Calculation Of Interlaminar Stresses Research Articles

The Hybrid Joints between an FRP Panel and a Steel Panel through Tubular Reinforcements: A Methodology for Interlaminar Stress Calculations

The advantages of laminates in terms of the chemical properties and mechanical properties/weight relationship have motivated several applications of fiber-reinforced plastic (FRP) composites in naval constructions due to the reduction in structural weight. This weight advantage has motivated multiple investigations dedicated to dissimilar material joints. We present a methodology for the interlaminar stress calculations of a tubular hybrid joint between an FRP panel and a steel panel through tubular reinforcements. The proposed formulas allow the estimation of the shear and normal stresses on the adhesive, which are generated in the bonding angle of the tubular hybrid joint. The stresses generated at the adhesive bonding ends influence on the adherent’s adjacent layer. A failure criterion is shown to check the accomplishment of the resulting stresses in the adherent laminate. Finally, the proposed formulas are validated using the finite element method and compared with the obtained interlaminar stresses.

Stress and Strain Analysis of Plywood Seat Shell

In this paper, the stress and strain analysis of common laminated wood seat shell is performed. Experimental stiffness evaluation is conducted by measuring displacement of the point on the backrest, and experimental stress analysis is carried out by tensometric measuring at the critical transition area from the seat to the backrest. Finite element analysis is carried out layer by layer with a “2D linear elastic model” for orthotropic materials. Good matching is found between numerical and experimental results of displacement. It is also shown that the results of the principal stress in the measurement points of the seat shell compare favourably with experimental data. The applied in-plane stress analysis of each individual veneer is not applicable for interlaminar stress calculations that are a significant factor in curved forms of laminated wood. Curved forms of laminated wood products require more complex numerical analysis, but the method can be used to achieve approximate data in early phase of product design.

Interlaminar Stresses Calculation Using a Stacked-Shell Finite Element Modeling Approach

The innovative stacked-shell modeling approach is investigated in the frame of an explicit finite element method for the prediction of laminated structural elements' static response, focusing on the interlaminar stress calculation. The main advantage of the investigated stacked-shell modeling technique is the lower computational cost compared to conventional methods, for the same accuracy in displacement and stress results. A laminated plate under sinusoidally distributed transverse loading, a laminated strip under three-point bending and a laminated cylindrical shell under cylindrical bending have been used in the assessment of the developed methodology; static results referring to displacement and both in-plane and out-of-plane stresses of the investigated cases have shown that the proposed technique is highly efficient in the calculation of interlaminar stresses of composite structures, which provides the background for an accurate and efficient delamination prediction.

Interlaminar stress calculation in composite and sandwich plates in NURBS Isogeometric finite element analysis

This research paper describes the development of NURBS Isogeometric finite element analysis and post-processor for interlaminar stress calculation in composite and sandwich plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Linear, quadratic, higher order and k-refined NURBS elements are constructed and numerical validation is performed for laminated composite and sandwich plates. Lagrange finite element suffers from higher order stress gradient oscillations due to Gibbs phenomenon and require alternative stress recovery procedures for accurate interlaminar stress calculations, especially interlaminar normal stress. In this paper, direct post-processing is performed which computes interlaminar shear and normal stresses from higher order gradients of NURBS basis in a single step procedure. Interlaminar stresses are found to be in an excellent agreement with 3D elasticity solution and FSDT along with k-refinement procedure of NURBS basis is found to compute equivalent or better interlaminar normal stress than higher-order shear deformation theory.

A mixed solid-shell element for the analysis of laminated composites

SUMMARY This paper presents a versatile low order locking-free mixed solid-shell element that can be readily employed for a wide range of linear elastic structural analyses, that is, from thick isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and few assumed stress parameters that provide very accurate interlaminar stress calculations through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The element formulation is based on the well-known Fraeijs de Veubeke–Hu–Washizu mixed variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid-shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar stress field in multilayer structures, which is achieved by the introduction of a constraint equation on the interlaminar stresses in the Fraeijs de Veubeke–Hu–Washizu principle-based enhanced assumed strains formulation. The intelligent computer coding of the present formulation makes the present element appropriate for a wide range of structural analyses. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, and shell and laminated composite analyses are investigated and the results are compared with those available in the literature. These benchmark examples reveal that the proposed formulation provides very good results for the structural analysis of shells and multilayer composites. Copyright © 2011 John Wiley & Sons, Ltd.

Stress analysis in adhesive joints with a multiparticle model of multilayered materials (M4)

We propose a new model to calculate the stresses in adhesive joints. It is well known that the classical models only deal with adhesive joints with constant layer thickness. The model we propose is up to calculate the stresses in adhesive joints with any geometry and with anisotropic adherends. If we consider an adhesive joint as a multilayered medium, our model describes it as a surface with as many particles in each point of the surface as the number of layers in the medium (three layers for a simple lap joint and six layers for a double lap joint). For this reason, it is named multiparticle modelisation of multilayered materials (M4 in the following of the text). The M4 models are developed at ENPC Chabot B. Thèse de l’école nationale des fonts et chaussées, 1997; Ehrlacher A, Caron JF, Chabot A, Douçot E, Naciri T. Modélisation multiphasique des plaques composites en flexion, 1er Congrès de Mécanique, 13–16 Avril 1993, E.N.I.M Rabat; Naciri T, Ehrlacher A, Chabot A. Compos. Sci. Technol. 1998; 58:337 for the calculation of interlaminar stresses in composite materials. The model we propose is an application of a M4 model to adhesive joints. It deals with every geometry which we can find in the literature. It only suffices to know the layer thickness in each point on the overlap to calculate the stresses in the joint. In this paper, we firstly present the classical steps to build the M4. This construction is based on the Hellinger–Reissner (Reissner E. JMath Phys, 1950; 29: 90–5) formulation. Secondly, through some joint shapes, we show that we can have a good prediction of stresses in the adhesive layer and that the M4 is a pertinent tool to study adhesive joints.

Calculation of interlaminar stresses in laminated plates using Walsh transforms

The Walsh differential operator approach has much to recommend it from the point of view of computational efficiency over the standard methods for determining the interlaminar tractions from finite element displacement data as may be seen from the simplicity of the Fortran routine and the ease with which the nonlinear traction tems may be modeled

A Boundary Layer Approach to Interlaminar Stresses in Composite Laminates with Curved Edges

A way for determining the interlaminar stresses in composite laminates with arbitrary curved edges is described using the boundary layer equations. A simple and efficient method for the calculation of interlaminar stresses is presented. The method gives a stress field that satisfies the zeroth order equilibrium equations and the stress boundary condi tions as well as the stress continuity between plies. Several laminates with a circular hole are dealt with by the present method. The results indicate that the method is of great versatility and has the ability to perform the analysis of thick laminates efficiently.

The Effect of Thickness on Interlaminar Stresses and Delamination in Straight-Edged Laminates

The effect of ply and laminate thickness on the fracture of graphite/epoxy laminates induced by delamination was investigated. Five laminate types were manufactured from AS1/3501-6 graphite/epoxy and tested: [±15n]s, [±15n/0n]s, [0n/±15n]s, [±45n/0n]s, and [[0/±15]s]n. “Effective ply thickness” was varied by stacking several plies of the same angular orientation together. It was found that an increase in effective ply thickness caused a decrease in fracture stress resulting from delamination in all cases. Interlaminar stress calculations indicate that this results from the fact that the region of high interlaminar stresses increases as the effective ply thickness increases. These calculations also suggest that interlaminar shear stresses are at least as important in causing delamination as interlaminar normal stresses. “Back-to-back” [[0/±15]s]n laminates were found to have the same strength for values of n from one to three. This indicates that reductions in strength are not simply a laminate thickness phenomenon but are related to the effective ply thickness.

Finite element formulation including interlaminar stress calculations

A quadrilateral plate element is developed on the basis of utilizing the compatibility equations to obtain the in-plane stresses, and the equilibrium equations to obtain both transverse shear and normal stresses. A plate as opposed to shell or solid formulation serves to provide efficient solutions for thin to moderately thick laminated composite configurations. The element formulation involves relaxation of the Kirchhoff hypothesis via superposition of a shear rotation upon a midplane rotation. The displacement field is carefully selected to obtain the desired transverse stress variation. Results are compared to both closed form and numerical solutions.

An Assessment of the Interlaminar Stress Problem in Laminated Composites

A review and assessment of the interlaminar delamination problem com mon to layered composite materials is presented. The work covers calcula tion of interlaminar stresses from a homogeneous and microstructural material viewpoint as well as background information on the singularity problem. The observation of edge delamination and experimental efforts are discussed together with recent fracture mechanics studies. The conclu sions provides an assessment of the problem and suggestions for future investigation.