scholarly journals Random vibration of laminated plates modeled within a high‐order shear deformation theory

1988 ◽  
Vol 84 (2) ◽  
pp. 660-666 ◽  
Author(s):  
Gabriel Cederbaum ◽  
Liviu Librescu ◽  
Isaac Elishakoff
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Random Vibration ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
High Order

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

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