• Structural Engineering and Mechanics
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• v.30 no.2
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• pp.225-245
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• 2008

T-splines are recently proposed mathematical tools for geometric modeling, which are generalizations of B-splines. Local refinement can be performed effectively using T-splines while it is not the case when B-splines or NURBS are used. Using T-splines, patches with unmatched boundaries can be combined easily without special techniques. In the present study, an analysis framework using T-splines is proposed. In this framework, T-splines are used both for description of geometries and for approximation of solution spaces. This analysis framework can be a basis of a CAD/CAE integrated approach. In this approach, CAD models are directly imported as the analysis models without additional finite element modeling. Some numerical examples are presented to illustrate the effectiveness of the current analysis framework.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.127-134
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• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.47-53
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• 2010

In this paper we propose a new type of splines-biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.672-677
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• 2007

Recently, the new finite element method which uses NURBS as shape functions was proposed. It is very promising because it can directly use CAD data to describe geometry and discretize problem domain. In this case, CAE models are not approximated but represent exact geometry. So, it can contribute to more accurate results. In addition, it can greatly reduce CAE costs in that simulation models don't have to be made up independently. But in spite of these advantages, the method using NURBS have also some disadvantages. NURBS surface cannot be refined locally. T-splines are recently developed surface modeling technique. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. The T-junctions enable T-spline surfaces to be refined locally. That is, it is possible to add a single control point to a T-spline control grid without propagating an entire row or column of control points and without altering the surface. In this research, the finite element analysis using T-splines is studied. In this analysis, CAD data are used directly for engineering analysis. Some problems with complex geometry are solved. And the results will be compared with ones of conventional FEM.

• Geomechanics and Engineering
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• v.7 no.4
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• pp.431-458
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• 2014

Construction of a new cavern close to an existing cavern will result in a modification of the state of stresses in a zone around the existing cavern as interaction between the twin caverns takes place. Extensive plane strain finite difference analyses were carried out to examine the deformations induced by excavation of underground twin caverns. From the numerical results, a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) has been used to relate the maximum key point displacement and the percent strain to various parameters including the rock quality, the cavern geometry and the in situ stress. Probabilistic assessments on the serviceability limit state of twin caverns can be performed using the First-order reliability spreadsheet method (FORM) based on the built MARS model. Parametric studies indicate that the probability of failure $P_f$ increases as the coefficient of variation of Q increases, and $P_f$ decreases with the widening of the pillar.

• Computers and Concrete
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• v.16 no.4
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• pp.569-585
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• 2015

Various computational tools are available for modeling highly nonlinear structural engineering problems that lack a precise analytical theory or understanding of the phenomena involved. This paper adopts a fairly simple nonparametric adaptive regression algorithm known as multivariate adaptive regression splines (MARS) to model the nonlinear interactions between variables. The MARS method makes no specific assumptions about the underlying functional relationship between the input variables and the response. Details of MARS methodology and its associated procedures are introduced first, followed by a number of examples including three practical structural engineering problems. These examples indicate that accuracy of the MARS prediction approach. Additionally, MARS is able to assess the relative importance of the designed variables. As MARS explicitly defines the intervals for the input variables, the model enables engineers to have an insight and understanding of where significant changes in the data may occur. An example is also presented to demonstrate how the MARS developed model can be used to carry out structural reliability analysis.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.791-800
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• 1999

Gross and Lai(1996) proposed a new approach for ordinary regression with left-truncated and right-censored (I.t.r.c) data. This paper shows how to apply nonparametric algorithms such as multivariate adaptive regression splines to 1.t.r.c data.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.269-284
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• 2016

Simplified techniques based on in situ testing methods are commonly used to assess seismic liquefaction potential. Many of these simplified methods were developed by analyzing liquefaction case histories from which the liquefaction boundary (limit state) separating two categories (the occurrence or non-occurrence of liquefaction) is determined. As the liquefaction classification problem is highly nonlinear in nature, it is difficult to develop a comprehensive model using conventional modeling techniques that take into consideration all the independent variables, such as the seismic and soil properties. In this study, a modification of the Multivariate Adaptive Regression Splines (MARS) approach based on Logistic Regression (LR) LR_MARS is used to evaluate seismic liquefaction potential based on actual field records. Three different LR_MARS models were used to analyze three different field liquefaction databases and the results are compared with the neural network approaches. The developed spline functions and the limit state functions obtained reveal that the LR_MARS models can capture and describe the intrinsic, complex relationship between seismic parameters, soil parameters, and the liquefaction potential without having to make any assumptions about the underlying relationship between the various variables. Considering its computational efficiency, simplicity of interpretation, predictive accuracy, its data-driven and adaptive nature and its ability to map the interaction between variables, the use of LR_MARS model in assessing seismic liquefaction potential is promising.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.