Continuum Shell Elements Research Articles

Stress analysis of functionally graded shells using a 7-parameter shell element

In this paper, finite element stress analysis of functionally graded structures using a high-order spectral/hp shell finite element is presented. The shell element is based on a seven-parameter first-order shear deformation theory in which the seventh parameter, in addition to the usual six degrees of freedom, is the thickness stretch. The continuum shell element is utilized for the numerical simulations of the fully geometrically nonlinear response of functionally graded elastic shell structures. Several nontrivial shell problems are considered to report deflections and stresses, the latter being the main focus of the current paper. It is found that the stresses computed in the current study agree only in some cases with those of ANSYS and/or ABAQUS and thus requires additional study to determine the cause of the disagreement.

Numerical analysis of bearing failure in countersunk composite joints using 3D explicit simulation method

In this paper, tensile experiments were conducted into single-lap bolted joint between composite laminate and steel with countersunk fastener, and two three-dimensional explicit finite element models were developed using Abaqus/Explicit. Continuum shell elements (SC8R) were used to model in-plane ply failure with built-in damage model while cohesive elements were selected to predict interlaminar damage in model I. 8-node reduced integration solid elements (C3D8R) were chosen to model all the parts with 3D Hashin-type initiation criteria and Camanho degradation law implemented in a VUSDFLD subroutine in model II. The results simulated by both models accurately predicted the elastic loading response and captured overall damage profile compared with the experimental results. The numerical analysis using explicit solver provided acceptable accuracy which highlighted the robust nature and high computational efficiency without convergence issues compared with implicit solver. In addition, the effect of cohesive elements on computational efficiency was investigated to simplify the countersunk joints analysis.

Finite element model for compression after impact behaviour of stitched composites

A finite element (FE) model using coupling continuum shell elements and cohesive elements is proposed to simulate the compression after impact (CAI) behaviour and predict the CAI strength of stitched composites. Continuum shell elements with Hashin failure criterion exhibit the composite laminate damage behaviour; whilst cohesive elements using traction-separation law characterise the laminate interfaces. Impact-induced delamination is explicitly modelled by reducing material properties of damaged cohesive elements. Computational results have demonstrated the trend of increasing CAI strength with decreasing impact-induced delamination area. Spring elements are introduced into the model to represent through-thickness stitch thread in the composite laminates. Results in this study validate experimental finding that CAI strength is improved when stitching is incorporated into the composite structure. The proposed FE model reveals good CAI strength predictions and indicates good agreement with experimental results, making it a valuable tool for CAI strength prediction of stitched composites.

Progressive damage modeling of open-hole composite laminates under compression

Despite the recent success of modeling progressive damage of open-hole fiber reinforced composites subjected to tension (OHT), it is still a challenging task to predict the strengths and the damage progression of open-hole composite laminates under compressive loading (OHC). Herein, we propose a progressive damage model for OHC based on our early model for OHT and apply it to study the size effects of OHC. In the proposed model, continuum shell elements are used to account for both in-plane and out-of-plane deformation and delamination is modeled using cohesive elements. A smeared crack model is used to model the progressive failure of composite plies. It is found that the proposed model can predict accurately the experimental strengths and damage patterns with the assumption that the translaminar fracture toughness for blocked plies increases. The different failure mechanisms of the sublaminate scaled laminates of the stacking sequence 45/90/-45/0ms and the ply-level scaled laminates of stacking sequence 45n/90n/-45n/0ns are found to be closely related to the in-plane shear stress of the central 0° ply block and the initiation of interface delamination.

Propagation of delamination in composite materials with isogeometric continuum shell elements

SummaryA continuum shell element based on the isogeometric analysis concept is extended to model propagating delaminations that can occur in composite materials and structures. The interpolation in the thickness direction is carried out using a quadratic B‐spline, and delamination is modelled by a double‐knot insertion to reduce the inter‐layer continuity. Within the discontinuity, the traction is derived from the relative displacement between the layers by a cohesive relation. A range of examples, including delamination propagation in straight and curved planes and buckling‐delamination, illustrate the versatility and the potential of the approach. Copyright © 2014 John Wiley & Sons, Ltd.

Simulating progressive failure of composite laminates including in-ply and delamination damage effects

A finite element (FE) model, which includes in-ply and delamination damage effects, is developed for the progressive failure analysis of composite laminates. A combined elastoplastic damage model which accounts for both plasticity and damage effects is used to represent the mechanical response of composite layers and is implemented in the FE code Abaqus using user-defined material subroutine UMAT. A cohesive zone model based on cohesive elements available in Abaqus is employed to simulate delamination behaviour in the adhesive interfaces. Continuum shell elements and cohesive elements are stacked together to simulate composite and adhesive layers, respectively. The model is applied to the progressive failure analysis of AS4/PEEK composite laminates subjected to in-plane tensile and out-of-plane transverse low-velocity impact loadings. It is shown that the model can be successfully applied to the simulations of composite laminates susceptible to delamination failure.

Fatigue modelling of aluminium plates reinforced with bonded fibre metal laminates

Purpose – This paper aims to present the implementation of a finite element (FE) model used to establish crack and delamination development in a Glare reinforced aluminium plate under fatigue loading. This model predicts the behaviour of bonded GLARE straps used as crack retarders for life extension of aircraft structures. In particular, it takes into account the interaction that exists between the substrate crack and the delamination crack at the interface with the reinforcement. Design/methodology/approach – In this work, a 3D FE model with three-layer continuum shell elements has been developed to calculate changes in substrate stress intensity and in fatigue crack growth (FCG) rate produced by bonded strap reinforcement. Both circular and elliptical strap delamination geometries were incorporated into the model. Calculated stress intensity factors (SIFs) were used together with measured FCG data for substrate material to predict FCG rates for the strapped condition. Findings – The model predicted a decrease in the SIF and a retardation of FCG rates. The SIF was predicted to vary through the thickness of the substrate due to the phenomenon of secondary bending and also the bridging effect caused by the presence of the strap. The influence of delamination shape and size on substrate crack stress intensity and delamination strain energy release rate has been calculated. Originality/value – This research aims at developing modelling techniques that could be used when studying larger reinforced structures found in aircraft.

Experiment and numerical simulation on delamination during the laminated steel sheet forming processes

Laminated steel sheets, which have advantages in reducing vibration and noise, are widely used in home appliances, automotive components and building structures. With polymer layer laminated in steel sheets, the unique failure mode—delamination may occur in the forming process if the process parameters are defined improperly. In the presented work, firstly, the delamination is investigated by U channel forming in bending mode. Then, a step-bottom square cup drawing is also conducted to study the delamination in the deep drawing of the laminated sheet metal in more complex stress state. Nonlinear visco-elastic material model is applied to describe the mechanical behavior of polymer layer. Cohesive element and continuum shell elements are utilized to discretize the polymer layer and the outer steel sheets, respectively. The results of U channel forming indicate that increasing forming speed somewhat decreases the tendency of delamination, and increasing blank holding force (BHF) significantly diminishes the occurrence of delamination. Meanwhile, the results of the step-bottom square cup drawing reveal that the wrinkling of facial sheets often induces delamination. Increasing the BHF and the frictional coefficient prevents the occurrence of wrinkling and the delamination induced by wrinkling. However, when wrinkling is suppressed, further rising in BHF and frictional coefficient will increase the risk of direct delamination.

Bird impact at aircraft structure – Damage analysis using Coupled Euler Lagrangian Approach

Numerical bird strike damage prediction procedure has been applied on the very detailed large airplane secondary structure consisting of sandwich, composite and metallic structural items. The impacted inboard flap finite element model is modelled using 3D, shell and continuum shell elements, coupled with appropriate kinematic constraints. The bird has been modelled using Coupled Euler Lagrangian approach, in order to avoid the numerical difficulties connected with mesh distortion. Various failure modes, such as Carbon Fibre Reinforced Plastics (CFRP) face layer rupture, failure of composite matrix, damage initiation / evolution in the sandwich structure Nomex core and elastoplastic failure of a metallic structure have been investigated. Besides, general contact has been applied as to efficiently capture the contact between Eulerian bird material and the structure, as well as large deformations of the different structural components. Compared to the classic Lagrangian modelling of the bird, the analysis has proven to be more stable, and the results, such as damage areas, physically more realistic. The impact has been applied in the area that is the most probably subjected to the impact damage during exploitation.

On the implementation of the EAS and ANS concept into a reduced integration continuum shell element and applications to sheet forming

This contribution deals with the application of a new solid-shell finite element based on reduced integration with hourglass stabilization in the field of sheet metal forming. The formulation includes the enhanced assumed strain (EAS) concept getting by with a minimum of enhanced degrees-of-freedom to overcome the volumetric locking and Pois- son’s thickness locking. To circumvent further the well-known effects of curvature thickness locking and transverse shear locking present in standard eight-node hexahedral finite elements the assumed natural strain (ANS) concept is applied. The implementation of the latter key feature is not straight-forward in reduced integration solid-shells. The second crucial point is a combined Taylor expansion of the compatible Green-Lagrange strain tensor with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization. Due to the three-dimensional modeling of the structure fully three-dimensional materials can be implemented without additional assumptions. Furthermore simulations of double-side contact problems (e.g. sheet metal forming) benefit from an exact modeling of the sheet thickness.

Micromechanical Material Model of Wooden Veneers for Numerical Simulations of Plywood Progressive Failure

The plywood material is widely used in civil engineering and furniture industry as cheap, strong, and lightweight material. The progressive failure of the plywood is difficult to be modeled and predicted because of the complexity of its structure and the interaction between different modes of orthogonal damages and interlayer failure. The microstructure of the wood determines the failure of the plies. A micromechanical material model of wooden veneers is developed, which is based on a representative volume cell (RVC) taken from the tubular microstructure of the wood and represented as a truss structure with longitudinal, transverse, and diagonal bar finite elements. The damage variables prescribed for each type of the bars determine the progressive degradation of the material stiffness. The 2-D damage material model of wooden veneers is utilized as user-defined material in continuum shell elements of ABAQUS™ finite element code. The parameters of the model are determined to simulate the behavior of single veneers in tension tests in different directions of loading. Together with cohesive elements representing the interface between the plies, the suggested model can be used to simulate and analyze the progressive failure and damage interaction in the plywood. The simulations could give us better understanding of the complex failure of the plywood, the succession of the damage development and reveal the weakest link in the material. The analysis can be used for optimization of the plywood layup.

Numerical modelling and investigation of plywood progressive failure in CT tests

The plywood is considered as a layered cross-ply unidirectional fiber reinforced composite. Based on the characteristics of damages found in experimental compact tension (CT) tests, the single veneers and their interface are modelled in order to simulate the main damage modes of fiber bundle rupture, matrix cracking along the fibers, and delamination at the ply interlayers of glue. The plywood CT specimens are modelled by continuum shell and cohesive finite elements with damage evolution in material models. The finite element (FE) model simulates the experimental behavior of plywood samples very well and allows deep investigation of the different types of damage development and interaction. The FE model of plywood is useful for its lay-up optimization and for development of more efficient in large-scale simulations computational models of plywood.

Experimental and numerical investigation of plywood progressive failure in CT tests

The plywood is considered as a layered cross-ply unidirectional fibre reinforced composite. The experimental Compact Tension (CT) tests carried out in different directions of plywood fibre orientation show that the characteristics of damages are fibre bundle rupture, matrix cracking along the fibres, and delamination at the ply interlayers of glue. The plywood CT specimens are modelled by continuum shell and cohesive finite elements with damage evolution in material models. The Finite Element (FE) model simulates the experimental behaviour of plywood samples very well and allows deep investigation of the different types of damage development and interaction. The FE model of plywood is useful for its lay-up optimization and for development of very efficient in large-scale simulations computational models of plywood.

Numerical Analysis of Stiffener Runout Sections

The recent trend of incorporating more composite material in primary aircraft structures has highlighted the vulnerability of stiffened aerostructures to through-thickness stresses, which may lead to delamination and debonding at the skin–stiffener interface, leading to collapse. Stiffener runout regions are particularly susceptible to this problem and cannot be avoided due to the necessity to terminate stiffeners at rib intersections or at cutouts, interrupting the stiffener load path. In this paper, experimental tests relating to two different stiffener runout specimens are presented and the failure modes of both specimens are discussed in detail. A thinner-skinned specimen showed sudden and unstable crack propagation, while a thicker-skinned specimen showed initially unstable but subsequent stable crack growth. Detailed finite element models of the two specimens are developed, and it is shown how such models can explain and predict the behaviour and failure mode of stiffener runouts. The models contain continuum shell elements to model the skin and stiffener, while cohesive elements using a traction-separation law are placed at the skin–stiffener interface to effectively model the debonding which promotes structural failure.

Three‐dimensional finite element analysis of lined tunnels

AbstractThis paper describes finite element procedures that have been developed to model the ground movements that occur when a shallow tunnel is installed in a clay soil. This study is part of a wider project concerned with the development of new methods to predict the likely extent of damage to surface structures caused by nearby shallow tunnelling. This particular paper, however, is concerned only with the numerical model of tunnel installation. The structural liner is an important component of this tunnel installation model; two different ways of modelling the liner (based on continuum elements and shell elements) are discussed in the paper. A test problem consisting of the installation of a lined tunnel in an elastic continuum is used to investigate the merits of these different approaches. When continuum elements are used to model the liner, the numerical results agree well with an analytical solution to the problem. When shell elements are used to model the liner, however, the results were found to be significantly influenced by the particular formulation adopted for the shell elements. Example analyses, involving incremental tunnel construction in a clay soil where the soil is modelled using a kinematic hardening plasticity model, are described. These analyses confirm that a thin layer of continuum elements may be used, satisfactorily, to model tunnel linings in a soil–structure interaction analysis of this sort. Copyright © 2001 John Wiley & Sons, Ltd.

Probabilistic methods for the analysis of metal-matrix composites

A probabilistic micromechanics-based non-linear analysis procedure is developed to predict and quantify the variability in the properties of high-temperature metal-matrix composites. Monte Carlo methods and assumed probabilistic distributions of the constituent level properties including fiber, matrix, and interphase properties, volume and void ratios, strengths, fiber misalignment, and non-linear empirical parameters are used to predict the resultant ply properties and quantify their statistical scatter. Graphite/copper and silicon-carbon/titanium-aluminide (SCS-6 T115) unidirectional plies are considered to demonstrate the predictive capabilities. The non-linear material response of continuous-fiber-reinforced metal-matrix composite structures has also been studied by using the macroscopic elastoplasticity theory and a continuum shell element. The procedures discussed have a high potential for use in material characterization and selection (to precede and assist in experimental studies) and determination of the structural response of new high-temperature metal-matrix composites.