Two-dimensional Cross-sectional Analysis Research Articles

Cross-sectional analysis of initially curved composite beams with rectangular and circular sections using an asymptotic meshless method

An analytical meshless cross-sectional dimensional reduction method is developed to perform structural analysis of initially curved composite beams. By introducing the Pascal polynomials in the Cartesian coordinates system for beams with rectangular cross-sections and in the polar coordinates system for the beams with circular cross-sections to the warping field, a three-dimensional beam problem can be split into a two-dimensional cross-sectional analysis and a one-dimensional along the reference line of the beam. The obtained cross-sectional stiffness matrix based on higher-order of the strain energy can be incorporated into a one-dimensional finite element solution for initially curved composite beams, for the purpose of strain and stress analysis. Finally, the three-dimensional strain through the thickness of the beam can be achieved by the recovery analysis. The present method takes advantage of Pascal polynomials so that the solution procedure will be more simplified and computationally more efficient compared to three-dimensional finite element (3D FE) method. The proposed method for different isotropic and anisotropic beams is examined and compared with the literature, 3D FE, and Variational Asymptotic Beam Sectional (VABS) package which is a finite element based cross-sectional analysis tool for composite beams.

Research on the conductivity and self-sensing properties of high strength cement-based material with oriented copper-coated steel fibers

In this paper, a cement-based sensor for monitoring the performance of high-strength concrete was prepared by adding 0.5 vol%, 1.0 vol%, 1.5 vol%, and 2.0 vol% copper-coated steel fibers (CCSF) as conductive fillers. The fresh cement-based mixture was poured into a funnel-type fiber alignment device, which used its fluidity of the mixture to achieve an aligned distribution of shear-induce fiber within the cementitious matrix. The analysis results indicate that the cement-based sensor with fiber oriented distribution exhibits enhanced electrical conductivity and lower percolation threshold. In addition, the aligned CCSF in the cement matrix mitigates the impact of temperature on resistivity. The resistivity and temperature of the copper-coated steel fibers cement-based sensors (CSFCS) between 5 °C and 70 °C conform to the Arrhenius relationship. The specimens with aligned fibers demonstrate greater flexural strength compared to those with randomly distributed fibers. Additionally, they also reflect greater piezoresistive response, including higher sensitivity, better repeatability as well as less hysteresis time. Through the two-dimensional cross-section analysis, the angle between CCSF and the cross-section of the fiber-aligned specimen is significantly reduced, and the fiber orientation factor and fiber orientation coefficient increased considerably. The funnel device for preparing fiber-reinforced cement-based materials can effectively improve fiber orientation.

Bending analysis of laminated beams using isogeometric variational asymptotic method

Variational asymptotic method (VAM) is a robust mathematical method employed to arrive at a reduced order governing equations in solid mechanics. VAM for beam analysis is accomplished in two stages: first stage involves performing a two-dimensional cross-sectional analysis, and the last stage is one-dimensional beam analysis. Cross-sectional analysis stage involves determining the stiffness coefficients for the beam cross section. VAM can be implemented either by developing analytical solutions or by adopting numerical methods. For beams with arbitrary cross-sectional shapes and material heterogeneity, cross-sectional analysis in VAM is generally carried out by adopting a finite element type procedure. In this study, a numerical procedure for the two-dimensional analysis and the one-dimensional beam analysis based on isogeometric framework is presented. NURBS functions are employed to model the geometry of a cross section and the warping displacement field. Warping represents the deformation of cross section of the beam. Stiffness coefficients obtained by cross-sectional analysis are input to the one-dimensional analysis. A NURBS-based one-dimensional method for bending analysis of laminated composite beams is proposed which can handle axial forces, twisting moments, in-plane and out-of plane bending moments. The one-dimensional analysis features four unknown variables, namely axial displacement, twist and two transverse displacements. The one-dimensional beam geometry and the unknown variables are modelled using NURBS functions. The one-dimensional formulation requires $$C^1$$ continuity which can be easily satisfied by NURBS functions. Numerical examples are solved to ascertain accuracy of the proposed methods. Results obtained were compared with exact solution and was found to be accurate. The one-dimensional analysis based on NURBS functions is non-intrinsic. Application of boundary conditions is far simpler to implement in comparison with the intrinsic one-dimensional analysis methods existing in traditional one-dimensional analysis of VAM literature.

Isogeometric-based cross-sectional analysis of pre-twisted composite beams

Abstract This paper is intended to investigate the static behavior of pre-twisted composite beams using an isogeometric-based cross-sectional analysis. The three-dimensional pre-twisted beam problem is decomposed into a two-dimensional cross-sectional analysis and a one-dimensional beam model. The cross-sectional analysis obtains stiffness constants by considering three-dimensional warping deformation effects. The influence of pre-twist ratio is investigated on the stiffness constants and one-dimensional deformations of isotropic beams, composite strips and box-beams. Inconsistencies in results of pre-twisted composite beam theories in the literature are addressed and discussed. The present method eliminates the costly use of three-dimensional finite element analysis in the initial design steps.

A composite beam theory for modeling nonlinear shear behavior

Accurate predictions of physically nonlinear elastic behaviors of a material point in the structure are essential to the further analyses which are beyond the linear elasticity regime, for example, the progressive damage and the failure. In light of substantial experimental evidence of nonlinear shear stress-strain responses in composites, it is necessary to consider them in the structure-level simulations rigorously. A variational asymptotic beam model is developed for this purpose. The three-dimensional continuum is rigorously reduced to a two-dimensional cross-sectional analysis and a one-dimensional Euler-Bernoulli beam analysis. The original three-dimensional continuum features material nonlinearities in longitudinal shear. The unknown cross-sectional warping is solved by finite element method using the principle of virtual work. Nonlinear beam constitutive relation and three-dimensional stress and strain fields are obtained.

Two-dimensional cross-sectional analysis of composite beams using Rayleigh-Ritz-based dimensional reduction method

In this paper, cross-sectional analysis of composite beams using a Rayleigh-Ritz-based dimensional reduction method is presented. In dimensional reduction method, the three-dimensional (3D) elasticity problem is reduced to a two-dimensional (2D) cross-sectional analysis which yields cross-sectional stiffness constants. Then a one-dimensional (1D) beam problem, with fidelity to 3D deformation effects, is attained. Using Rayleigh-Ritz method, the cumbersome procedure of mesh generation on beam section is eliminated in contrast to finite element-based cross-sectional analysis. Shear deformation effects and B-spline basis functions in Rayleigh-Ritz-based cross-sectional analysis are considered in this study. Different isotropic and composite beams are examined. Moreover, the effects of considering transverse shear deformation, coupling stiffness constants and honeycomb core for composite thin-walled beams are investigated. Using the present method, a fast and precise tool for analysis of composite beams with arbitrary cross-section geometry and material anisotropy is available for design of composite beam-like structures.

Nonlinear Variational Asymptotic Sectional Analysis of Hyperelastic Beams

A nonlinear sectional analysis is developed for modeling beams made of hyperelastic materials and subject to finite deformation. Exploiting the fact that the cross-sectional dimension is much smaller than the wavelength of the global beam deformation, the three-dimensional hyperelasticity is rigorously reduced to a one-dimensional nonlinear beam analysis and a two-dimensional cross-sectional analysis featuring both geometric and material nonlinearities. The deformation gradient is directly used to enable the capability of dealing with various types of hyperelastic material models defined by the strain energy function. This new theory can predict phenomena from both material and geometric nonlinearities of beam-like structures, such as the trapeze and Poynting effects. The present theory is implemented using the finite element method in variational asymptotic beam sectional analysis, a general-purpose cross-sectional analysis tool that deals with composite beams. Examples are used to validate the theory and the companion code.

Three-Dimensional Blood Vessel Segmentation and Centerline Extraction based on Two-Dimensional Cross-Section Analysis.

The segmentation of tubular tree structures like vessel systems in volumetric datasets is of vital interest for many medical applications. In this paper we present a novel, semi-automatic method for blood vessel segmentation and centerline extraction, by tracking the blood vessel tree from a user-initiated seed point to the ends of the blood vessel tree. The novelty of our method is in performing only two-dimensional cross-section analysis for segmentation of the connected blood vessels. The cross-section analysis is done by our novel single-scale or multi-scale circle enhancement filter, used at the blood vessel trunk or bifurcation, respectively. The method was validated for both synthetic and medical images. Our validation has shown that the cross-sectional centerline error for our method is below 0.8 pixels and the Dice coefficient for our segmentation is 80%±2.7%. On combining our method with an optional active contour post-processing, the Dice coefficient for the resulting segmentation is found to be 94%±2.4%. Furthermore, by restricting the image analysis to the regions of interest and converting most of the three-dimensional calculations to two-dimensional calculations, the processing was found to be more than 18 times faster than Frangi vesselness with thinning, 8 times faster than user-initiated active contour segmentation with thinning and 7 times faster than our previous method.

SNUF뒷전 플랩 블레이드 메커니즘의 설계 개선

SNUF(Seoul National University flap) 블레이드는 고주파 영역에서 진동 감쇠를 위하여, 압전작동기에 의해 움직이는 뒷전 플랩이 장착되어 있는 축소형 로터 블레이드이다. 이 블레이드를 설계하기 위하여 2차원 단면 해석과 1차원 기하학적 정밀 보 해석이 수행되었고, 사용할 재료의 특성을 확인하였다. 이전 연구자들의 실험을 참조하여, <TEX>${\pm}4^{\circ}$</TEX>의 플랩 변위각을 진동감쇠를 위한 설계요건으로 선정하였다. 플랩의 연결 메커니즘을 설계하고, 설계된 메커니즘의 성능을 확인하기 위하여 정적 벤치 시험을 수행하였다. 개선된 버전의 플랩 장치를 설계하고 시험하였으며, 압전작동기로는 APA 200M을 선정하였다. 장비의 개선을 통하여, 최대 플랩변위가 <TEX>${\pm}3.7^{\circ}$</TEX>에 도달하였다. 성능을 평가하기 위하여 고주파 실험을 수행하였으며, 플랩 장치의 전달 함수를 실험적으로 결정하였다. 정적 시험을 완료하여, 훨타워 시험을 위하여 필요한 로터의 요구마력을 계산하였고, 그 이외의 준비가 진행 중에 있다. Seoul National University flap(SNUF) blade is a small-scale rotor blade incorporating a small trailing-edge flap control surface driven by piezoelectric actuators at higher harmonics for vibration attenuation. Initially, the blade was designed using two-dimensional cross-section analysis and geometrically exact one-dimensional beam analysis, and its material configuration was finalized. A flap-deflection angle of <TEX>${\pm}4^{\circ}$</TEX> was established as the criterion for enhanced vibration reduction based on an earlier simulation. The flap-linkage mechanism was designed and static bench tests were conducted for verifying the performance of the flap-actuation mechanism. Different versions of test beds were developed and tested with the designed flap and the selected APA 200M piezoelectric actuators. Through significant improvements, a maximum deflection of <TEX>${\pm}3.7^{\circ}$</TEX> was achieved. High-frequency experiments were conducted for evaluating the performance, and the transfer function of the test bed was determined experimentally. With the static tests almost complete, the rotor power required for testing the blade in a whirl tower (centrifugal environment) was calculated, and further preparations are underway.

On the Modeling of Coupled Vibration of Rotating Thin-Walled Closed-Section Composite Beams

The free vibration model of a rotating composite thin-walled closed-section beams is presented in this paper. The two-dimensional cross-sectional analysis based on the variational-asymptotical method(VAM) is combined with the Hamilton’s principle to derive the equations of motion and associated boundary conditions of the beams. The Galerkin method is employed in order to solve the coupled differential equations. The natural frequency results obtained for the present model are compared with those of the existing models. Numerical results are obtained for the laminated composite cantilevered box beam with Circumferentially Uniform Stiffness(CUS) configuration, the effects of the fiber orientation, pitch and precone on the natural frequencies associated with coupled vibration modes are investigated.

General Purpose Cross-section Analysis Program for Composite Rotor Blades

A two-dimensional cross-section analysis program based on the finite element method has been developed for composite blades with arbitrary cross-section profiles and material distributions. The modulus weighted approach is used to take into account the non-homogeneous material characteristics of advanced blades. The CLPT (Classical Lamination Plate Theory) is applied to obtain the effective moduli of the composite laminate. The location of shear center for any given cross-sections are determined according to the Trefftz' definition while the torsion constants are obtained using the St. Venant torsion theory. A series of benchmark examples for beams with various cross-sections are illustrated to show the accuracy of the developed crosssection analysis program. The cross section cases include thin-walled C-channel, Ibeam, single-cell box, NACA0012 airfoil, and KARI small-scale blades. Overall, a reasonable correlation is obtained in comparison with experiments or finite element analysis results.

유한요소법 기반의 복합재료 블레이드 단면 특성치 계산에 관한 연구

유한요소법을 적용하여 고형, 박벽 및 혼합형 단면을 갖는 복합재료 블레이드의 2차원 단면 해석 프로그램을 개발하였다. 이종 적층 복합재료에 대한 물성치는 가중 계수법을 도입하여 결정하였다. 전단 중심치와 비틀림 강성 계수는 St. Venant 비틀림 이론 및 Trefftz 의 정의를 토대로 구하였다. 해석 과정에서 발생하는 단면 강성 행렬의 특이치 문제는 고유치 해석으로부터 강체 모드를 제거함으로써 해결하였다. 다양한 단면 형상에 대한 강성치, 중심치 및 관성치에 대한 수치계산을 수행하였다. 기존의 상용해석 소프트웨어 및 여타 문헌에 제시된 단면 해석 결과와 폭 넓은 비교, 검증 연구를 수행하였으며, 이를 토대로 본 해석 프로그램의 타당성을 보였다. A two-dimensional cross-section analysis program based on the finite element method has been developed for composite blades with solid, thin-walled and compound cross-sections. The weighted-modulus method is introduced to determine the laminated composite material properties. The shear center and the torsion constant for any given section are calculated according to the Trefftz' definition and the St. Venant torsion theory, respectively. The singular value problem of cross-section stiffness properties faced during the section analysis has been solved by performing an eigenvalue analysis to remove the rigid body mode. Numerical results showing the accuracy of the program obtained for stiffness, offset and inertia properties are compared in this analysis. The current analysis results are validated with those obtained by commercial software and published data available in the literature and a good correlation has generally been achieved through a series of validation study.

Ovarian imaging by magnetic resonance in obese adolescent girls with polycystic ovary syndrome: a pilot study

To determine whether magnetic resonance (MR) imaging can serve as a useful investigational tool in the assessment of the polycystic ovary as compared with transabdominal ultrasound (US) for obese adolescents with polycystic ovary syndrome (PCOS). Prospective observational study. Tertiary university hospital. Eleven obese adolescents with PCOS. Pelvic MR and US imaging and blood sampling. Total ovarian volume and follicle count; mean follicle count per longitudinal cross-section; stromal area; biochemical correlations with measured ovarian parameters. With MR, the mean (+/-SE) total follicle count (21.9 +/- 1.3) was significantly greater than that observed with US (5.5 +/- 1.7) and significantly correlated with total ovarian volume. Two-dimensional cross-sectional analysis of the ovary by MR revealed a significantly greater mean follicle count (12.1 +/- 0.8) compared with the results obtained by US (3.0 +/- 0.5). The stromal area (173.3 +/- 25.1 mm2) was approximately 35% of the total ovarian surface area. No correlations were observed between biochemical indices and measured ovarian parameters. In contrast to US, MR provides vastly greater delineation of the structural components of the ovary in obese girls with PCOS and thus can serve as an excellent investigational technique to assess the morphological transformation of the adolescent ovary.