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Thermal buckling of laminated composite plates
Author(s)
Simelane, Philemon Sphiwe
Date Issued
1998
Type
Thesis
Publisher
Peninsula Technikon
Abstract
However, studies were also conducted for the buckling of composite laminates
involving temperature distribution. Chen and Chen (1991) studied thermal buckling
of laminated plates under uniform and nonuniform temperature distribution using the
eight-node Serendipity finite element. Mathew, Singh and Rao (1992) investigated
thermal buckling of antisymmetric cross-ply composite laminates with a onedimensional
furite element having two nodes and six degrees of freedom.
Chandrashekhara (1992) accounted for transverse shear flexibility by using the
thermo-elastic version of the first-order shear deformation theory. This will also be
the case in this report. Literature on buckling and laminated composites abounds.
Brush and Aimroth (1975) published a book on Buckling of Bars, Plates, and Shells,
while Bushnell (1985) surveyed the Methods and Modes of Behaviour in Static
Collapse. The foundation for the study of composite materials was based on the
references [8], [10], [15] and [18]. The use of the Finite Element Method to analyse
the buckling behaviour of laminated structures comes from references [I], [4]. [I2].
[16], [24] and [32]. Reference [14] provided the basis for the formulation of the
variation of the governing equations. Most of the ideas in this report are based on
these publications and references.
Chapter I of this report introduces the concept of a composite. the formation of a
composite and a brief overview of the elements of a composite material. This chapter
also presents the concept of buckling that will form the basis of the development of
this project. At the end of this chapter the choice of the element that is used in this
study is justified. Chapter 2 provides the fundamentals of elasticity that relate to the
deformation of a loaded body. In this Chapter the stresses and strains are defined and
the temperature terms are introduced. In Chapter 3 the Mindlin plate theory is
presented with a view to laying the foundation for the analysis of laminated plates,
and as a starting point in the formulation of thermal buckling behaviour of laminated
plates. In Chapter 4 the elements of a composite material are discussed and the
constitutive equations of a laminated composite plate are built. Also the idea of
lamination is introduced and the various simplifications that can be introduced as a
result of lamination are discussed. The non-linear equilibrium equations and the
stability analysis of a composite plate are formulated in Chapter 5 using the
conventional anal}1ical method. The resulting equations justify the use of the Finite
Element Method as introduced in Chapter 6 and it is the method by which the
governing equations will be solved in ABAQUS computer analysis. The results for
various computer runs are presented for a normal plate, a plate with a square hole, and
the plate ""ith a circular cut-out in Chapter 7. Also in chapter 7 a comparison is made
between the laminate "ith a central hole and a normal plate to study the effect of a
cut-out on a critical buckling temperature. Appendices A deals the transverse shear in
plates, and Appendix B deals with the transformation of the laminate elastic constants
form the principal material direction to the general Cartesian co-ordinates. Also in
Appendix B the laminate stiffness matrices and these matrices are briefly evaluated
analytically. Appendix C is about the governing equations of laminated composites,
while Appendix D gives a full representation of the abbreviated finite element
equations of Chapter 6. Appendix E presents the list of ABAQUS input files that
were used in the computer simulation of Chapter 7.
involving temperature distribution. Chen and Chen (1991) studied thermal buckling
of laminated plates under uniform and nonuniform temperature distribution using the
eight-node Serendipity finite element. Mathew, Singh and Rao (1992) investigated
thermal buckling of antisymmetric cross-ply composite laminates with a onedimensional
furite element having two nodes and six degrees of freedom.
Chandrashekhara (1992) accounted for transverse shear flexibility by using the
thermo-elastic version of the first-order shear deformation theory. This will also be
the case in this report. Literature on buckling and laminated composites abounds.
Brush and Aimroth (1975) published a book on Buckling of Bars, Plates, and Shells,
while Bushnell (1985) surveyed the Methods and Modes of Behaviour in Static
Collapse. The foundation for the study of composite materials was based on the
references [8], [10], [15] and [18]. The use of the Finite Element Method to analyse
the buckling behaviour of laminated structures comes from references [I], [4]. [I2].
[16], [24] and [32]. Reference [14] provided the basis for the formulation of the
variation of the governing equations. Most of the ideas in this report are based on
these publications and references.
Chapter I of this report introduces the concept of a composite. the formation of a
composite and a brief overview of the elements of a composite material. This chapter
also presents the concept of buckling that will form the basis of the development of
this project. At the end of this chapter the choice of the element that is used in this
study is justified. Chapter 2 provides the fundamentals of elasticity that relate to the
deformation of a loaded body. In this Chapter the stresses and strains are defined and
the temperature terms are introduced. In Chapter 3 the Mindlin plate theory is
presented with a view to laying the foundation for the analysis of laminated plates,
and as a starting point in the formulation of thermal buckling behaviour of laminated
plates. In Chapter 4 the elements of a composite material are discussed and the
constitutive equations of a laminated composite plate are built. Also the idea of
lamination is introduced and the various simplifications that can be introduced as a
result of lamination are discussed. The non-linear equilibrium equations and the
stability analysis of a composite plate are formulated in Chapter 5 using the
conventional anal}1ical method. The resulting equations justify the use of the Finite
Element Method as introduced in Chapter 6 and it is the method by which the
governing equations will be solved in ABAQUS computer analysis. The results for
various computer runs are presented for a normal plate, a plate with a square hole, and
the plate ""ith a circular cut-out in Chapter 7. Also in chapter 7 a comparison is made
between the laminate "ith a central hole and a normal plate to study the effect of a
cut-out on a critical buckling temperature. Appendices A deals the transverse shear in
plates, and Appendix B deals with the transformation of the laminate elastic constants
form the principal material direction to the general Cartesian co-ordinates. Also in
Appendix B the laminate stiffness matrices and these matrices are briefly evaluated
analytically. Appendix C is about the governing equations of laminated composites,
while Appendix D gives a full representation of the abbreviated finite element
equations of Chapter 6. Appendix E presents the list of ABAQUS input files that
were used in the computer simulation of Chapter 7.
Additional information
Thesis (MTech (Mechanical Engineering))--Peninsula Technikon, 1998
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