Buckling and postbuckling of thin elliptical anisotropic plates

The Rayleigh-Ritz method has been used to analyse the buckling and postbuckling behaviour of thin elliptical anisotropic plates. Different layups and ellipse orientations were analysed and compared with finite element results showing good agreement in displacements and total energies in the postbuckled regime. The energy release rates along the half axes which govern the onset of unstable delamination growth were computed for strains up to the third buckling mode.     

Buckling and postbuckling of imperfect cylindrical shells under axial compression

A solution methodology is described for the complete analysis of a geometrically imperfect, thin, circular, cylindrical shell loaded by a uniform axial compression. The analysis includes pre-limit point behavior, the establishment of critical conditions (limit point) and post-limit point behavior. The solution scheme is then utilized to study the effects of various geometrical parameters (radius to thickness and length to radius ratios) on the response characteristics of an imperfect, unstiffened, thin, cylindrical shell. These effects are assessed for a virtually axisymmetric-type of geometric imperfection.     

Buckling of multi-annular plates

Buckling of multi-annular plates is considered. The plate is loaded by axisymmetric radial in-plane forces, either at the outer edge or at one of the circumferential joints or a combination of the two. The plate is simply supported or clamped at the outer boundary or at one of the common joints. The various annular sections are fully connected, and they differ either in geometry or in material properties. Each annular section is homogeneous. A power series solution is used because of its applicability to various boundary conditions. A computer code is employed for the solution. Numerical examples are given for a two-part plate. The procedure is general and can be employed in various problems, such as buckling of annular plates resting on an elastic foundation, vibration analysis of annular plates, etc.     

Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM

In this study, a buckling analysis was carried out of a woven–glass–polyester laminated composite plate with an circular/elliptical hole, numerically. In the analysis, finite element method (FEM) was applied to perform parametric studies on various plates based on the shape and position of the elliptical hole. This study addressed the effects of an elliptical/circular cutout on the buckling load of square composite plates. The laminated composite plates were arranged as symmetric cross-ply [(0°/90°)₂]_s and angle-ply [(15°/−75°)₂]_s, [(30°/−60°)₂]_s, [(45°/−45°)₂]_s. The results show that buckling loads are decreased by increasing both c/a and b/a ratios. The increasing of hole positioned angle cause to decrease of buckling loads. Additionally, the cross-ply composite plate is stronger than all other analyzed angle-ply laminated plates.     

Buckling of rectangular mindlin plates

The elastic buckling of rectangular Mindlin plates is considered using two related methods of analysis. These methods are the Rayleight-Ritz method and one of its piece-wise forms, the finite strip method. Arbitrary combinations of the standard boundary conditions of clamped, simply-supported and free edges are accommodated by the use in the assumed displacement fields of the normal modes of vibration of Timoshenko beams. The applied membrane stress field leading to buckling can comprise biaxial direct stress plus shear stress. A range of numerical applications is described for isotropic and transversely isotropic plates of thin and moderately thick geometry. The results obtained using the two methods compare closely to one another and to other published results where these are available. A direct relationship between unidirectional buckling stress and frequency of vibration is demonstrated for a category of plates having one pair of opposite edges simply supported.     

A comparison of the postbuckling behavior of plates and shells

There is a basic difference in the mathematical treatment of postbuckling of plates and shells. Whereas for plates the classical methods of bifurcation theory (Liapunov-Schmidt method, Singularity Theory) in general are applicable, these methods fail for the analysis of thin-walled shells. For shells in general solutions of the boundary layer type are found and hence the methods of singular perturbation theory are required for an appropriate analysis. Applications are given for the postbuckling of a rectangular plate and a spherical shell.     

Detection of bubbles as concentric circular arrangements

The paper proposes a method for the detection of bubble-like transparent objects in a liquid. The detection problem is non-trivial since bubble appearance varies considerably due to different lighting conditions causing contrast reversal and multiple interreflections. We formulate the problem as the detection of concentric circular arrangements (CCA). The CCAs are recovered in a hypothesize-optimize-verify framework. The hypothesis generation is based on sampling from the partially linked components of the non-maximum suppressed responses of oriented ridge filters, and is followed by the CCA parameter estimation. Parameter optimization is carried out by minimizing a novel cost-function. The performance was tested on gas dispersion images of pulp suspension and oil dispersion images. The mean error of gas/oil volume estimation was used as a performance criterion due to the fact that the main goal of the applications driving the research was the bubble volume estimation. The method achieved 28 and 13 % of gas and oil volume estimation errors correspondingly outperforming the OpenCV Circular Hough Transform in both cases and the WaldBoost detector in gas volume estimation.     

Numerical analysis of nonsymmetric postbuckling behaviour of elastic annular plates

A modified shooting method is used combined with the Kantorovich orthogonalization method. An appropriate formulation of equations and an algorithm are given. Numerical examples illustrate the efficiency of the proposed method.     

Buckling analysis of laminated plates by wavelets

This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes.     

Thermal post-buckling of circular plates

The thermal post-buckling behaviour of isotropic circular plates has been studied in this paper through a simple finite element formulation. The accuracy of the solution by finite element method is established through a solution by Rayleigh-Ritz method for simply-supported circular plates. Effect of non-linearity on the load parameter is found to be much higher in the case of thermal loading than in the case of mechanical loading.     

Buckling and postbuckling of composite panels with cutouts subjected to combined edge shear and temperature change

The results of a detailed study of the buckling and postbuckling responses of composite panels with central circular cutouts are presented. The panels are subjected to combined edge shear and temperature change. The panels are discretized by using a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the panel. The fundamental unknowns consist of the average mechanical strains through the thickness and the displacement components. The effects of geometric nonlinearities and laminated anisotropic material behavior are included.The stability boundary, postbuckling response and hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the panel stiffnesses, and the material properties of both the individual layers and the constituents (fibers and matrix). Numerical results are presented for composite panels with central circular cutouts subjected to combined edge shear and temperature change, showing the effects of variations in the hole diameter, laminate stacking sequence and fiber orientation, on the stability boundary and postbuckling response and their sensitivity to changes in the various panel parameters.     

Asymmetric vibration and stability of circular plates

The asymmetric vibration and stability of circular and annular plates using the finite element method is discussed. The plate bending model consists of one-dimensional circular and annular ring segments using a Fourier series approach to model the problem asymmetries. Using displacement functions which are the exact solutions of the static plate bending equation, the stiffness coefficients corresponding to the 1st and nth harmonics are used in closed form. By assuming that the static displacement function closely represents the vibration and stability modes, the mass and stability coefficient matrices for an annular and circular element are also constructed for the 1st and nth harmonics. Several numerical examples are presented to demonstrate the efficiency and accuracy of the finite element model with that of classical methods.     

A parallel implementation of seeker optimization algorithm for designing circular and concentric circular antenna arrays

In this paper, a parallel version of seeker optimization algorithm (SOA) is proposed for designing circular and concentric circular antenna arrays with the low sidelobe levels at a fixed beamwidth. The SOA is a relatively new evolutionary optimization algorithm based on the concept of simulating the act of humans’ intelligent search with their memory, experience, and uncertainty reasoning. In this work, The SOA has been parallelized by benefiting from its dividable population form. The numerical results show that the design of circular and concentric circular antenna arrays using the parallel SOA provides good sidelobe levels with a fixed beamwidth. The quality of results obtained by the parallel SOA is checked by comparing with those of several evolutionary algorithms in the literature.     

Elastic buckling of tapered circular plates

This paper is concerned with the elastic buckling of tapered circular plates. The study is prompted by the fact that results hitherto available are restricted to a narrow range of taper parameters and are somewhat different from each other. For the buckling analysis, a simple and yet accurate numerical method is presented. It is based on the shooting method and the Rayleigh-Ritz approach. Comprehensive generic buckling results of circular plates with linearly and parabolically varying thicknesses are generated. Comparison studies of the buckling results showed that some of the existing results were erroneous. Optimal values of taper parameters for such tapered plates are also given.     

Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge

A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.     

Axisymmetric buckling of bimodulus thick circular plates

The static buckling of bimodulus thick circular and annular plates subjected to a combination of a pure bending stress and compressive stress is investigated. The thick finite element model, which includes the effect of transverse shear deformation, are created for axisymmetric buckling problems. The obtained results of buckling coefficient are compared with the exact solutions for ordinary thin plates. The accuracy of the finite element solutions are shown to be very good. The effects of various parameters on the buckling coefficients and neutral surfce locations are studied. The bimodulus properties are shown to have significant influences on the buckling coefficient.     

Nonlinear transient response of isotropic circular plates

The present work investigates the nonlinear transient response for stresses and deflection of thin linear elastic circular plates subjected to different time-dependent loads. Space-wise discretisation has been done using collocation method with the zeros of a Chebyshev polynomial as collocation points. Newmark-β scheme has been used for time-marching. Time and space-wise convergence studies have been carried out. Both the linear and nonlinear transient response of clamped and simply supported circular plates under six different sets of transient loads have been obtained. Several new useful results are reported in the present study.     

Bending of circular plates with variable profile

The technique of Dynamic Relaxation is invoked in analysing the bending of circular plates with variable profile and the results are compared with available exact solutions. The excellent correlation suggests that the technique can serve as an alternative for computing the magnitudes and distributions of moments and deflections in circular plates of anisotropic material with variable profile.     

Axisymmetric vibration of bimodulus thick circular and annular plates

The fundamental natural frequencies of axisymmetric circular and annular plates subjected to a combination of a pure bending stress and extensional stress in the plane of the plate are investigated. The thick plate ring element model which includes the effect of transverse shear deformation is created for axisymmetric free vibration problems. The obtained results of non-dimensional natural frequency coefficient compared with the closed form solutions for ordinary plates are shown to be very good. The effects of various parameters on the natural frequency and neutral surface locations are studied. The bimodulus properties are shown to have significant influence on the natural frequency.     

Compressional stability behavior of composite plates with through-the-width and embedded delaminations by using first order shear deformation theory

In this paper, the compressive, i.e. bucking and post-buckling, behavior of composite laminates with through-the-width and embedded delaminations is investigated analytically. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh–Ritz approximation technique. In the case of the multiple delaminations, the contact phenomenon has significant effects on the compressional behavior of the laminates. Thus, the contact between the delaminated sublaminates is also considered in the presented FSDT analytical method. The method can handle both local buckling of the delaminated sublaminates and global buckling of the whole plate. Also, the three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model. The agreement between the results is very good.