• Journal of Korean Society of Steel Construction
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• v.23 no.4
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• pp.475-481
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• 2011

In this study, a simplified method of improving not only transverse shear stress but also shear strain based on the first-order shear deformation theory was developed. Unlike many established methods, such as the higher-order shear deformation and layerwise theories, this method can easily apply to finite elements as only $C^0$ continuity is necessary and the formulation of equations is very simple. The basic concept in this method, however, must be corrected:the distribution of the transverse shear stresses and shear strains through the thickness from the formulation based on the higher-order shear deformation theory. Therefore, the shear correction factors are no longer required, based on the first-order shear deformation theory. Numerical analyses were conducted to verify the validity of the proposed formulations. The solutions based on the simplified method were in very good agreement with the results considering the higher-order shear deformation theory.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.3
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• pp.249-257
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• 2011

In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.3
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• pp.735-750
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• 1991

본 연구에서는 적층 복합판의 충격 해석을 위하여 Reddy의 고차 전단 변형 이 론에 기초를 두고, 정적 압입 실험에 의한 접촉 법칙을 고려한 동적 유한 요소 해석 (dynamic finite element analysis)을 행하여 충격 실험에 의한 결과와 1차 전단변형 이론에 의한 해와 비교 검토하므로서, 그 유용성과 우수성을 입증하고, 적층 복합재의 충격 응력 및 응력파 전파 특성에 대하여 연구하고자 한다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.3
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• pp.751-756
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• 1991

본 연구에서는 Ashwell이 제시한 변형률요소를 전단효과를 고려한 두꺼운 곡 선보 요소에 적용 하였다. 막 변형률, 곡률, 전단변형률 각각에 독립된 변형률 함수 를 가정하여 미분 방정식의 일반해를 구하면 정확한 강체변위의 표현은 물론, 강성과 잉현상을 피할 수 있고 얇은 곡선보에서 두꺼운 곡선보에 이르기까지 보의 해석에 있 어서, 2절점으로 구성되는 적은 자유도수에서 높은 정확도를 보여주는 간편하고도 효 율적인 요소를 개발하고자 하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.512-519
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• 2002

본 연구에서는 임의의 형상의 다중세포 단면을 갖는 복합재료 블레이드에 대한 유한요소 구조해석을 수행하였다. 보 해석 모델은 구조연성 효과와 단면 벽의 두께, 횡 전단변형, 비틀림과 연관된 워핑 및 워핑구속효과 등을 고려하고 있다. 블레이드 힘-변위 관계식은 Reissner의 반복족에너지 함수를 이용한 혼합이론을 적용하여 유도하였다. 이 관계식은 굽힘 및 전단에 대해서는 Timoshenko 보의 형태로 그리고 비틀림 변형은 Vlasov 이론으로 근사하고 있다. 결과적인 [7×7] 구조강성 행렬은 전단변형 및 전단강성계수들을 특이한 가정에 의존하지 않고도 해석적으로 기술하고 있다. 본 정식화 과정을 통해서 구한 보 이론을 이중세포로 구성된 에어포일 형상의 복합재료 블레이드에 적용하였으며, 기존의 실험 연구 및 다차원 유한요소해석 결과들과 비교 연구를 수행하여 본 해석모델의 타당성을 보이고자 하였다.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.1
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• pp.77-89
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• 1996

An enormous amount of efforts has been devoted to the development of finite elements for the bending problem of thick plates, especially based on Mindlin plate theory. Here, an approximate Constant Shear Angle Theory is usually used to take a transverse shear deformation of thick plate into consideration, which cannot be effectively considered the influence of transversal warping of cross-section with an increase of thickness. It might be the best way to represent the exact cross-sectional warping of the plate. The overall objective of this study is to develop a new formulation of plate including shear deformation and transversal warping, to perform extensive parametric studies comparing its results with those from Mindlin plate formulation, and to gain further insight into the influence of shear deformation and transversal warping of thick plate.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.4
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• pp.107-114
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• 2004

In this paper, a simple improved 8-node finite element for the finite element analysis of fibrous composite plates is presented by using the direct modification. We drive explicit expressions of shape functions for the 8-node element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian coordinates. The refined first-order shear deformation theory is proposed, which results in parabolic through-thickness distribution of the transverse shear strains and stresses from the formulation based on the third-order shear deformation theory. It eliminates the need for shear correction factors in the first-order theory. This finite element is further improved by combined use of assumed strain, modified shape function, and refined first-order theory. To show the effectiveness of our simple modification on the 8-node finite elements, numerical studies are carried out the static, buckling and free vibration analysis of fibrous composite plates.