^{\circ}/45^{\circ}/0^{\circ}/-45^{\circ}/0^{\circ}]_s$ stacking sequences. The effectiveness of this simulation for qualitative and quantitative evaluations in composite materials subjected to foreign object impact was established.

• Smart Structures and Systems
• /
• 제26권3호
• /
• pp.311-318
• /
• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.