In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

In this study, the random material parameter, especially the Poisson's ratio is taken into account in the stochastic finite element formulation for composite laminate plate. Since the parameter is embedded into the constitutive relation in the fraction form, direct consideration of the parameter in the formulation is not ease. In order to overcome this difficulty, we applied the Taylor's expansion to the fraction form to obtain a series expansion in ascending order of stochastic field function. With this, the formulation that considers the randomness in the Poisson's ratio is established. The adequacy of the proposed formulation is observed by means of Monte Carlo simulation.

본 논문에서는 일차전단변형이론(FSDT)을 이용한 복합재료 적층평판의 고정밀 해석기법을 소개한다. 전단수정계수가 자동적으로 포함되도록 횡방향 전단 변형에너지를 혼합변분이론(mixed variational theorem)을 이용하여 개선하였다. 혼합변분이론에서는 변분을 횡방향 응력들에 대해서만 취하였다. 가정된 횡방향 전단응력은 효율적인 고차이론(Cho and Parmerter, 1993)으로부터 구하였다 횡방향 수직응력은 3차 다항식으로 가정하였고, 무전단 응력조건과 평판의 윗면과 아랫면에서의 응력을 만족하는 조건을 부과함으로써 얻었다. 한편, 변위들에 대해서는 일차전단변형이론의 변위장을 사용하였다. 이렇게 해서 얻어진 변형 에너지를 본 논문에서는 EFSDTM3D이라고 명명 하였다. 본 논문에서 개발된 EFSDTM3D는 변위와 응력의 계산에서 고전적인 FSDT와 같은 정도의 계산 효율을 가지면서, 동시에 변위와 응력의 두께방향의 정확도를 면내 방향 응력들에 대한 최소오차자승법에 기초하여 응력 회복 과정을 적용함으로써 개선하였다. 계산된 결과는 고전적인 FSDT, 3차원 탄성해, 그리고 참고문헌 중에서 이용 가능한 결과들과 비교하여 검증하였다.