ES-PIM applied to buckling of variable angle tow laminates

Abstract

The increasing need for automatic mesh generation has led to the development of efficient triangulation algorithms that are able to discretize any 2D or 3D domain. Modern finite element formulations based on strain smoothing techniques (SFEM) provide enhanced convergence properties, preventing yet the stiffening behavior of triangular meshes. Recent research has shown that meshless methods based on triangular mapping of the integration domain can be used to produce even better convergence properties than SFEM. The present study will explore the Edge-based Smoothed Point Interpolation Method (ES-PIM) as a meshless solution to investigate linear buckling on variable angle tow (VAT) laminates. Such advanced composite structures show a heterogeneous distribution of constitutive properties and thickness, presenting additional challenges to the numerical solution. Important aspects related to the transverse shear correction herein adopted are investigated, leading to interesting conclusions regarding the possibility to use the ES-PIM for conservative estimates of the critical buckling load of VAT laminates.

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

“…This approach showed to be in good comparison with experiments of the manufactured cylinder with overlaps [40]. Upon the variable thickness phenomena, Castro et al [10] proposed a smeared thickness formulation to approximate the local thickness due to overlaps in AFP-manufactured laminates. The formulation is based on the tow width approximation from Blom et al [5], whilst applying a constantvolume constraint.…”

“…Castro et al [10] proposed a smeared thickness formulation for AFP-manufactured laminates, where the local thickness is approximated by Equation 8. The thickness has a non-linear dependency with the manufacturing steering angle defined in Figure 12, and being respectively the local smeared thickness and nominal tow thickness.…”

“…Comparing the values of the maximum thickness in Table 5 it can be noted that, for the discrete case, higher thicknesses are achieved due to the locally overlapping tows; whereas in the smeared case these overlaps are averaged out, resulting in a smoother thickness distribution and therefore a lower value for . The quantitative accuracy of the obtained thickness pattern is performed by means the same volume requirement [10], here translated to an average thickness requirement. Table 5 presents the relative average thickness error calculated using the discrete and smeared configurations, showing that a maximum error of 0.14% occurred for Case 1.…”

“…Since, the benefits of VAT have been used and researched numerically into increasing mechanical properties, such as stiffness [19], buckling [10,18,20,44] and post-buckling [43,42,35] capabilities for laminates alone, or along the interac- tion of stiffeners in a bay design [15,32] and linear buckling of VAT filament-wound cylinders [38]. These benefits have been proven in experiments to increase properties in different applications, such as bending [37] and buckling for cylinders [24,25] and plates [27,29].…”

“…The resulting information is a discrete thickness distribution that can be used either in a FEM or a semi-analytical model. The potential of the smeared thickness approximation by Castro et al [10] is assessed for representing the influence of overlaps on the buckling behaviour of the AFP laminates herein studied, and compared with the modelling approach using discrete overlaps. Finally, guidelines on the use of the simpler smeared thickness modelling are given for a wide range of design possibilities and manufacturing parameters.…”