A robust numerical approach for the simulation of skin–stringer debonding growth in stiffened composite panels under compression

In this paper, a numerical study on skin–stringer debonding growth in stiffened composite panels has been carried out. A novel numerical methodology is proposed here to investigate the compressive behaviour of a stiffened composite panel in the presence of skin–stringer partial separation. The novel numerical methodology, able to overcome the mesh size and time increment dependency of the standard Virtual Crack Closure Technique (VCCT), is an evolution of a previously developed and tested numerical approach for the circular delaminations growth. The enhancements, with respect to the previously developed approach, rely mainly in the capability to deal with the different defect shapes characterising a skin–stringer debonding. The proposed novel methodology has been implemented in a commercial finite element platform and tested over single stiffener composite panels. The effectiveness of the suggested numerical methodology, in predicting the compressive behaviour of stiffened panels with skin stringer debondings, has been preliminary confirmed by comparisons, in terms of load versus applied displacement and debonding size at failure, with literature experimental data and numerical results obtained with the standard VCCT approach.     

Weight functions for composite repairs to stiffened panels

This paper presents a weight function technique for calculating the stress intensity factors for composite repairs to cracks emanating from an internal notch, corrosion blend out, or a free edge under arbitrary loading in rib stiffened panels. The predictions are compared with both finite element and experimental values. This methodology represents a significant extension to existing assessment and design formulae that are currently limited to the case of uniform loading and flat unstiffened panels.     

Onset of multiple site damage and widespread fatigue damage in aging airplanes

This paper presents a methodology for predicting the thresholds of multiple site damage and widespread fatigue damage in fuselage lap slices. Widespread fatigue damage is a type of multiple cracking that reduces the airframe residual strength to a level below the damage tolerant requirement. The MSD threshold refers to the point in the lifetime of an airplane when two adjacent collinear fatigue cracks can linkup at the allowable stress. The WFD threshold is the point in time when linkup of a primary crack created from accidental damage and secondary cracks created from fatigue can result in a catastrophic failure. The methodology presented in this paper combines results from residual strength analysis and fatigue crack growth testing to determine these thresholds. In particular, a displacement compatibility approach is adopted to calculate residual strength in curved stiffened panels tested in the laboratory. The laboratory experiments also include fatigue testing of full-scale panels containing a debonded lap slice. Based on this methodology, the threshold of widespread fatigue damage for these laboratory panels, adjusted to zero minimum-stress cycling, is between 32,000 and 40,000 cycles, and the threshold of multiple site damage is about 70,000 cycles. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analytical Prediction of Crack Coalesce in Multiple Site Damaged Structures

An analytical methodology for predicting the condition when interacting cracks coalesce and estimate the residual strength under Multiple Site Damage situations is proposed. Dominating magnitudes of the criterion are the changes in elastic and plastic strain energy due to crack ligament fracture. The strain energy magnitudes of interest are calculated using analytical formulations, such that the methodology is efficiently applicable in the design of real aircraft panels. Link-up stress predictions using the present methodology are in very good correlation to the experiments and in most cases better, as compared to the alternative crack link-up prediction models.     

Fracture analysis of strength undermatched Al‐Alloy welds in edge cracked tensile panels using FITNET procedure

This paper presents a methodology for the assessment of the remaining load carrying capacity of thin‐walled components under tension containing highly strength undermatched welds and edge cracks. The analysis is based on the strength mismatch option of the fracture module, part of the newly developed European fitness‐for‐service (FFS) procedure FITNET. The mismatch option of the FITNET fracture module allows weld features such as weld tensile properties and weld geometry to be taken into account in the fracture analysis of cracked welded components. The methodology described was verified for centre cracked Al‐alloy large tensile panels containing undermatched welds in Ref. [ 1 ] and hence the present work provides validation with experimental results of the single edge cracked (SEC) and double edge cracked (DEC) panels. The material used is an age‐hardening aluminium alloy 6013 in T6 temper condition used in welded airframe components. The welds in the form of butt joints were produced using the CO₂ laser beam welding process. The results show that by using the FITNET FFS methodology with an appropriate selection of the input parameters, safe acceptable predictions of the maximum load carrying capacity of the welded panels can be obtained. It should also be noted that one of the main difficulties that engineers encounter when applying mismatch analysis for first time is its apparent complexity. A step‐by‐step analysis is proposed here in order to provide guidance for this kind of assessments.     

Composite and non-composite behaviors of foam-insulated concrete sandwich panels

The structural behaviors of foam-insulated concrete sandwich panels subjected to uniform pressure have been evaluated. This study showed that the interface conditions such as composite and non-composite had a significant effect on the response of foam-insulated concrete sandwich panels, indicating that the simulated shear tie resistance should indeed be incorporated in numerical analyses. Finite element models were developed to simulate the detailed shear resistance of connectors and the nonlinear behaviors of concrete, foam and rebar components. The models were then validated using data from static tests performed at the University of Missouri. The modeling approach used here was compatible with the American Concrete Institute (ACI) Code and existing design practices. The results of this study will therefore provide improved methodology for the analysis and design of foam-insulated sandwich panels under both static and blast loadings.     

Process Factors and Edgewise Compressive Properties of Scarf-repaired Honeycomb Sandwich Structures

Bonded repairs were conducted on flat and edge-closed composite sandwich panels that had undergone different levels of initial damage, and edgewise compression behaviors of repaired panel were tested. Experimental results indicate that these repair techniques can restore the compression performance of damaged panels effectively. The repaired specimens recovered an average of over 83 % of their strength. A k-sample Anderson-Darling test was used to analyze the influence of various parameters, including curing temperature, curing pressure, and repair configurations. After a thorough comparison, it was concluded that a high-temperature, high-pressure treatment can improve the mechanical performance of repaired panels, but the improvement is closely related to the structural complexity of the repaired region. A double-side repair scheme could be used to prevent the degradation of mechanical performance caused by the additional bending moment. The conclusions drawn in the present study provide further insight into the mechanical performance of repaired sandwich panels under edgewise compressive loads. These data facilitate the improved design methodology on bonded repair of composite sandwich structures.     

Computational strategy for multiobjective optimization of composite stiffened panels

This paper presents a multiobjective optimization methodology for composite stiffened panels. The purpose is to improve the performances of an existing design of stiffened composite panels in terms of both its first buckling load and ultimate collapse or failure loads. The design variables are the stacking sequences of the skin and of the stiffeners of the panel. The optimization is performed using a multiobjective evolutionary algorithm specifically developed for the design of laminated parts. The algorithm takes into account the industrial design guidelines for stacking sequence design. An original method is proposed for the initialization of the optimization that significantly accelerates the search for the Pareto front. In order to reduce the calculation time, Radial Basis Functions under Tension are used to approximate the objective functions. Special attention is paid to generalization errors around the optimum. The multiobjective optimization results in a wide set of trade-offs, offering important improvements for both considered objectives, among which the designer can make a choice.     

An elastic-plastic finite element alternating method for analyzing wide-spread fatigue damage in aircraft structures

In this paper, a new analytical technique to study the effect of wide-spread fatigue damage in ductile panels is presented. The main purpose of the study is to develop an efficient methodology to predict the maximum load carrying capacity of panels with cracks. The problem arises especially in the fuselage skin of aging airplanes, in which cracks initiate from a row of rivet holes. This problem is known as Multi Site Damage (MSD) in aging aircraft. It is very important to estimate the load carrying capacity. Usually, the approach based on elastic fracture mechanics may overestimate the load capacity. It is very important for the aircraft structure with MSD to estimate the load carrying capacity of such damaged structures. Approaches based on elastic fracture mechanics often lead to a considerable error. In this paper, the Elastic Finite Element Alternating Method (EFEAM) has been extended to the case of elastic-plastic fracture of panels with MSD cracks. In EFEAM, analytical solutions to crack problems in an infinite plate are employed. In this study, we adopted an analytical solution for a row of cracks in an infinite panel. Furthermore, the plastic deformation is accounted for, by using the initial stress algorithm. The T _inf ^sup* integral is employed for the fracture criterion. The methodology developed in the present study can be called as Elastic-Plastic Finite Element Alternating Method (EPFEAM) for MSD problems. A series of studies on the maximum load capacity of panels with a row of cracks has been conducted.The support of this work by the Federal Aviation Administration through a grant to the Center of Excellence for Computational Modeling of Aircraft Structures, at the Georgia Institute of Technology, is sincerely appreciated.     

Viscoelasticity of multi-layer textile reinforced polymer composites used in soccer balls

This paper gives details of a comprehensive dynamic mechanical analysis (DMA) material characterisation activity for all constituent layers of two modern-day thermoformed soccer balls. The resulting material data were used to define a series of viscoelastic finite element (FE) models of each ball design which incorporated the through-thickness composite material properties, including an internal latex bladder, woven fabric-based carcass and polymer based outer panels. The developed FE modelling methodology was found to accurately describe the viscoelastic kinetic energy loss characteristics apparent throughout a soccer ball impact at velocities which are typical of those experienced throughout play. The models have been validated by means of experimental impact testing under dynamic loading conditions. It was found that the viscoelastic material properties of the outer panels significantly affected ball impact characteristics, with outer panel materials exhibiting higher levels of viscous damping resulting in higher losses of kinetic energy.     

Influence of material properties and stamping conditions on the stiffness and static dent resistance of automotive panels

The use of thinner sheets and the introduction of new materials has meant that the stiffness and dent resistance of exterior panels has become more focused in the automotive industry during the last years. The objective of this study was to investigate the influence of material choice and the effect of varying stamping process conditions on the stiffness and static dent resistance of automotive panels. The experiments were performed on a double-curved panel. Four different materials were included in the study: an aluminium grade, a mild steel, a high-strength steel and a stainless steel. For each material, two different stamping-process conditions were adopted to obtain different strain, stress and thinning distributions in the panels. The same stamping process conditions were applied to all four materials. It can be concluded that the material grade significantly influences the static dent properties. The high-strength steel showed considerably better dent resistance than the other materials. The aluminium panels had slightly better dent resistance than the mild steel panels, although having much lower stiffness. The stainless steel grade had the lowest dent resistance, despite its high yield stress. An effect of the stamping process conditions was also found. Increased blankholding, with consequent increased strain levels in the panels, was generally beneficial to the static dent resistance. The experiments show very little scatter, indicating that the testing methodology developed worked satisfactorily.     

Three-dimensional vibration of cylindrical shell panels – solution by continuum and discrete approaches

 This paper presents a three-dimensional elasticity solution to the free vibration problem of thick cylindrical shell panels of rectangular planform. The natural frequencies and corresponding mode shapes were obtained for thick cylindrical shell panels and detailed parametric investigations were carried out. Comparisons were also made with corresponding finite element simulation results. To validate the accuracy of the results as well as the stability of the present methodology, comprehensive convergence studies were also carried out. Further comparisons of present results were made with existing experimental and numerical results (classical, first-order and higher-order shell theories) available in open literature and the validity and range of applicability of the various shell theories examined.     

Rapid decompression of pressurized aircraft fuselages

A methodology for determining compartment pressures at any point during a rapid decompression of a pressurized aircraft fuselage is presented. The approach takes into consideration the mass and mass moment of inertia of panels and doors through which pressurized air must pass. Failure to consider vent panel mass is shown to severely underestimate the pressure differential across partitions separating compartments during a rapid-decompression event.     

Design of Cellular Composite Sandwich Panels for Maximum Blast Resistance Via Energy Absorption

This paper presents a design methodology for optimizing the energy absorption under blast loads of cellular composite sandwich panels. A combination of dynamic finite element analysis (FEA) and simplified analytical modeling techniques are used. The analytical modeling calculates both the loading effects and structural response resulting from user-input charge sizes and standoff distances and offers the advantage of expediting iterative design processes. The FEA and the analytical model results are compared and contrasted then used to compare the energy response of various cellular composite sandwich panels under blast loads, where various core shapes and dimensions are the focus. As a result, it is concluded that the optimum shape consists of vertically-oriented webs while the optimum dimensions can be generally described as those which cause the most inelasticity without failure of the webs. These dimensions are also specifically quantified for select situations. This guidance is employed, along with the analytical method developed by the authors and considerations of the influences of material properties, to suggest a general design procedure that is a simple yet sufficiently accurate method for design. The suggested design approach is also demonstrated through a design example.     

A study of interlaminar stresses in variable stiffness plates

Variable stiffness composite panels have been in continuous development for the last two decades. Several studies have been carried out to evaluate their structural response under different hypotheses. It is known that correct prediction of the onset of delamination in multilayer composite laminates requires an accurate evaluation of interlaminar stresses. Although finite element codes provide results for interlaminar stresses, they are not continuous both across and along layer interfaces due to the use of C⁰ interpolated elements. In this work, a methodology for obtaining interlaminar stresses is extended and applied to the case of variable stiffness composite panels. Pagano’s three layer reference case is investigated for both constant stiffness and variable stiffness cases. A set of analyses are carried out to demonstrate the performance of the method and the variation in the stress response of the panel due to changes in composite layup. Results show that the distribution of shear stresses in the panel presents an significant variation depending on the stacking sequence. A debonding failure criteria is used to evaluate the performance of different variable stiffness configurations, obtaining improvements compared with constant stiffness panels.     

Residual strength prediction of multiple cracked stiffened panels

Prediction of the coalescence of adjacent cracks is critical for residual strength estimation of structures under multiple site damage conditions. A methodology successfully developed for the case of crack link‐up prediction of un‐stiffened plates, is extended for the case of typical cracked stiffened aircraft panels. The proposed link‐up criterion is based on the change in the magnitudes of elastic and plastic strain energies of the stiffened panel, before and after the cracks coalesce. The strain energy magnitudes of interest are calculated using non‐linear elastic–plastic finite‐element analysis. For the application and verification of the method, experimental results from the open literature are used. Residual strength values calculated by the proposed methodology are in good agreement with the experimental results. The present criterion provides superior results when compared to the existing and commonly applied link‐up criteria.     

Weight optimal design of lateral wing upper covers made of composite materials

The present investigation is devoted to the development of a new optimal design of lateral wing upper covers made of advanced composite materials, with special emphasis on closer conformity of the developed finite element analysis and operational requirements for aircraft wing panels. In the first stage, 24 weight optimization problems based on linear buckling analysis were solved for the laminated composite panels with three types of stiffener, two stiffener pitches and four load levels, taking into account manufacturing, reparability and damage tolerance requirements. In the second stage, a composite panel with the best weight/design performance from the previous study was verified by nonlinear buckling analysis and optimization to investigate the effect of shear and fuel pressure on the performance of stiffened panels, and their behaviour under skin post-buckling. Three rib-bay laminated composite panels with T-, I- and HAT-stiffeners were modelled with ANSYS, NASTRAN and ABAQUS finite element codes to study their buckling behaviour as a function of skin and stiffener lay-ups, stiffener height, stiffener top and root width. Owing to the large dimension of numerical problems to be solved, an optimization methodology was developed employing the method of experimental design and response surface technique. Optimal results obtained in terms of cross-sectional areas were verified successfully using ANSYS and ABAQUS shared-node models and a NASTRAN rigid-linked model, and were used later to estimate the weight of the Advanced Low Cost Aircraft Structures (ALCAS) lateral wing upper cover.     

Predictions of crack propagation using a variational multiscale approach and its application to fracture in laminated fiber reinforced composites

Predictions of crack propagation is a valuable resource for ensuring structural integrity and damage tolerance of aerospace structures. Towards that end, a variational multiscale approach to predict mixed mode in-plane cohesive crack propagation is presented here. To demonstrate applicability and to provide validation of the finite element based predictive methodology, a comparative study of the numerical results with the corresponding experimental observations of crack propagation in laminated fiber reinforced composite panels is presented.