Showing papers on "Orthotropic material published in 1983"

Geometrically nonlinear transient analysis of laminated composite plates

Abstract: Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.

Comment on Orthotropic Models for Concrete and Geomaterials

Abstract: Incrementally linear constitutive equations that are characterized by an orthotropic tangential stiffness or compliance matrix have recently become widely used in finite element analysis of concrete structures and soils. It does not seem to be, however, widely appreciated that such constitutive equations are limited to loading histories in which the prinicipal stress directions do not rotate, and that a violation of this condition can sometimes have serious consequences. It is demonstrated that in such a case the orthotropic models do not satisfy the form‐invariance condition for initially isotropic solids, i.e., the condition that the response predicted by the model must be the same for any choice of coordinate axes in the initial stress‐free state. An example shows that the results obtained for various such choices can be rather different. The problem cannot be avoided by rotating the axes of orthotropy during the loading process so as to keep them parallel to the principal stress axes, first, because t...

Dynamic (transient) analysis of layered anisotropic composite‐material plates

Abstract: A shear-flexible finite element is employed to investigate the transient response of isotropic, orthotropic and layered anisotropic composite plates. Numerical convergence and stability of the element is established using Newmark's direct integration technique. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The present results agree very closely with the results available in the literature for isotropic plates, and the results for composite plates should serve as bench marks for future comparisons by other investigators.

Generic buckling curves for specially orthotropic rectangular plates

Abstract: Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Postbuckling of orthotropic composite plates loaded in compression

Abstract: The nonlinear large deflection equations of von Karman are written for 'specially' orthotropic plates. The equations are then manipulated to determine the parameters required to establish postbuckling behavior. It is found that only two new parameters are needed beyond those required for buckling. By assuming trigonometric functions in one direction, the plate equations are converted into ordinary nonlinear differential equations which are solved numerically using a two point boundary problem solver that makes use of Newton's method. The postbuckling behavior is obtained for simply supported and clamped, long, rectangular, orthotropic plates covering the complete range of dimensions and material properties.

Analysis of the stress state in an Iosipescu sheartest specimen

Abstract: The state of stress in an Iosipescu shear test specimen is analyzed, utilizing a finite element computer program. The influence of test fixture configuration on this stress state is included. Variations of the standard specimen configuration, including notch depth, notch angle, and notch root radius are modeled. The purpose is to establish guidelines for a specimen geometry which will accommodate highly orthotropic materials while minimizing stress distribution nonuniformities. Materials ranging from isotropic to highly orthotropic are considered. An optimum specimen configuration is suggested, along with changes in the test fixture.

Elastic Constants And Tensile Strength Of Anisotropic Rocks

Abstract: A closed-form solution is proposed for the distribution of stresses and strains within a thin disc of anisotropic material loaded diametrically by a line or a strip load. This solution is then incorporated into a procedure to measure the elastic constants and the tensile strength of rocks that can be idealized as linearly elastic, homogeneous, orthotropic or transversely isotropic continua. The number of the covering abstract of the congress is TRIS no. 385148. (Author/TRRL)

Flutter of Orthotropic Panels in Supersonic Flow Using Affine Transformations

Abstract: Affine transformations are used in analyzing the flutter problem of rectangular simply supported orthotropic panels subjected to supersonic flow over one surface. With the help of certain defined characteristic and bounded quantities a comprehensive solution, which has the isotropic panels solution as a subset, is found to this problem. The physics of this very important aeroelastic problem which has been so obscure for a long time because of the presence of so many parameters is thus clearly exposed by showing how the aerodynamic and the elastic forces interact to produce the panel flutter phenomenon. Both the aerodynamic strip (Ackeret) theory and lifting surface theory are compared and found to agree very well in the analysis. Hence, complete stability boundaries are determined for both flat and buckled panels using the aerodynamic strip theory, the simpler of the two theories.

Buckle Pattern of Biaxially Compressed Simply Supported Orthotropic Rectangular Plates

Abstract: Simply supported orthotropic elastic rectangular plates in biaxial compres sion are considered, and it is proved that such plates will buckle with m or n (or both) equal to 1, where m and n are the...

An inelastic finite element model of 4D carbon-carbon composite

Abstract: Sepcarb 4D is a carbon-carbon composite material wherein the reinforcing fibers are bundled in four directions It is widely and successfully used in integral solid rocket nozzles However, an accurate prediction of the material behavior is difficult, due to the anisotropy and above all to the nonlinear inelasticity of the composite An elastoplastic finite element model, including homogenized monoaxial stiffnesses, is presented A consistent set of constitutive constants is obtained from test data The adequacy of the model is demonstrated through comparisons between predicted and measured test results of Sepcarb 4D uniaxial specimens and rings Results showing the significant influence of the orientation of the 4D reinforcement s relative to the applied load are discussed The model can be extended to an increased number of directional composites and offers new possibilities in the stress analysis of such materials

An Experimental and Analytical Study of the Dynamic Response of a Linkage Fabricated from a Unidirectional Fiber-Reinforced Composite Laminate

Abstract: A large class of industrial machinery and commercial equipment is operated at high speed to satisfy the demands for high productivity. In order to further improve performance, it is proposed herein that the designer should consider fabricating the mechanism components in one of the commercially available composite materials because they offer many desirable characteristics with the promise of even higher speeds of operation. This paper presents an experimental and computational study of a flexible planar four-bar linkage fabricated from one of these composites. This fiber-reinforced material is modeled as an elastic solid by using a continuum theory which accommodates laminae with orthotropic properties, and differing densities, thicknesses, and elastic moduli. The theory is embodied in a variational theorem which serves as the basis for a finite element analysis of the mechanism.

Investigations of axisymmetric deformation of geometrically nonlinear, rotationally orthotropic, circular plates

Abstract: Some results of qualitative investigations and of numerical solutions to the problem of axisymmetrical deformations of circular, geometrically non-linear, rotationally orthotropic plates are presented. The qualitative studies reveal certain general characteristics of behavior and proofs are obtained only on the basis of form, in analogy to the qualitative theory of differential equations. For numerical solutions we employ the shooting method in combination with the ‘deformation map’, which is similar to Poincare's phase plane.

Smooth Contact Between a Rigid Indenter and an Initially Stressed Orthotropic Beam

Abstract: The elastostatics problem of a rigid punch in smooth contact with an initially stressed transversely isotropic layer is investigated. The problem is formulated by writing the field equations in terms of suitable displacement potentials. In addition, an elementary beam theory solution is superimposed on the elasticity solution to satisfy the support boundary conditions for a finite beam. The cases studied are those of a simply supported beam and a clamped beam.

Minimum-Weight Design of an Orthotropic Shear Panel with Fixed Flutter Speed

Abstract: THIS paper deals with the weight minimization of rectangular flat panels placed in a high supersonic flowfield and subject to a flutter speed constraint. In the establishing of the structural operator a pure transverse shear plate model was used, which may, be considered as a complement of the Love-Kirchhoff type model. By using the theory of optimal control of distributed parameter systems, necessary conditions for the minimum-weight panel are derived. These are supplemented with a condition ensuring that the flutter speed of the optimal panel coincide with the prescribed one. It is shown that the optimal thickness distribution is symmetrical with respect to the panel midpoint. Numerical rough estimates obtained via Galerkin's method are presented. Contents The field of weight minimization of panels subjected to aeroelastic constraints has been investigated thoroughly during the past decade, as it may be inferred from the specialized literature. Throughout these investigations, whether dealing with one-dimensional (see Refs. 1-4) or twodimensional aeroelastic optimization problems,5-8 the appropriate structural operator was established on the basis of the Love-Kirchhoff type model. As it is known, this model involves the ab-initio disregard of transverse shear effects. In contrast to this approach, a somewhat opposite structural type model is used here, in which the rigidities in transverse shear are considered as finite, and in bending as negligible (such a panel will be termed a pure transverse shear panel). This model—first introduced by Armand 9—is practically motivated by the advent of new composite materials that enjoy exotic properties. A generalized form of this structural model, including transverse shear orthotropicity effects, will be used here for approaching the present aeroelastic optimization problem. The structure to be analyzed consists of an elastic, rectangular flat thin panel (axb) of nonuniform thickness h = h(x]yx2), where OxjX2 denotes the in-plane coordinate system (Ox2 is the stream wise coordinate, while Ox2—the span wise one—coincides with the panel leading edge). The panel is exposed to a high supersonic gas flow over its upper face. The aeroelastic optimization problem dealt with here consists of finding the thickness distribution which minimizes the panel weight, while maintaining the same flutter speed as that of a uniform-thickness reference panel. As usual, 8 the reference panel is defined as the panel of uniform thickness H0 having the same ofthbtropy characteristics and boundary conditions as its counterpart of nonuniform thickness.

Optimization of openings in plates under plane stress

Abstract: An analytical/nu merical procedure for optimizing certain geometrical and material aspects in the design of openings for both isotropic and anisotropic plate structures under in-plane loading is described. The procedure is based on first developing symbolic boundary-stress expressions as functions of opening geometry, plate material, amount of reinforcement , and specified loading. These stress expressions are then used to construct a meaningful objective function. Minimization of this function with respect to the opening geometry, the plate material constants, and the amount of reinforcement gives the desired optimum values. Four typical examples are included to demonstrate the procedure: 1) optimization of the shape of a square-like opening in a large isotropic plate, 2) optimization of the amount of reinforcement for a circular opening in a large isotropic plate, 3) optimization of the amount of reinforcement for a square-like opening in a large isotropic plate, and 4) optimization of the material constants for a circular opening in a large orthotropic plate. Results for these problems with several types of boundary loads are included.

The Instability of Composite Channel Sections

Abstract: At previous conferences the authors have examined the buckling and postbuckling behaviour of reinforced plastic plates subject to in plane loading, both theoretically1 and experimentally.2 That work has been extended to cover the buckling and post buckling behaviour of orthotropic box sections.3 The present contribution extends this work further to examine the instability of orthotropic channel sections. The sections are considered as a series of linked plates with rotationally restrained unloaded edges or rotationally restrained and free unloaded edges. These conditions have been considered for the plates alone. The linking procedure enables the instability of the section to be evaluated.

Stresses around pin-loaded holes in composite materials

Abstract: Stresses have been calculated for infinite orthotropic plates with a circular hole loaded by a perfectly fitting rigid pin with arbitrary load direction. The effect of friction at the interface between pin and plate material is evaluated. The calculations are based on the analytical method of complex stress functions. A numerical approach was used for satisfying the displacement boundary conditions of the contact area between pin and hole. Stress concentration factors based on the nominal bearing stress are presented graphically for three carbon fibre reinforced plastic laminates. A quadratic failure criterion was used to predict the bearing stress at which first significant damage occurs. The results indicate that the presence of friction has a significant influence on the stress distribution.