Showing papers on "Orthotropic material published in 1973"

Theories for the Dynamic Response of Laminated Plates

Abstract: The effect of the heterogeneous shear deformation over the thickness of the plate on the dynamical behavior of laminated plates is investigated. Three sets of governing equations are derived according to different assumptions on the local transverse shear deformation and the interface conditions. The equations are evaluated by comparing the solutions with the exact solution for harmonic wave propagations. A special formulation for laminates with midplane symmetry is also presented and discussed. It is found that the effect of the local shear deformation depends highly on the transverse shear rigidities of the constituent layers.

Bending and vibration of multilayer sandwich beams and plates

Abstract: A finite element displacement analysis of multilayer sandwich beams and plates, each with n stiff layers and n−1 weak cores, is presented. Each layer of the sandwich structure may have individual orthotropic properties of its own and the bending rigidities of the stiff layers are taken into account while direct stresses in cores are neglected in the analysis. The condition of common shear angle for all cores, which has been used by several authors is not implied in the formulation. Several examples on bending problems have been solved using lower-order elements and the accuracy of the results has been shown to be excellent. Two higher-order elements have also been developed but have not been found to yield much better results. The free vibration problems of multilayer sandwich structures have also been solved, and good accuracy is demonstrated.

Shear Coefficients for Orthotropic Beams

Abstract: Because of their high stiffness-to-weight ratios, fiber reinforced composites are being studied for use in weight-critical compression members. Davis [1] pointed out that unidirectional or nearly unidirectional composites typically have a low transverse shear stiffness and the calculation of the critical column load for compression members should account for transverse shear effects. He presents experimental data for unidirectional Boron/Epoxy tubes which fall significantly below the Euler curve at higher stress levels. The column equations with shear effects included, as presented in Reference [ 2 ] , include in their derivation the expression for shear strain NQIA G. Cowper [ 3 ] presents a derivation for 1 /n or K as he defines it for isotropic materials and presents equation results for many commonly used cross sections. The factor K was shown to be dependent on the column material’s Poisson’s Ratio (v). The presence of a material property in K suggested that a new derivation should be undertaken

Experimental Buckling Loads of Sandwich Panels with Carbon Fibre Faceplates

Abstract: Experiments to determine the overall buckling and faceplate wrinkling loads of sandwich panels with carbon fibre reinforced plastic faces and honeycomb cores when loaded under uniaxial compression are described. The results are compared with theoretical predictions which assume that the faceplates are orthotropic. The effect on the experimental loads of certain coupling terms, which occur in the constitutive equations of those faceplates which are not orthotropic, is then considered.

Buckling of Laminated Anisotropic Imperfect Circular Cylinders under Axial Compression

Abstract: A new design approach is presented to provide a conservative estimate of the buckling strength of laminated anisotropic circular cylinders under axial compression. The analysis is based on Koiter's "special theory" for uniform axisymmetric shape imperfections which is valid for imperfections of the order of the shell wall thickness. Fourteen three-ply, glass-epoxy cylinders containing random imperfections of small mean square amplitude were characterized in terms of an equivalent axial imperfection component. Good agreement was found between theory and experiment for the range of imperfection amplitudes encountered.

Dynamic buckling of a rectangular orthotropic plate

Abstract: The elastic buckling of a simply-supported rectangular orthotropic plate, with initial imperfections, under a rapidly applied compressive load is analyzed. The large deflection plate equations are used to study inertial effects in the postbulkling phase. Numerical results for a controlled rate of load application show that the critical load is increased over the corresponding static case. The load-deflection relation is oscillatory in the postbuckling phase, thereby increasing the stresses in the plate over those in the static case. Initial imperfections decrease the critical load as well as increase the frequency and decrease the amplitude of the oscillations.

Post-Buckling Behaviour of Rectangular Orthotropic Plates

Abstract: An analysis is presented for the post-buckling behaviour of a simply supported, rectangular, orthotropic plate subjected to biaxial compression. The solution of von Karman-type large deflection equations of the plate satisfying the prescribed boundary conditions is expressed in the form of a double Fourier series for the transverse deflection and a double series for the stress function consisting of the appropriate beam functions. The effect of plate properties on stresses and deflections has been studied for three fibre-reinforced materials. Numerical results indicate good convergence of the present series solution and are compared with the available data.

Static and dynamic non-linear behaviour of heated orthotropic circular plates

Abstract: The fundamental quasilinear, decoupled equations of equilibrium and motion of heated orthotropic circular plates are derived from the energy equation in the light of a generalised analysis of a Berger-type which is based on the assumption that the effect of second strain invariant in the expression for total energy may be neglected. Solutions are obtained by Poincare's method of successive approximation and numerical results are given in graphical form for both static and dynamic cases of orthotropic circular plates, simply supported or clamped throughout the edge.

The Influence of Orthotropy on the Stability of some Multi-plate Structures in Compression

Abstract: Three computer programmes have been written for the stability analysis of both isotropic and orthotropic, multi-plate structures in compression. The bases of these programmes are the exact and approximate Finite Strip methods. A considerable number of results for a range of multi-plate structures fabricated from both carbon fibre reinforced (orthotropic) and aluminium (isotropic) materials are presented in graphical form. These graphs serve to illustrate not only the influence of material orthotropy on the buckling response, but also the possible savings in weight that may be achieved by employing orthotropic materials in place of conventional isotropic materials.

Nonlinear analysis of orthotropic skew plates.

Abstract: The nonlinear analysis of clamped orthotropic skew plates of constant thickness subjected to a uniformlydistributed transverse load has been presented. The recently developed numerical technique of dynamic relaxation which is specially suited for nonlinear problems has been used in the present analysis. A detailed study of the large deflection behavior of rhombic-ortho tropic skew plates has been made by varying the skew angle and load. Numerical results have been obtained for a particular case of orthotropy. These results have been specialized for the case of a square plate and compared with available solutions. Representative nondimensional solutions are presented in the form of graphs to elucidate the nonlinear effect due to large deflection at higher loads. The effect of skew on the deflection and stress resultants are also discussed. Suggestions have been made for arriving at an approximate estimate of the time increment At suitable for orthotropic skew-plate analysis, which assures stability of numerical calculations.

Photoelastic Analysis of an Orthotropic Ring under Diametral Compression

Abstract: N this paper an improved model material for photoorthotropic-elasticity, with better transparency and more favorable fiber distribution, is described. A unidirectional ly reinforced circular ring, subjected to diametral compression at 0°, 45°, and 90° to the reinforcement direction, is investigated. The resulting isochromatic fringes are converted to tangential stresses on the inner and outer boundaries after correction for the residual birefringence of the model material. The stress distributions are compared with the corresponding values for an isotropic ring. Contents Two different methods have been employed so far in the preparation of unidirectiona lly reinforced model materials for transmission photoelastic applications. The method used by Pih and Knight1 as well as by Sampson2 involves filament winding and the application of vacuum to eliminate entrapped air. The method employed by Dally and Prabhakaran3 utilizes commercial glass fabrics and does not require the application of vacuum. However, the twist of the yarns in the glass fabric gives rise to two problems. First, air entrapped between the fibers is not completely removed by the simple squeezing operation and consequently maximum possible transparency is not achieved, in spite of careful matching of the refractive indices of the matrix and the glass reinforcement. Secondly, the glass fibers are grouped together in discrete bundles resulting in poor fringe resolution in regions of high fringe gradient.4 To eliminate the disadvantages of twisted yarns while retaining the simplicity of fabrication technique, in the present study woven roving has been used as the reinforcement. With only ten plies of the glass roving, a thicker laminate (0.18 in.) was obtained. Far greater transparency was achieved, without resorting to vacuum. Most important of all, the photoelastic response was much better, with improved fringe resolution. In Fig. 1 the lightfield isochromatic fringe pattern for a notched beam in four-point bending is presented for the old and new model materials. The reason for the difference in fringe resolution is apparent from the photomicrographs. The glass fibers in the material prepared from roving are more uniformly distributed, thus better justifying the treatment of the heterogeneous orthotropic material as a homogeneous orthotropic material. A circular ring, with the outside and inside diameters 3 in. and 1.5 in., respectively, was machined from a f-in.-thick unidirectionally-reinforeed laminate consisting of 35% volume fraction of glass fibers. The machining stresses were annealed by heating the

Tire Stress and Deformation from Composite Theory

Abstract: The pneumatic tire is treated as a laminated, anisotropic, toroidal shell of revolution possessing bending rigidity. The plies, which are constructed of elastic textile cords embedded in an elastic rubber matrix, are considered homogeneous and orthotropic on a macroscopic scale. The tire shell is considered to deform according to the classical Love hypothesis. The equilibrium, strain‐displacement, and laminate constitutive equations governing the tire shell are reduced to a system of six first order, nonlinear, ordinary differential equations with variable coefficients which are solved numerically by a multi‐segment forward integration technique. The geometrical nonlinearities due to finite displacements are accounted for by an incrementing process using transient coordinates. The theory is illustrated by a numerical calculation which shows good agreement with actual measurements.

Nonlinear Vibration of Elastic Skew Plates Exhibiting Rectilinear Orthotropy

Abstract: The governing equations for large amplitude flexural vibrations of orthotropic skew plates are obtained from the corresponding static equations derived in this paper. Making use of an approximation originally due to Berger, corresponding simplified equations are also derived. Considering the large amplitude free flexural vibration of orthotropic skew plates clamped along all the edges, it is shown that the Berger approximation leads to results good enough for engineering purposes. Amplitude vs period curves are presented for different aspect ratios and skew angles of the plate under two in-plane edge conditions. It is observed that the amplitude vs period behaviour is of the hardening type, i.e. period decreases with increasing amplitude.