• Advances in aircraft and spacecraft science
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• v.1 no.1
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• pp.93-123
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• 2014

A variational asymptotic composite beam model has been developed for thermoelastic analysis. Composite beams, including sandwich structure and laminates, under different boundary conditions are examined. Previously developed beam model, which is based on variational-asymptotic method, is extended to incorporate temperature-dependent materials experiencing large temperature changes. The recovery relations have been derived so that the temperatures, heat fluxes, stresses, and strains can be recovered over the cross-section. The present theory is implemented into the computer program VABS (Variational Asymptotic Beam Sectional analysis). Numerical results are compared with the 3D analysis for the purpose of demonstrating advantages of the present theory and use of VABS.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.2
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• pp.72-79
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• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.

• Journal of Aerospace System Engineering
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• v.1 no.3
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• pp.26-31
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• 2007

This paper addresses a method for structural optimum design of composite rotor blade. The basic model of a composite helicopter main rotor blade is designed and its parameters determining the structural/dynamic properties are studied. Through the investigation of flap/lag/torsional stiffness, the structural properties of the model are analyzed. In this study, helicopter rotor blades are analyzed by using VABS. The computer program VABS (Variational Asymptotic Beam Section Analysis) uses the variational asymptotic method to split a three-dimensional nonlinear elasticity problem into a two dimensional cross-sectional analysis and a one-dimensional nonlinear beam problem. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. In addition, the rotational stability of the blade is estimated by the frequency diagram from FE analysis(MSC.Patran/Nastran) to understand its vibrational property. From the result, design parameters to determine and optimize the properties of the model are presented.

• Journal of Power System Engineering
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• v.19 no.3
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.7
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• pp.35-40
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• 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.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.11a
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• pp.198-201
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• 2005

This study investigates the difference between single-cell and multi-cell cross-sections of thin-walled beams. The variationally and asymptotically consistent theory is used in order to model the two-cell thin- walled beam. The theory is based on an asymptotical analysis of two-dimensional shell energy. In addition, the method allows for the development of closed-form expressions for the displacement, stress field and beam stiffness coefficients. The numerical results show the difference between the cross-sectional stiffness of single-cell and that of multi-cell.

• Journal of Aerospace System Engineering
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• v.2 no.1
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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.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.213-234
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• 2010

A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

• Journal of the Korean Solar Energy Society
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• v.36 no.3
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.