Analytical Solutions of Refined Plate Theories of Cross-Ply Composite Laminates

1991 ◽  
Vol 113 (4) ◽  
pp. 570-578 ◽  
Author(s):  
A. A. Khdeir ◽  
J. N. Reddy
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Composite Laminates ◽  
Laminated Composite ◽  
Composite Plates ◽  
Third Order ◽  
State Space Approach ◽  
Various Boundary Conditions ◽  
Shear Deformation Theories ◽  
Space Approach

Exact solutions of rectangular laminated composite plates with different boundary conditions are studied. The Le´vy-type solutions of the classical, first-order and third-order shear deformation theories are developed using the state-space approach. The finite-element solutions for the three theories are also computed and compared with the exact solutions for various boundary conditions.

scholarly journals State space approach with FEM for the determination of structural behaviour of composite plates

2017 ◽  
Vol 8 (4) ◽  
pp. 468-483
Author(s):  
Asad Shukri Albostami ◽  
Zhangjian Wu ◽  
Zhenmin Zou
Keyword(s):  
Plate Thickness ◽  
Composite Plates ◽  
Thickness Direction ◽  
Middle Plane ◽  
Structural Behaviour ◽  
State Space Approach ◽  
Content Type ◽  
Simply Supported ◽  
Space Approach

Purpose An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues. Design/methodology/approach SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS. Findings The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant. Originality/value This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

scholarly journals SrTiO3—Glimpses of an Inexhaustible Source of Novel Solid State Phenomena

2020 ◽  
Vol 5 (4) ◽  
pp. 58
Author(s):  
Wolfgang Kleemann ◽  
Jan Dec ◽  
Alexander Tkach ◽  
Paula M. Vilarinho
Keyword(s):  
Solid Solution ◽  
Solid State ◽  
Boundary Conditions ◽  
Power Law ◽  
Mesoscopic Physics ◽  
Third Order ◽  
Spin Cluster ◽  
Various Boundary Conditions ◽  
Glass Forming ◽  
Quantum Paraelectric

The purpose of this selective review is primarily to demonstrate the large versatility of the insulating quantum paraelectric perovskite SrTiO3 explained in “Introduction” part, and “Routes of SrTiO3 toward ferroelectricity and other collective states” part. Apart from ferroelectricity under various boundary conditions, it exhibits regular electronic and superconductivity via doping or external fields and is capable of displaying diverse coupled states. “Magnetoelectric multiglass (Sr,Mn)TiO3” part, deals with mesoscopic physics of the solid solution SrTiO3:Mn2+. It is at the origin of both polar and spin cluster glass forming and is altogether a novel multiferroic system. Independent transitions at different glass temperatures, power law dynamic criticality, divergent third-order susceptibilities, and higher order magneto-electric interactions are convincing fingerprints.

A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges

2007 ◽  
Vol 74 (6) ◽  
pp. 1114-1124 ◽  
Author(s):  
Tarun Kant ◽  
Sandeep S. Pendhari ◽  
Yogesh M. Desai
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Coupled System ◽  
Integration Model ◽  
Numerical Integrators ◽  
Support Conditions

An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

Bubble Complex Finite Strip Method in the Stability and Vibration Analysis of Orthotropic Laminated Composite Plates

2020 ◽  
Vol 12 (09) ◽  
pp. 2050106
Author(s):  
Mohammad Sekhavatjou ◽  
Mojtaba Azhari ◽  
Saeid Sarrami-Foroushani
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
Finite Strip ◽  
Finite Strip Method ◽  
The Stability ◽  
Zigzag Theory

In this study, a bubble complex finite strip method (BCFSM) with the higher-order zigzag theory is formulated for mechanical buckling and free vibration analysis of laminated composite plates, including cross-ply and angle-ply laminates. Few studies have been done to obtain the analytical solutions for clamped and free boundary conditions in the longitudinal and transverse edges. Therefore, this study, for the first time, investigates the effects of various boundary conditions on the stability and vibration results of laminated composite plates subjected to axial or pure shear forces with the use of higher-order zigzag theory and BCFSM. Following this, both the interlaminar continuity conditions of transverse shear stresses and the shear-free surface conditions are satisfied by applying a cubic displacement and a zigzag linear varying displacement with the same number of unknowns as the first-order shear deformation theories. Moreover, the effects of width-to-thickness ratio, fiber orientation, number of modes, different dimensional ratios of the plate, and finally, the number of layers are investigated through numerical examples. The bubble shape functions are exploited in the transverse direction to improve the convergence of the method. Finally, the shearing and axial interaction diagrams of composite laminated plates are presented for various types of boundary conditions.

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