• International Journal of Aeronautical and Space Sciences
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• 제14권4호
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• pp.310-323
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• 2013

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUF-XFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane cross-section deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Structural Engineering and Mechanics
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• 제8권5호
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• pp.465-476
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• 1999

A structural optimization process is presented for arches with varying cross-section. The optimality criteria method is used to develop a recursive relationship for the design variables considering displacement, stresses and minimum depth constraints. The depth at the crown and at the support are taken as design variables first. Then the approach is extended by taking the depth values of each joint as design variable. The curved beam element of constant cross section is used to model the parabolic and circular arches with varying cross section. A number of design examples are presented to demonstrate the application of the method.

• 한국소음진동공학회논문집
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• 제17권4호
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• pp.310-316
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• 2007

This paper presents a theoretical approach to describe the characteristics of vibration transmission in the waveguide with varying cross-section. The waveguide considered in this paper has a tapered section in the middle of an axisymmetric stepped rod. The distributions of the vibration displacement and stress along the waveguide were derived and they were verified by comparing the theoretically-calculated results with those obtained by the finite-element analysis. The vibration magnification and the concentrated stress under forced vibration were calculated for this rod according to the taper length. The paper established a theoretical basement of designing waveguides for maximizing the vibration transmission under minimum stress concentration.

• 항공우주시스템공학회지
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• 제2권1호
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• pp.7-12
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• 2008

The three-dimensional finite element modeling of a composite rotor blade is very hard and requires much computation effort. The efficient method to model a composite beam is necessary for the dynamic and aeroelastic analyses of rotor blades. In this study, the beam modeling method of a composite rotor blade is studied using VABS. The computer program, VABS (Variational Asymptotic Beam Section Analysis), uses the variational asymptotic method to split a 3-D nonlinear elasticity problem into 2-D cross-sectional analysis and 1-D nonlinear beam problem. The VABS can produce the sectional stiffness coefficients of composite rotor blades with various cross section and initial twist/curvatures, and recover the original 3-D distribution of displacement/strain/stress fields. The results of various cross section beams show that VABS gives us the accurate results comparared to commercial codes and does not need much computation effort. It can be concluded that VABS provides the efficient method to establish the FE model of a composite rotor blade.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• 한국지반신소재학회논문집
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• 제17권1호
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• pp.111-118
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• 2018

단층 등 취약지반 조건에서의 터널굴착 시 터널천단 및 측벽변위의 억제를 목적으로 하는 각부보강공이 일반적으로 적용되고 있으며, 터널 단면증가 변화율에 따른 각부보강공 설치각도 및 길이를 고려한 지보안전성 확인을 위한 주요 인자로서 내공변위 천단침하 각부침하 각부축력 등의 여러 응력변위 특성 변수들이 있다. 이러한 굴착중 안전성확인을 위한 변수들에 대한 검토 결과, 우각부 침하영향성이 단면증가율 보다 더 큰 변위경향을 보이는 가장 중요한 중점관리 지배요소로 분석되었으며, 터널단면 증가 변화율에 대한 각 보강공 길이별 축력의 변화관점에서는 큰 연관성을 보여주지 못하는 터널단면 증가율 대비 작은 증가율을 나타냈다. 또한, 각부 보강공 축력의 발생경향은 터널 단면증가율보다 보강공 마찰지지 개념 메커니즘에 따른 거동 영향성을 보여주는 것으로 분석되었다. 본 연구결과, 일정한 길이의 각부 보강공이 선정될 경우 지반불량 구간에서의 터널 단면이 다소 대단면화하여도 무리하게 각부보강공의 길이를 연장시키지 않는 것이 시공성 및 경제성을 고려한 보다 더 합리적인 방법으로 판단된다.

• Smart Structures and Systems
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• 제13권4호
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• pp.517-546
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• 2014

This paper proposes a refined electro-mechanical beam formulation. Lagrange-type polynomials are used to interpolate the unknowns over the beam cross section. Three- (L3), four- (L4), and nine-point(L9) polynomials are considered which lead to linear, bi-linear, and quadratic displacement field approximations over the beam cross-section. Finite elements are obtained by employing the principle of virtual displacements in conjunction with the Carrera Unified Formulation (CUF). The finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumptions made. Additional refined beam models are implemented by introducing further discretizations, over the beam cross-section. Some assessments from bibliography have been solved in order to validate the electro-mechanical formulation. The investigations conducted show that the present formulation is able to detect the electro-mechanical interaction.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2011년도 추계학술대회 논문집
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• pp.130-135
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• 2011

A study of the bending-extension-transverse shear coupled random response of the composite beams with thin-walled open sections subjected to various types of concentrated and distributed random excitations is dealt with in this paper. First of all, equations of motion of thin-walled composite H-type cross-section beams incorporating a number of nonclassical effects of transverse shear and primary and secondary warping, and anisotropy of constituent materials are derived. On the basis of derived equations of motion, analytical expressions for the displacement response of the composite beams are derived by using normal mode method combined with frequency response function method.

• 한국소음진동공학회논문집
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• 제16권10호
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• pp.1024-1035
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• 2006

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (circumferentially closed), circular rings with an elliptical or circular cross-section. Displacement components $u_r,\;u_\theta\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the circular rings are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. Novel numerical results are presented for the circular rings having an elliptical cross-section based upon 3-D theory. Comparisons are also made between the frequencies from the present 3-D Ritz method and ones obtained from thin and thick ring theories, experiments, and another 3-D method.