Papers by Keyword: Post-Buckling

Abstract: This paper presents a methodology to carry out Reliability-Based Design Optimization (RBDO) in composite stiffened panels. The target is to maximize the reaction force that the panel can withstand before collapse, setting the shortening of failure as the probabilistic constraint. The design variables are the stacking sequence orientations of the composite plies while the random parameters are the elastic properties of the material. In order to predict the collapse load properly, post-buckling and progressive failure analyses are considered within the FE solver employed.

Abstract: An overview of a specific reduced order modelling technique for Finite Element nonlinear buckling analysis of structures under static and dynamic loading is presented. The reduction method applied makes use of an available, well-established analytical perturbation procedure for static buckling and dynamic buckling analysis. This procedure has in the past years been used as the foundation for the development and implementation of a Finite Element framework for reduced order nonlinear buckling analysis. These achievements are reported, including a concise description of the underlying theory and certain characteristic examples. A basic example of a composite plate and other examples related to aircraft applications demonstrate the capabilities of this reduced order modelling framework for nonlinear buckling and dynamic response analysis and illustrate the current status of its development.

Abstract: This paper presents a numerical and experimental study on the pre and post-buckling behavior of adhesively bonded stiffened panels subjected to in-plane compression loading. An experimental programme was carried out to characterize the buckling load, buckling modes and collapse loads. The mechanical tests were performed in the Aerospace Structures Laboratory at ITA. The structural performance of the bonded stiffened panels in terms of buckling and collapse loads was compared to conventional riveted stiffened panels. Finite element models accounting for material, geometrical nonlinearities as well as progressive failure in the bonded interface were developed and validated experimentally. A good agreement between numerical and experimental results was found for buckling and collapse loads through number of semi-waves and measured strains. The experimental and numerical results indicate a superior performance in buckling load and failure load of the bonded stiffened panels over the riveted panels. Both numerical and experimental results showed that the bonded stiffened panels had over 19% higher failure load in comparison with the riveted panels.

Abstract: The article deals with the computational model of an elastic von Mises planar truss. The description of a mathematical concept, which is intended for the creation of computational programmes based on a finite number of segments, is presented. The mathematical solution is suitable for the analysis of load-deflection curves. Structural deformation is evaluated by seeking the minimal potential energy. The article examines the effects of change in the vertical displacement of the top joint on strut axes. The step by step incremental method is used in combination with the Newton-Raphson method. The presented study is aimed at the evaluation of the force in the bifurcation point, which determines the moment when loading of the model causes passing from the pre-critical effect (attainment of maximum vertical load action) to the post-critical effect. Symmetric and asymmetric initial axis imperfections are considered and relevant symmetric and asymmetric shapes of buckling are identified. The stability problem of the von Mises truss is discussed in connection with the random effects of imperfections.

Abstract: Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

Abstract: 1D nonlinear model of a thin plate (or beam) with delamination was developed earlier. Large deflections and membrane strains of a plate in buckled state, as well as the strain energy described using elliptic integrals. The Griffith-type energy condition was used as a criteria of delamination propagation. The analysis of the destruction of the plate was performed depending on the geometrical dimensionless parameters of a plate and the material strength performance. Here the mentioned model is extended to the general mode of delamination and it allows to describe the post-buckling stage and damage propagation. Model application as a base for the alternative determination of the interlaminar fracture toughness of the layered composites is indicated.

Abstract: Using the geometric non-linear theory (The Total Lagrange Description) in dynamics we can establish the problem of the natural vibration of the structure including the effects of the structural and geometrical imperfections. The incremental stiffness matrix can take into account the residual stresses (structural imperfections) and the geometrical initial displacements (geometrical imperfections) as well. The behaviour of columns, frames and thin-walled structures is sensitive to imperfections. This theory and results can be used as a base for the non-destructive method for the evaluation of the level of the load and the imperfections.

Abstract: As a consequence of post-buckling due to high residual stresses caused by the cold-rolling process, long free thin strips frequently show excessive wavy surface. In this paper, a new analytical approach by extending a classic post-buckling analysis method based on the minimum potential energy principle is used to study on the influence of strip thickness and width on the post-buckling deformation for the center and edge wave. It is concluded that the thickness of the strip has significant effect on the flatness defects, while the width does not.

Abstract: The structural performance of thin-walled compression members are subject to the effects of local buckling, interaction between buckling modes, loading end conditions and material yielding and that due to these effects the compressive carrying capability of thin-walled members can be significantly diminished. This paper employs the finite element simulation to examine the local-overall flexural interaction response of pinned-ended thin-walled I-section columns that covers the complete compressed loading history from the onset of elastic local buckling through the nonlinear elastic and elasto-plastic post-buckling interactive phases of behaviour to final collapse and unloading. A detailed account of the growth and redistribution of stresses on the surfaces is given in the paper. Pinned-ended conditions means, of course, simply supported conditions at the column ends with respect to global rotations and the ends of the constituent plates of the cross-section can be treated as either locally rotationally constrained or locally rotationally free. The numerical simulations take into account the influence of material nonlinearity and geometrical imperfections on the compressive ultimate failures of the sections, however, the study is limited to the interaction of local buckling with overall flexural bending as well as locally rotationally constrained condition. This paper shows that the ultimate failure of the columns is related with yielding on the compression sides of the outer surfaces of the section walls at the web, flanges and section junctions mostly located along the length of the columns.

Abstract: The designs of thin structure components of aerospace vehicles require the consideration of thermal buckling and post-buckling problems. Thermal buckling of the structures in the aerospace environment may occur due to non-uniformly distributed temperature field. A finite element method study on the post-buckling of composite plates with embedded shape memory alloy wires was conducted. The plates were subjected to in-plane and through-thickness non-uniform thermal loadings where the non-uniform temperature distributions considered were parabolic in-plane and linearly varying through-thickness thermal loadings that may act separately or in combination. Recovery stress induced by the shape memory alloy was exploited to improve the thermal buckling behaviours of the composite plates. A non-linear finite element model along with its source codes that considered the recovery stress of the shape memory alloy, the non-uniform temperature field, the temperature dependent properties of the SMA and the composite matrix were developed. The post-buckling paths that showed the effect of the shape memory alloy on the thermal post-buckling behaviour of composite plates were generated using the source codes. It was found that the strain energy tuning method of the shape memory alloy greatly improved the post-buckling behaviour of composite plates subjected to the non-uniform temperature distributions.