Deflection of Rectangular Laminated Composite Plates using Dynamic Relaxation Method

Deflection of Rectangular Laminated Composite Plates using Dynamic Relaxation Method
اسم المؤلف
Osama Mohammed Elmardi Suleiman, Mahmoud Yassin Osman
11 مارس 2021
(لا توجد تقييمات)

Deflection of Rectangular Laminated Composite Plates using Dynamic Relaxation Method
Osama Mohammed Elmardi Suleiman
Assistant Professor in Mechanical Engineering, Faculty of Engineering and Technology, Nile Valley University, Atbara, Sudan
Mahmoud Yassin Osman
Professor in Mechanical Engineering, Faculty of Engineering, Kassala University, Kassala, Sudan
Dedication i
Acknowledgement iii
Abstract iv
Contents v
Notations vii
Preface viii
CHAPTER (1) : Historical Background
. Introduction
. Macro and Micro Structure of Composites
1.2.1 Mechanical Behavior of a Fiber-Reinforced Lamina
1.2.2 Analytical Modeling of Composite Laminates
. Literature Review in the Theories of Laminated Plates
1.4 The Objectives of the Present Study
CHAPTER (2) : Mathematical Formulation of Plates
2.1 Linear Theory
2.1.1 Assumptions
2.1.2 Equations of Equilibrium
. . Strain-displacement equations
2.1.4 The constitutive equations
2.1.5 Boundary conditions
2.2 Non-linear theory
2.2.1 Assumptions
2.2.2 Equations of equilibrium
2.2.3 The strain-displacement relations
2.2.4 The constitutive equations
2.2.5 Boundary conditions
2.3 Transformation equations
2.3.1 Stress-strain equations
2.3.2 Transformation of stresses and strains
2.3.3 Transformation of the elastic moduli
CHAPTER (3) : Numerical Technique
3.1 DR formulation
3.2 The plate equations
3.2.1 Dimensional plate equationsvi
3.2.2 Non-dimensional plate equations
3.3 The finite difference approximation
3.3.1 Interpolating function F(x,y)
3.4 Finite difference form of plate equations
3.4.1 The velocity equations
3.4.2 The displacement equations
3.4.3 The stress resultants and couples equations
3.4.4 Estimation of the fictitious variables
3.5 The DR iterative procedure
3.6 The fictitious densities
3.7 Remarks on the DR technique
CHAPTER (4) : Validation of the Computer Program
4.1 Small deflection comparisons
4.2 Large deflection comparisons
CHAPTER (5) : Generation of New Results
5.1 Effect of load
5.2 Effect of length to thickness ratio
5.3 Effect of number of layers
5.4 Effect of material anisotropy
5.5 Effect of fiber orientation
5.6 Effect of reversing lamination order
5.7 Effect of aspect ratio
5.8 Effect of boundary conditions
5.9 Effect of lamination scheme
CHAPTER (6): Conclusions and Recommendations
6.1 Conclusions
. Recommendations
Appendix (A) :Tables
Appendix (B): Graphs
Appendix (C) : Boundary conditions
Appendix (D) : Estimation of the fictitious densitiesvii
A Plate length.
Aij i, j  1,2,6 Plate in-plane stiffnesses.
Aij i, j  4,5 Plate transverse shear stiffnesses.
B Plate breadth.
Bij i, j 1,2,6 Plate coupling stiffnesses.
Dij i, j 1,2,6 Plate flexural stiffnesses.
E ,E ,G Longitudinal, transverse, and in-plane shear moduli of
a lamina.
G ,G Transverse shear moduli in the x – z and y – z planes,
Zk , Zk+1 Distance of upper and lower surfaces of the lamina
from the plate mid-plane.
H Plate thickness.
K Lamina number.
2 5
2 4
K , K Shear correction factors.
M1,M2,M6 Stress couples.
M1 M1a2E21h4, M2, M6 Dimensionless stress couples.
N Number of layers.
N1, N2, N6 Stress resultants.
N1 N1a2E21h3, N2, N6 Dimensionless stress resultants.
q Transverse pressure.
q qa2E21h4 Dimensionless Transverse pressure.
Q1,Q2 Transverse shear resultants.
u ,v In-plane displacements.
W Deflections.
w wh1 Dimensionless deflections.
x ,y ,z Cartesian co-ordinates.
 t Time increment.
o o o
1 ,2 ,6 Extensional and shear strain components of plate
o o
5 ,4 Transverse shear strain components of plate midplane.
, Rotations of the original normal to the plate midplane.
12 Poisson’s ratio.
u ,v ,w,, In-plane, out-of-plane and rotational fictitious
o o o
1 ,2 ,6 Curvature and twist components
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