Thermal buckling of laminated composite plates

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.