구조물에 포함되어 있는 불확실성에 의한 영향은 논리적으로 구조물의 안전도 해석에 활용할 수 있는 신뢰성 평가방법에 의해 안전성 검토를 수행하는 것이 합리적일 것이다. 따라서 본 연구에서는 지진하중을 받는 사장교 구조물을 대상으로 확률유한요소법을 기존의 신뢰성이론에 적합하도록 정식화하여 구조물의 동적응답해석 및 신뢰성해석을 보다 효율적으로 수행할 수 있는 프로그램을 작성하였다. 이를 바탕으로 하여 확률변수에 따른 변위, 부재력 및 케이블긴장력 등에 대한 평균, 표준편차 및 변동계수 등을 검토함으로써 동적응답특성을 정량적으로 분석하였다. 또한 신뢰성지수 및 파괴확률을 검토하여 사장교 구조물의 안전성을 평가하였다.

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.

Response variability of reinforced concrete frame subjected to material property randomness has been evaluated with the aid of the finite element method. The spatial variation of Young's modulus is assumed to be a two-dimensional homogeneous stochastic process. Young's Modulus of concrete material has been investigated based on the uiaxial strength of concrete cylinder. Direct Monte Carlo simulation method is used to investigate the response of reinforced concrete frame due to the variation of Young's modulus with the Neumann expansion method and the pertubation method. The results by three analytic methods are compared with those by deterministic finite element analysis. These stochastic technique may be an efficient tool for evaluating the structural safety and reliability of reinforced concrete structures.