To correctly predict the neutron behavior based on diffusion calculations, it is necessary to adopt well-specified boundary conditions using suitable diffusion approximations to transport boundary conditions. Boundary conditions such as the zero net-current, the Marshak, the Mark, the zero scalar flux, and the Albedo condition have been used extensively in diffusion theory to approximate the reflective and vacuum conditions in transport theory. In this paper, we derive and analyze these conditions to prove their mathematical validity and to understand their physical implications, as well as their relationships with one another. To show the validity of these diffusion boundary conditions, we solve a sample problem. The results show that solutions of the diffusion equation with these well-formulated boundary conditions are very close to the solution of the transport equation with transport boundary conditions.

In this paper, we address some issues in existing seismic hazard closed-form equations and present a novel seismic hazard equation form to overcome these issues. The presented equation form is based on higher-order polynomials, which can well describe the seismic hazard information with relatively high non-linearity. The accuracy of the proposed form is illustrated not only in the seismic hazard data itself but also in estimating the annual probability of failure (APF) of the structural systems. For this purpose, the information on seismic hazard is used in representative areas of the United States (West : Los Angeles, Central : Memphis and Kansas, East : Charleston). Examples regarding the APF estimation are the analyses of existing platform structure and nuclear power plant problems. As a result of the numerical example analyses, it is confirmed that the higher-order-polynomial-based hazard form presented in this paper could predict the APF values of the two example structure systems as well as the given seismic hazard data relatively accurately compared with the existing closed-form hazard equations. Therefore, in the future, it is expected that we can derive a new improved APF function by combining the proposed hazard formula with the existing fragility equation.

부구조화에 근거한 대형 구조의 효율적 근사재해석방법을 제시한다. 대형 구조시스템의 설계최적하에 있어서 가장 큰 문제는 반복되는 해석과 설계시에 드는 많은 계산비용 및 시간이다. 따라서 본 연구에서는 설계 최적화문제의 주요한 도구의 하나인 근사화기법에 근거한 몇가지 재해석방법을 비교.분석하여 효율적 구조재해석 방법을 제시하였다. 대형 구조에 대한 효율적 해석 방법의 하나인 부구조화의 틀에 테일러급수전개와 차원축소방법을 결합한 이 재해석기법은 반복되는 거동해석에 효율적일 뿐아니라, 설계민감도 벡터를 이용하기 때문에 최적설계에도 많은 잇점을 제공한다. 본 알고리즘을 트러스 구조에 적용하여 효율적 및 타당성을 검증하였다.