Theoretical modelling of laminated composite plates

Formulation of appropriate governing equations, simpler than the three-dimensional equations of elasticity yet capable of predicting, fairly accurately, all important response parameters such as stress and strain, is attempted in modelling a structural component. Several theoretical models are available in the literature for the analyses of plates. The emergence of fibre-reinforced plastics as an attractive form of structural construction, added a new complexity to the modelling considerations of laminates by requiring the estimation of the interlaminar stresses and strains. In this paper, modelling considerations of laminated composite plates are discussed. The classical laminated plate theory and higher-order shear deformation models are reviewed to bring out their interlaminar stress predictive capabilities, and some new modelling possibilities are indicated

Design considerations with reference to glass/ carbon fibre reinforced polymer composites as structural materials

Composite materials involving fibre reinforcement are replacing traditional materials at a rapid rate, The driving force for this change is extraordinary properties that can be obtained when the material is in the fibre form. The inherently superior fibre properties combined with a matrix phase 9f complementary properties result in a high performance composite. Thus the fibre reinforced composites have brought about an extraordinary facility in design engineering, in effect forcing the design-analyst to create different material for each application as he pursues the objective of minimizing weight and cost an:d maximizing safety and operational life. The fields of application of compositeS cover a wide range from sports, agriculture, automobiles of electronics and aerospace. In this paper, design considerations with reference to glass/carbon fibre reinforced polymer composites are discussed

Torsional vibrations of multi-cell tubes

This paper presents torsional vihraTion analYJis of multi-cell tubes. The main difference between the single and multi-cell tube analysis lies in the determination of the cross-sectional constants. Derivation of cross-sectional constants, involved in the governing equations, is illustrated by considering a four-cell tube. The improvement, in the estimation of the natural frequency by the present proposal, is brought out by comparing the theoretical value with the experimental observation in a specific case

Modeling of plate flexure satisfying normal stress conditions at the plate surfaces

Modeling of plate flexure, based on cubic variation of inplane displacements and quartic variation of the normal displacement has been discussed. Displacement functions satisfy the zero shear stress condition at top and bottom surfaces of the plate. The normal stress condition at the surfaces of the plate and the elemental equilibrium eqUlltions are enforced through the use of the Lagrangian multipliers in the variational procedure used. Several new models are available as special cases in this formulation. An illustrative example of a simply-supported plate subjected to sinusoidal loading is included to indicate relative merits of the special cases

General theory of cylindrical vibrations tubes. Part IV. Uncoupled torsional vibrations of open tubes

Based on the ease in satisfying the free edge boundary conditio/I, open tubes are classified into two types, A and B. Type B tubes have more complicated free-edge boundary condition than that of type A tubes. An alternate formulation is evolved for type B tubes; this makes the free-edge boundary condition as simple as in type A tubes. A simply-supported open tube with the cross-section given by p=S/2π sin 2πS/S, is analysed exactly as well as by using approximation equations; errors in using the first order approximation equations are discussed. A simply-supported open tube of I-section, representative of type B tubes, is analysed by using first and second approximation equations

General theory of cylindrical vibrations tubes. Part V. Uncoupled flexural vibrations of open tubes

Based on the simplicity in satisfying free-edge boundary condition, open tubes vibrating injlexural mode are classified as type C and type D. Compared to type D tubes, type C tubes have relatively simpler free-edge boundary condition. An alternate formulation is developed for type D tubes in which the satisfaction of the free-edge condition is as simple and direct as in type C tubes. Analysis of type C tubes is very similar to that of closed tubes. In this paper we study the flexural vibration characteristics of a simply-supported lipped-I-section which is a typical open tube of type D

General theory of vibrations of cylindrical tubes

The equations governing torsional vibrations of unstiffened cylindrical tubes have been presented. Methods proposed in Part I are illustrated by considering the torsional vibrations of doubly symmetric tubes. An exact solution of a simply supported tube with the boundary of the cross section given by p=s/2π cos 2π S/S is presented. A free- free tube of rectangular cross section is analysed by using first order approximation equations and the results are in good agreement with earlier work

General theory of vibrations of cylindrical tubes. PART-III. Uncoupled flexural vibrations of closed tubes

Flexural vibration characteristics of unstiffened doubly symmetric cylindrical tubes are studied using the theory proposed by the authors in part I. An exact solution of a simply supported tube with the cross-section given by x= s2/4π2 sin 2πS/S is presented. Natural frequencies of a 'simply supported tube of rectangular cross-section are obtained by using first and second order approximation equations. Numerical results indicate that it is essential to consider, at least, second order approximation equations to study the flexural vibration characteristics of doubly symmetric tubes

A comparative study of the consistent and simplified finite element analyses of Eigenvalue, problems

Classical displacement method of the finite element analysis of eigenvalue problems requires the use of consistent and conforming elements. However, simpler approaches based on relaxing the condition of consistency of the element descriptions, such as lumped inertia force method and others are also found to yield satisfactory results. In this paper we make a comparative study of the consistent and simplified approaches with reference to four representative problems. In the simplified approach studied in this paper, the contribution of straining modes in the derivation of the mass and geometric stiffness matrices is neglected and this simplifies their derivation substantially. The results indicate that this simplification introduces only small errors in the eigenvalues

Structural behaviour of tapered rods subjected to axial compressive loads in the post-buckling range

The equation governing the behaviour of rods of variable cross-section subjected to compressive load" is deduced using the classical assumption-that the plane sectioIis of the rod before bending remain plane even after bending; the stress-strain relationship can be either the conventional Ramberg-Osgood Law or the alternative form developed by Rao and Krishna Murthy; the deformations are considered to be large, 'The governing equation is nonlinear and an iterative' method is used to obtain numerical results. A dass of rods whose variation of the cross-section ,can be represented by I=I0(1-βS)n(where s is the curvilinear coordinate) are considered to study,the post-buckling behnviour. Numerical results have been obtained for various values of the geometric parameters involved in the problem, and the results are in good agreement with those available in the literature