Analysis Of Mode Interaction Research Articles

Fiber bragg grating based detection of part-thickness cracks in bent composite laminates using feature-guided waves

Composite structures with bends are widely used in aerospace and industrial sectors. However health monitoring of such structures is challenging due to their complex topographical features. Recent literature shows that bends in composite laminates can confine and guide ultrasonic energy along their length, known as feature-guided waves (FGW). This article demonstrates a fiber Bragg grating based technique using FGW modes for defect detection and identification in bent composite laminates. In addition, the effects of defect depth and excitation frequency on the FGW mode reflection coefficient are reported using 3D finite element simulations. Physical insight into the reflection behavior is discussed based on an analysis of mode interaction with part-thickness cracks.

FE based mode interaction analysis of thin-walled steel box columns under axial compression

This paper presents the Finite Element (FE) analysis based mode interaction analysis of thin-walled steel box columns under axial compression. Earlier theoretical results on the optimum design of axially compressed box columns were validated through FE analysis. The study was then extended to cover factors that were previously omitted. These factors included column out-of-straightness, residual stresses and plasticity. Emphasis was given on imperfection sensitivity and its effect on optimum design.

Mode interactions in chirowaveguides

Chirality may provide the coupling, and hence the conversion, between two eigen polarization modes: TE and TM modes. In this paper an analysis of mode interaction in chirowaveguides is realized, taking into account longitudinal components of polarization currents. Special consideration is given to so-called induced polarization effects which are caused by abrupt discontinuities of longitudinal polarization currents on the boundary of chiral–nonchiral media. Because of induced polarization effects, an asymmetry in mode coupling may take place. The method of investigation may be a powerful tool for the analysis of mode interactions due to both material and geometric effects.

FINITE ELEMENTS FOR THREE-MODE INTERACTION IN BUCKLING ANALYSIS

SUMMARY This paper presents a finite element formulation for the buckling mode interaction analysis of structures modelled as plate assemblies. The main assumptions are linear elasticity, a linear fundamental path, the existence of distinct critical states that.are coincident or near coincident, and a coupled path arising from a linear combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set ofincremental co-ordinates measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal co-ordinate basis and the coupled solution arising from interaction is computed. An example of a fibre­ reinforced composite I-beam subjected to axial compression illustrates the procedure. The results are compared to a simplified model developed by the authors. Also, an imperfection sensitivity analysis is performed.

Interactive Buckling Analysis of Fiber-Reinforced Thin-Walled Columns

An analytical approximate model, leading to a closed form solution, is presented to account for buckling mode interaction in composite I section columns. Three buckling modes are considered in the analysis: a global mode (Euler mode about the weak axis); a primary local mode (rotation of the flanges and bending of the web); and a secondary local mode (bending of the flanges), which are modeled using analytical functions and four degrees of freedom. The fundamental state is shown to be linear and the three critical states for the isolated modes are found to be stable symmetric bifurcations. Mode interaction analysis in terms of the amplitudes of first order fields is carried out, for the first time, for prismatic sections of composite material. The tertiary (coupled) path involves coupling between the two local modes and it describes the sensitivity to imperfections of the buckling behavior of the composite column. A salient feature of the model presented is the closed form of the resulting solution, which enables the designer to easily perform parametric studies. Also, this is the first buckling mode interaction study for thin-walled composite columns. Numerical examples are presented to validate the results and to show the influence of the geometry and properties of the composite on the interaction phenomenon.

Mode interaction analysis of stiffened shells using “locally buckled” elements

A novel methodology for the analysis of local and overall instabilities in stiffened plates and shells is proposed. The method consists of embedding the local buckling deformation—the buckling mode together with the associated second order fields—in an appropriate shell element. The local buckling deformation is controlled by a relatively small number of degrees of freedom which also allow for amplitude modulation. Examples of stringer-stiffened plates and shells subjected to axial compression are presented. Excellent agreement is found to exist between the results given by the method and those obtained from full blown nonlinear analysis and experiments. It is shown that the proposed technique offers a simple and considerably less expensive approach to mode interaction problems than conventional nonlinear finite element analysis. Imperfection-sensitivity under coincident buckling of axially compressed stringer-stiffened cylindrical shells is explored and it is shown that there can be an erosion of 50% of the load carrying capacity under imperfections of the kind unavoidable in practice.

Interactive buckling in thin-walled beams—I. Theory

A method is derived for the analysis of mode interaction in thin-walled elastic beams. A nonlinear plate theory is employed for the plate segments of the beam, in which the exact nonlinear expressions are used for the middle surface strain measures, but the bending measures are linearized. The beam is subjected to a combination of axial compression and a constant bending moment, and it is assumed to be simply supported at the ends. In the calculation of the total potential energy, the influence of the prebuckling deformations is neglected. The finite strip method is used with the transverse variation of all three displacement components described by cubic polynomials in the arc length. The nonlinear mode interaction is analysed by means of Koiter's asymptotic theory of stability. Some applications of the method to representative problems are presented in a subsequent paper by the authors. This shows that significant mode interaction and imperfection sensitivity occur in these structures.

An improved interactive buckling analysis of thin-walled columns having doubly symmetric sections

A comprehensive mode interaction analysis is presented for thin-walled columns having doubly symmetric cross-sections and carrying axial compression. It is shown that as a result of interaction of overall bending with the primary local mode, a “secondary” local mode having the same wavelength as the primary, is triggered. The problem is therefore viewed as one of interaction of three modes: viz. the overall (Euler) buckling mode and the two local modes. The analysis is based on Koiter's theory of mode interaction and employs finite strips to describe local buckling deformation. The column is treated as being loaded by a prescribed end compression at the centroid and a suitably prescribed end rotation to maintain concentricity of load application. Examples are presented to compare the results of the present theory with the currently available analytical results and to examine the behavior of typical cross-sections. Of particular interest is the considerably reduced imperfection-sensitivity of columns with well-separated critical stresses in comparison to that reported earlier in published literature.

A perturbation analysis of mode interaction in postbuckling behavior and imperfection sensitivity

A perturbation method is presented for the analysis of postbuckling behavior and imperfection sensitivity of elastic structures which have more than one buckling mode. The method is exemplified by analyzing a complete spherical shell under external hydrostatic pressure. For this analysis, use is made of two- and three-mode models of the shell derived earlier from the shallow shell equations.