• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.67-76
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• 1992

A hierarchical formulation based on p-version of the finite element method for linear elastic axisymmetric stress analysis is presented. This is accomplished by introducing additional nodal variables in the element displacement approximation on the basis of integrals of Legendre polynomials. Since the displacement approximation is hierarchical, the resulting element stiffness matrix and equivalent nodal load vectors are hierarchical also. The merits of the propoosed element are as follow: i) improved conditioning, ii) ease of joining finite elements of different polynomial order, and iii) utilizing previous solutions and computation when attempting a refinement. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, robustness and overall superiority of the present formulation. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions.

• Asian-Australasian Journal of Animal Sciences
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• v.31 no.10
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• pp.1542-1549
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• 2018

Objective: Because lactation periods in dairy cows lengthen with increasing total milk production, it is important to predict individual productivities after 305 days in milk (DIM) to determine the optimal lactation period. We therefore examined whether the random regression (RR) coefficient from 306 to 450 DIM (M2) can be predicted from those during the first 305 DIM (M1) by using a RR model. Methods: We analyzed test-day milk records from 85,690 Holstein cows in their first lactations and 131,727 cows in their later (second to fifth) lactations. Data in M1 and M2 were analyzed separately by using different single-trait RR animal models. We then performed a multiple regression analysis of the RR coefficients of M2 on those of M1 during the first and later lactations. Results: The first-order Legendre polynomials were practical covariates of RR for the milk yields of M2. All RR coefficients for the additive genetic (AG) effect and the intercept for the permanent environmental (PE) effect of M2 had moderate to strong correlations with the intercept for the AG effect of M1. The coefficients of determination for multiple regression of the combined intercepts for the AG and PE effects of M2 on the coefficients for the AG effect of M1 were moderate to high. The daily milk yields of M2 predicted by using the RR coefficients for the AG effect of M1 were highly correlated with those obtained by using the coefficients of M2. Conclusion: Milk production after 305 DIM can be predicted by using the RR coefficient estimates of the AG effect during the first 305 DIM.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.2
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• pp.147-154
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• 2017

The impedance approximation has been widely used to model an earth surface such as ocean surface. In calculation of the dyadic Green's function for the impedance half plane, Sommerfeld integral and its partial derivatives are required. It is known that two far-field approximation of the Sommerfeld integral can be represented in terms of Legendre or Laguerre polynomials. Hence, a criterion is required to choose one of two far-field approximations for a given application, which can be expressed in a complex plane of the surface impedance. Also, we approximate the required partial derivatives of Sommerfeld integral and numerically verify the accuracy of the approximation.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.603-619
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• 2018

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.78.2-78.2
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• 2019

We develop an Alcock-Paczynski (AP) test method that uses the evolution of redshift-space two-point correlation function (2pCF) of galaxies. The method improves the AP test proposed by Li et al. (2015) in that it uses the full two-dimensional shape of the correlation function. Similarly to the original method, the new one uses the 2pCF in redshift space with its amplitude normalized. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF. This is because the 2pCF should not change apart from the expected small non-linear evolution if galaxy clustering is not distorted by incorrect choice of cosmology used to convert redshift to comoving distance. Our new method decomposes the redshift difference of the 2-dimensional correlation function into the Legendre polynomials whose amplitudes are modelled by radial fitting functions. The shape of the normalized 2pCF suffers from small intrinsic time evolution due to non-linear gravitational evolution and change of type of galaxies between different redshifts. It can be accurately measured by using state of the art cosmological simulations. We use a set of our Multiverse simulations to find that the systematic effects on the shape of the normalized 2pCF are quite insensitive to change of cosmology over \Omega_m=0.21 - 0.31 and w=-0.5 - -1.5. Thanks to this finding, we can now apply our method for the AP test using the non-linear systematics measured from a single simulation of the fiducial cosmological model.

• Animal Bioscience
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• v.34 no.4
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• pp.499-505
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• 2021

Objective: The objective of this study was to evaluate the genetic behavior of a population of Holstein cattle in response to the variation of environmental temperature by analyzing the effects of genotype by environment interaction (GEI) through reaction norms for the somatic cell score (SCS). Methods: Data was collected for 67,206 primiparous cows from the database of the Paraná Holstein Breeders Association in Brazil, with the aim of evaluating the temperature effect, considered as an environmental variable, distinguished under six gradients, with the variation range found being 17℃ to 19.5℃, over the region. A reaction norm model was adopted utilizing the fourth order under the Legendre polynomials, using the mixed models of analysis by the restricted maximum likelihood method by the WOMBAT software. Additionally, the genetic behavior of the 15 most representative bulls was assessed, in response to the changes in the temperature gradient. Results: A mean score of 2.66 and a heritability variation from 0.17 to 0.23 was found in the regional temperature increase. The correlation between the environmental gradients proved to be higher than 0.80. Distinctive genetic behaviors were observed according to the increase in regional temperature, with an observed increase of up to 0.258 in the breeding values of some animals, as well as a reduction in the breeding of up to 0.793, with occasional reclassifications being observed as the temperature increased. Conclusion: Non-relevant GEI for SCS were observed in Holstein cattle herds of southern Brazil. Thus, the inclusion of the temperature effect in the model of genetic evaluation of SCS for the southern Brazilian Holstein breed is not required.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.437-452
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• 2022

For the first time, the higher-order shear and normal deformable plate theory (HOSNDPT) is used for the vibration and flutter analyses of the multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates under supersonic airflow. For modeling the supersonic airflow, the linear piston theory is adopted. In HOSNDPT, Legendre polynomials are used to approximate the components of the displacement field in the thickness direction. So, all stress and strain components are encountered. Either uniform or three kinds of non-uniform distribution of graphene platelets (GPLs) into polymer matrix are considered. The Young modulus of the FG-GPLRC plate is estimated by the modified Halpin-Tsai model, while the Poisson ratio and mass density are determined by the rule of mixtures. The Hamilton's principle is used to obtain the governing equations of motion and the associated boundary conditions of the plate. For solving the plate's equations of motion, the Galerkin approach is applied. A comparison for the natural frequencies obtained based on the present investigation and those of three-dimensional elasticity theory shows a very good agreement. The flutter boundaries for FG-GPLRC plates based on HOSNDPT are described and the effects of GPL distribution patterns, the geometrical parameters and the weight fraction of GPLs on the flutter frequencies and flutter aerodynamic pressure of the plate are studied in detail. The obtained results show that by increasing 0.5% of GPLs into polymer matrix, the flutter aerodynamic pressure increases approximately 117%, 145%, 166% and 196% for FG-O, FG-A, UD and FG-X distribution patterns, respectively.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.533-541
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.11
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• pp.1741-1754
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• 2020

Objective: This study was conducted to estimate genetic parameters for milk yield traits using daily milk yield records from parlour data generated in an intensively managed commercial dairy farm with Jersey and Jersey-Friesian cows in Sri Lanka. Methods: Genetic parameters were estimated for first and second lactation predicted and realized 305-day milk yield using univariate animal models. Genetic parameters were also estimated for total milk yield for each 30-day intervals of the first lactation using univariate animal models and for daily milk yield using random regression models fitting second-order Legendre polynomials and assuming heterogeneous residual variances. Breeding values for predicted 305-day milk yield were estimated using an animal model. Results: For the first lactation, the heritability of predicted 305-day milk yield in Jersey cows (0.08±0.03) was higher than that of Jersey-Friesian cows (0.02±0.01). The second lactation heritability estimates were similar to that of first lactation. The repeatability of the daily milk records was 0.28±0.01 and the heritability ranged from 0.002±0.05 to 0.19±0.02 depending on day of milk. Pearson product-moment correlations between the bull estimated breeding values (EBVs) in Australia and bull EBVs in Sri Lanka for 305-day milk yield were 0.39 in Jersey cows and -0.35 in Jersey-Friesian cows. Conclusion: The heritabilities estimated for milk yield in Jersey and Jersey-Friesian cows in Sri Lanka were low, and were associated with low additive genetic variances for the traits. Sire differences in Australia were not expressed in the tropical low-country of Sri Lanka. Therefore, genetic progress achieved by importing genetic material from Australia can be expected to be slow. This emphasizes the need for a within-country evaluation of bulls to produce locally adapted dairy cows.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.491-499
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• 2002

A p-version finite element model based on degenerate shell element is proposed tot the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted tot in the sense of yon Karman hypothesis. The material model is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized lot anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed P-version finite element model is demonstrated through several comparative points of iew in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic tone.