• Advances in Computational Design
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• 제9권2호
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• pp.81-96
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• 2024

Modeling and analyzing the dynamic behavior of fluid-soil-structure interaction problems are crucial in structural engineering. The solution to such coupled engineering systems is often not achievable through analytical modeling alone, and a numerical solution is necessary. Generally, the Finite Element Method (FEM) is commonly used to address such problems. However, when dealing with coupled problems with complex geometry, the finite element method may not precisely represent the geometry, leading to errors that impact solution quality. Recently, Isogeometric Analysis (IGA) has emerged as a preferred method for modeling and analyzing complex systems. In this study, IGA based on Non-Uniform Rational B-Splines (NURBS) is employed to analyze the seismic behavior of concrete gravity dams, considering fluid-structure-foundation interaction. The performance of IGA is then compared with the classical finite element solution. The computational efficiency of IGA is demonstrated through case studies involving simulations of the reservoir-foundation-dam system under seismic loading.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.577-582
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• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Steel and Composite Structures
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• 제37권6호
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• 한국재난정보학회 논문집
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• 제16권4호
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• pp.832-841
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• 2020

연구목적: 본 연구에서는 고차전단변형이론을 적용한 등기하해석 방법을 이용하여 기능경사복합재 판의 휨에 의한 역학적 거동을 해석하고자 하였다. 연구방법: 기능경사복합재 판의 역학적 거동을 보다 더 정확하게 해석하기 위해서 전단보정계수를 도입할 필요가 없는 기하학적 비선형을 고려한 고차전단변형이론을 이용하여 휨을 받는 기능경사복합재 판의 평형방정식과 지배방정식을 도출하였으며, 등기하 해석방법에 의한 수정된 Newton-Raphson 반복법을 이용하여 방정식들을 풀었다. 연구결과: 판의 용적비, 길이-두께 비 및 경계조건은 기능경사복합재 판의 휨 거동에 상당한 영향을 미치는 것을 알 수 있었다. 결론: 제안된 등기하해석 방법은 휨을 받는 기능경사복합재 판의 역학적 거동을 해석하는데 있어 정확하고 효과적인 수치해석 방법임을 확인하였다.