Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions

Abstract

The concept of Variable angle tow placement is explored for enhancing the buckling resistance of composite plates subjected to axial compression under different plate boundary conditions. The buckling problem of VAT plate is complicated because of variation in stiffness properties across planform of the plate due to curvilinear fiber path distribution. The problem requires prebuckling analysis to be performed first to determine the non-uniform stress distribution and then the buckling analysis of VAT plates. In the present work, a solution methodology based on the Differential quadrature method (DQM) is developed for solving the partial differential equations of VAT plates with linear fiber angle orientations. Within the framework of DQM, a stress function formulation for inplane analysis and displacement formulation for buckling analysis was employed to derive the governing differential equations based on classical laminated plate theory. The novel aspect of the present work is the use of Airy's stress function to model the prebuckling analysis of VAT plates which considerably reduces the problem size and computational effort. This approach provides more generality to handle pure stress and mixed boundary conditions more effectively when compared to the exisiting analytical models. Furthermore, the governing differential equation derived for buckling analysis of VAT panels considers the effect of bendingtwist coupling terms on the buckling load. DQM was applied first to solve the inplane elasticity problem of VAT plates subjected to cosine distributed compressive loads. DQM was then extended to solve the inplane problem of VAT plates under uniform end shortening for which the unknown stress distribu- * Corresponding author Email address: paul.weaver@bristol.ac.uk (Paul Weaver) December 7, 2011 tions are non-uniform. Stress distributions along the edges of the plate were expanded using Legendre polynomials and the unknown coefficients were determined using a least square approach such that the displacment boundary conditions are satisfied. Later, the DQM was applied to solve the buckling problem of rectangular VAT plates subjected to axial compression under different boundary conditions, viz., simply supported, clamped and free edge boundary conditions. Comparisons were made with finite element results obtained using ABAQUS and the accuracy and efficiency of the proposed DQM approach were studied. Preprint submitted to Composite Structures

A numerical study on impact and compression after impact behaviour of variable angle tow laminates

“…The recent manufacturing developments [3] in Variable Angle Tow (VAT) technology (where stiff carbon fibres are steered along curves to maximize structural performance) seem to meet the expectation of the aircraft industry. Other work at the University of Bristol [4][5][6] made a preliminary assessment of the manufacturability of the embroidery-based VAT process. This produced flat, low voidage, constant thickness, and high volume fraction VAT panels with high resistance to buckling as well as improved stiffness in deeper post-buckling.…”

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

“…Numerous works have shown that tailoring the in-plane stiffness of a plate allows prebuckling stresses to be redistributed to supported regions, thereby increasing the critical buckling load [5][6][7][8][9][10][11][12][13]. Specifically, Gürdal et al [6] have shown that varying the stiffness of the panel perpendicular to the direction of applied end compression results in greater improvements than varying the stiffness in the direction of loading.…”

Mass Optimisation of Variable Angle Tow, Variable Thickness Panels with Static Failure and Buckling Constraints

“…Various studies have shown that fiber variations perpendicular to applied end-compression provide greater improvements in buckling load than fiber variations along the load direction. [5][6][7] This occurs due to the favorable redistribution of prebuckling stresses towards supported edges that do not buckle. Referring to Figure 1 with axial compression applied in the x-direction, such an effect is achieved with fiber variations in the y-direction, requiring φ k = 90…”