Refined First-Order Shear Deformation Theory Models for Composite Laminates

2003 ◽  
Vol 70 (3) ◽  
pp. 381-390 ◽  
Author(s):  
F. Auricchio ◽  
E. Sacco
Keyword(s):  
Shear Deformation ◽  
Analytical Solutions ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Quadratic Functions ◽  
Shear Stresses ◽  
Stress Profile ◽  
First Order ◽  
Out Of Plane

In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stresses can be derived without post-processing procedures. Some numerical applications are presented in order to verify the effectiveness of the proposed formulations. In particular, analytical solutions obtained using the developed models are compared with the exact three-dimensional solution, with other classical laminate analytical solutions and with finite element results. Finally, we note that the proposed formulations may represent a rational base for the development of effective finite elements for composite laminates.

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.

Geometrically nonlinear finite element simulation of smart laminated shells using a modified first-order shear deformation theory

2019 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Hanen Mallek ◽  
Hanen Jrad ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Nonlinear Finite Element ◽  
Shear Stresses ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
First Order

This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear function through the thickness of each active sub-layer. Several numerical tests for different piezolaminated geometries are conducted to highlight the reliability and efficiency of the proposed implementation in linear and geometrically nonlinear finite element analysis.

scholarly journals A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2385 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Nguyen Dinh Quang ◽  
Do Van Thom
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Shear Stresses ◽  
Transverse Shear Strain ◽  
First Order ◽  
Advanced Composite

A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

Peridynamic Analysis of Laminated Composite Plates Based on First-Order Shear Deformation Theory

2020 ◽  
Vol 12 (03) ◽  
pp. 2050031 ◽  
Author(s):  
Mehmet Dorduncu ◽  
Kadir Kaya ◽  
Omer Faruk Ergin
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations ◽  
First Order ◽  
Aspect Ratios

A nonlocal Peridynamic Differential Operator (PDDO) is presented for static analysis of laminated composite plates based on the First-order Shear Deformation Theory (FSDT). The equilibrium equations and boundary conditions of the FSDT were derived from the principle of virtual work. The local spatial derivatives in these equations were replaced with their nonlocal PD forms. The continuous transverse shear stresses were achieved by integrating the stress equilibrium equations through the thickness of the plate. This approach was validated against an existing analytical solution by considering a simply supported laminated composite plate under uniformly distributed sinusoidal load for different aspect ratios. The performance of this formulation was investigated by comparing through-the-thickness stress variations against the analytical solutions.

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

2021 ◽  
pp. 095440622110127
Author(s):  
Mohammad Reza Salehi Kolahi ◽  
Hossein Rahmani ◽  
Hossein Moeinkhah
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Fe Simulation ◽  
Shear Deformation Theory ◽  
Mechanical Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
First Order ◽  
Analytical Functions ◽  
Plane Elasticity Theory

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

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