Izhak Sheinman

Buckling of Multiply Delaminated Beams

An analytical model is developed for buckling of multiply delaminated composite beams or long plates under cylindrical bending, and their interactive effects are studied. The prebuckling and buckling equations, formulated for one-dimensional cases with an arbitrary configuration of through-the-width cracks, are solved in a closed-form manner. The effects of crack length and location are studied, showing different trends of behavior for global and local mode shapes, including a decrease in the buckling load when cracked zones overlap. In some cases, where inadmissible interlaminar penetration in the first mode is involved, higher eigenvalues and the corresponding eigenmodes are needed to define the buckling state. In other cases, where all eigen modes exhibit penetration, the present model can be used only as indicated for the behavior, and a nonlinear analysis with contact constraints is called for. Considering the scanty work done to-date in the field of multiply delaminated beams, the proposed model-even though restricted to a contactless situation-can also serve as the basis for more general nonlinear analysis. A parametric study of several beam configurations is presented through examples.

Coupling Between Symmetric and Antisymmetric Modes in Shells of Revolution

An analytical-numerical procedure is applied for composite laminated shells of revolu tion in investigating the coupling effect between symmetric and antisymmetric modes and its overall influence. The numerical solution is based on separating the variables in Fourier series in the circumferential direction and conical finite elements in the meridional direc tion. The contribution of the coupling effect is examined by means of parametric analysis.

Post-buckling analysis of composite delaminated beams

Abstract A general one-dimensional geometrical non-linear model of a composite delaminated beam under arbitrary axial and transverse loading for any boundary conditions is derived for predicting the post-buckling behavior. The model comprises nonlinear equations based on the Von Karman kinematic approach, suitable for checking the effect of delamination and initial imperfection on the overall non-linear behavior. The differential equations, which incorporate the bendingstretching coupling effect, are solved by Newtons method using a finite-difference scheme. The delamination ratio parameter, bending stretching coupling and the initial imperfection are examined by means of parameteric analysis.

Dynamic Analysis of Laminated Shells of Revolution

A general analytical and numerical procedure is developed for free and forced vibra tion of thin-walled shells of revolution made of arbitrarily laminated orthotropic elastic material. The equations of motion are derived with the aid of Hamiltons variational principle. A numerical solution is obtained by expanding the variables in Fourier series in the circumferential direction, and using conical finite elements in the meridional direction. Several examples involving different shell geometries are considered, in cluding the effects of fiber orientation and boundary conditions.

Straight-sided, buckling-driven delamination of thin films at high stress levels

The fracture mechanics of a straight-sided, thin film delamination at stress levels, which are high compared to the stress required to initiate the delamination is investigated. Buckling at a bifurcation point of the delaminated region, resulting from incompletely relieved stresses in this region, is analysed by a semi- analytical approach for delaminations of infinite extent. The results are compared to numerical predictions based on finite element calculations for finite sized delaminations. The finite element calculations are carried out in the post-buckling regime showing that parts of the crack front will close as a result of bifurcation buckling, while other parts will experience enhanced energy release rate and mode I stress intensity factor. The mode III stress intensity factor is shown to be negligible at the stress levels analysed.

Post-Buckling Analysis of Stiffened Laminated Panel

An analytical-numerical procedure is applied to investigate the post-buckling behavior of a composite laminated stiffened panel. The panel is modeled by plate elements for which the nonlinear equations are derived (via a variational principle) in terms of the lateral displacement and Airy stress function, and treated by resolving the variables into eigenfunctions in conjunction with a finite-difference scheme.

Inperfection sensitivity of laminated cylindrical shells in torsion and axial compression

Abstract The imperfection sensitivity of thin cylindrical shells, made out of fiberreinforced composite material and subjected to either uniform axial compression or torsion, and the effects upon it of certain parameters, are investigated. The sensitivity is established through plots of critical loads (limit point loads) versus imperfection amplitude. The larger the drop in critical load value with increasing amplitude, the greater the sensitivity. Results are presented for four- and six-ply laminates with simply supported boundaries and various stacking sequences. These sequences lead to symmetric, antisymmetric and asymmetric configurations with respect to the laminate midsurface. The material for all configurations is boron/epoxy. The parametric studies include primarily the effect of lamina stacking and length-to-radius ratio on the critical loads. Among the important findings are that (a) laminated cylindrical shells are more imperfection sensitive under axial compression than under torsion, (b) the imperfection sensitivity decreases as the length-to-radius ratio increases and (c) lamina stacking has a pronounced effect on the imperfection sensitivity of the laminated shell.

Damage detection and updating of stiffness and mass matrices using mode data

A new simple and efficient algorithm for damage detection and for updating of stiffness and mass matrices is presented, based on minimum static and/or dynamic measured modes and preserving connectivity. A special algorithm was written for grouping uncoupled damage regions, significantly reducing the order of the problem and suitable for any structure size. A mode-scanning procedure is employed for finding the minimum measured modes needed for completing the process. Three illustrative examples are provided.

Buckling Analysis of Laminated Cylindrical Shells with Arbitrary Noncircular Cross Section

Buckling analysis of laminated cylindrical shells with noncircular cross section of arbitrary closed shape is presented. The equations, in terms of the normal displacement and Airy stress function, of the Donnell type, are derived via the Hu-Washizu mixed formulation. The curvature, which is a function of the circumferential coordinate, is expanded in Fourier series. The circumferential dependence is eliminated by a combination of Fourier expansion and Galerkins method. The resulting ordinary differential equations are then reduced to matrix equations by the use of finite differences. The configurational aspect is investigated parametrically. Unlike the circular cylindrical shells, coupling of the wave number in the circumferential direction is significantly high.

Effect of delamination on stability of laminated composite strip

Abstract A general one-dimensional model of a composite delaminated elongated strip (wide beam) under arbitrary axial and transverse loading and boundary conditions is used for predicting the classical buckling load, with the bending-stretching coupling effect as well as the prebuckling geometrical nonlinearity taken into account. The differential equations are solved by Newtons method, using a finite-difference scheme. The contribution of the coupling effect is examined by means of parametric analysis.