Andrzej Teter

A review on the mechanical behaviour of curvilinear fibre composite laminated panels

A review on works that investigate the mechanical behaviour of variable stiffness composite laminated panels is carried out in this paper. The review mostly focuses on buckling, failure and vibrations in laminates reinforced by curvilinear fibres, although other issues related to variable stiffness laminates are also addressed. The peculiarities in the formulation of curvilinear fibre reinforced plates are briefly described. As an illustration, the natural frequencies of vibration of variable stiffness composite laminated plates with curvilinear fibres are computed by an h-version type finite element code and are compared with the ones calculated using another model, based on a Third-order Shear Deformation Theory. Areas of research to explore on variable stiffness composite laminates are suggested.

Interactive buckling and load carrying capacity of thin-walled beam–columns with intermediate stiffeners

Abstract The design of thin-walled beam–columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam–columns with central intermediate stiffeners under axial compression and a constant bending moment. The columns are assumed to be simply supported at their ends. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed by means of the transition matrix method and Godunov’s orthogonalisation. Instead of the finite strip method, the exact transition matrix method is used in this case. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The paper’s aim is to expand the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained, the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The calculations are carried out for a few beam–columns. The results are compared to those obtained from the design code and to the data reported by other authors. The results discussed in the present study represent the most important results obtained by the authors in earlier investigations devoted to central intermediate stiffeners (Int. J. Solid Struct. 32 (1995) 1501; Eng. Trans. 43 (1995) 383; Int. J. Solid Struct. 37 (2000) 3323; Int. J. Solid Struct. 33 (1996) 315; Thin Wall. Struct. 39 (2001) 649; Arch. Mech. Eng. XLVIII (2001) 29).

Interactive buckling of thin-walled beam-columns with intermediate stiffeners or/and variable thickness

Abstract The design of thin-walled beam-columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam-columns with central intermediate stiffeners or/and variable thickness under axial compression and a constant bending moment. The columns are assumed to be simply supported at the ends. The asymptotic expansion established by Byskov and Hutchinson (1977: Byskov, E. and Hutchinson, J. W. (1977). Mode interaction in axially stiffened cylindrical shells. AIAA J., 15(7), 941–948) is employed in the numerical calculations performed using the transition matrix method. The present paper is a continuation of the papers by Kolakowski and Teter (1995a,b: Kolakowski, Z. and Teter, A. (1995a). Interactive buckling of thin-walled closed elastic column-beams with intermediate stiffeners. Int. J. Solids Structures, 32(11), 1501–1516; Kolakowski, Z. and Teter, A. (1995b). Influence of local post-buckling behaviour on bending of thin-walled elastic beams with central intermediate stiffeners. Engineering Transactions, 43(3), 383–396) and Teter and Kolakowski (1996: Teter, A. and Kolakowski, Z. (1996). Interactive buckling of thin-walled open elastic beam-columns with intermediate stiffeners. Int. J. Solids Structures, 33(3), 315–330) where the interactive buckling of thin-walled beam-columns with central intermediate stiffeners in the first order approximation was considered. The paper’s aim is to improve the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and shear lag phenomenon is included. The calculations are carried out for a few beam-columns.

Natural frequencies of a thin-walled structures with central intermediate stiffeners or/and variable thickness

Abstract The present paper deals with a dynamic analysis of stability of thin-walled beam-columns with central intermediate stiffeners or/and variable thickness when the shear lag phenomenon and the distortional deformations are taken into account. This investigation is concerned with thin-walled structures under axial compression and a constant bending moment. The structures are assumed to be simply supported at the ends. In order to obtain the equations of motion of individual plates, the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s principle, taking into account Lagrange’s description, full Green’s strain tensor for thin-walled plates and Kirchhoff’s stress tensor. The disturbance theory has been applied in order to obtain an approximate analytical solution to the equations. The problem of linear dynamic stability has been solved with the transition matrix method, taking into account Godunov’s orthogonalization. The calculations are carried out for a few beam-columns.

Interactive buckling of thin-walled closed elastic beam-columns with intermediate stiffeners

Abstract The design of thin-walled beam-columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled closed cross-section beam-columns with central intermediate stiffeners under axial compression and constant bending moment. The beams are assumed to be simply supported at the ends. The asymptotic expansion established by Byskov and Hutchinson is employed in the numerical calculations performed using the transition matrix method. The papers aim is to contribute to the study of the equilibrium path in the post-buckling behaviour of imperfect structures using the first order approximation. The calculations are carried out for a few closed beam-columns.

Lower bound estimation of load-carrying capacity of thin-walled structures with intermediate stiffeners

The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with the interactive buckling of thin-walled structures with central intermediate stiffeners under axial compression and/or a constant bending moment. The structures are assumed to be simply supported at the ends. The lower bound estimation of load-carrying capacity on the basis of the post-buckling behaviour of thin-walled structures with imperfections is studied when the distortional deformations are taken into account. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed using the transition matrix method. The present paper is a continuation of previous work by the authors (Int. J. Solids Struct. 32 (1995) 1501; 33 (1996) 315; 37 (2000) 3323), where the interactive buckling of thin-walled beam-columns with central intermediate stiffeners in the first- and the second-order approximation were considered. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The results obtained are compared with data reported by other authors.

Experimental and Numerical Study of the Buckling of Composite Profiles with Open Cross Section under Axial Compression

The object of the research are short, thin-walled columns with an open top-hat cross section made of multilayer laminate. The walls of the investigated profiles are made of plate elements. The entire columns are subjected to uniform compression. A detailed analysis allowed us to determine critical forces and post-critical equilibrium paths. It is assumed that the columns are articulately supported on the edges forming their ends. The numerical investigation is performed by the finite element method. The study involves solving the problem of eigenvalue and the non-linear problem of stability of the structure. The numerical analysis is performed by the commercial simulation software ABAQUS®. The numerical results are then validated experimentally. In the discussed cases, it is assumed that the material operates within a linearly-elastic range, and the non-linearity of the FEM model is due to large displacements.

Coupled Static and Dynamic Buckling Modelling of Thin-Walled Structures in Elastic Range Review of Selected Problems

Abstract A review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.

Non-linear parametric vibrations of a composite column under uniform compression

Parametric oscillations of a prismatic, thin-walled composite column with a channel section are considered in the article. The simply supported column is made of a seven-layer composite with a symmetric ply alignment. The non-linear problem of buckling is solved with Koiter’s asymptotic theory within the first-order approximation by adoption of a plate model. The asymptotic approximation leads to non-linear equations allowing evaluation of the two mode buckling effect. Parametric vibrations, produced by a periodically changing load component, are investigated near the principal parametric resonances. The approximate analytical solutions are determined by the multiple time scales of method. The influence of amplitude and frequency of parametric excitation on the structure response is investigated. An example bifurcation scenario and a possible transition to chaotic oscillations are also presented.

Application of 3-D Laser Scanning Vibrometer in Determination of Free Vibration Frequencies of Composite Plates with Damage

The paper deals with experimental estimation of the frequencies of free vibrations for composite plates with damage. Two different glass-epoxy composite plates with damage were tested and their mechanical behavior was compared with their non-damaged counterparts. Dynamical properties of the tested structures were examined with the Laser Scanning Vibrometer. Finite Element Analysis (FEA) was performed simultaneously for free vibration frequencies and mode shapes. The numerical results agreed well with the experiment.