Direct Assessment of Interlaminar Stresses in Composite Multilayered Plates Using a Layer-Wise Mixed Finite Element Model

An accurate determination of intedaminar transversal stresses in composite multilayered plates, especially near free-edge, is of great importance in the study of inter-ply damage modes, mainly in the initiation and growth of delamination. In this paper, interlaminar stresses are determined by layer-wise mixed finite element model. Each layer is analyzed as an isolated one where the displacement continuity is ensured by means of Lagrange multipliers （which represent the statics variables）. This procedure allows the authors to work with any single plate model, obtaining the interlaminar stresses directly without loss of precision. The FSDT （first shear deformation theory） with transverse normal strain effects included is assumed in each layer, but Lagrange polynomials are used to describe the kinematic instead of Taylor＇s polynomial functions of the thickness coordinates, as is common. This expansion allows the authors to pose the interlaminar displacements compatibility simpler than the second one. The in-plane domain of the plate is discretized by four-node quadrilateral elements, both to the field of displacement and to the Lagrange multipliers. The mixed interpolation of tensorial components technique is applied to avoid the shear-locking in the finite element model. Several examples were carried out and the results have been satisfactorily compared with those available in the literature.

INTERLAMINAR STRESSES OF A LAMINATED COMPOSITE LAP JOINT

The energy method has been successfully applied to solving interlaminar stresses of laminated composite lap joint with an adhesive layer of a certain thickness. This method has the merit of reckoning not only the stress component σ_y, in adherents but also the variation of stresses through the thickness of the adhesive layer. Thus we have the possibility to rectify some mistakes that have long frustrated the solution to joint problems. As all the series encountered can be summed, the solutions are, as usual, neat in closed forms. Furthermore, solutions can be confirmed by the load to be taken by the joint.

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

An interlaminar damage shell model for typical composite structures

Using the plate/shell elements in commercial software,accurate analysis of interlaminar initial damage in typical composite structures is still a challenging issue.To propose an accurate and efficient model for analysis of interlaminar initial damage,the following work is carried out:(A)A higher-order theory is firstly proposed by introducing the local Legendre polynomials,and then a novel shell element containing initial damage prediction is developed,which can directly predict transverse shear stresses without any postprocessing methods.Unknown variables at each node are independent of number of layers,so the proposed model is more efficient than the 3D-FEM.(B)Compression experiment is carried out to verify the capability of the proposed model.The results obtained from the proposed model are in good agreement with experimental data.(C)Several examples have been analyzed to further assess the capability of the proposed model by comparing to the 3D-FEM results.Moreover,accuracy and efficiency have been evaluated in different damage criterion by comparing with the selected models.The numerical results show that the proposed model can well predict the initial interlaminar damage as well as other damage.Finally,the model is implemented with UEL subroutine,so that the present approach can be readily utilized to analyze the initial damage in typical composite structures.

Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables,displacements,and their dual variables,stresses,the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper.In contrast to the traditional technique using only one kind of variables,the symplectic dual variables include displacement components as well as stress components.Therefore,the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously.After being introduced into the symplectic dual system,the uniform schemes,such as the separation of variables and symplectic eigenfunction expansion method,can be implemented conveniently to analyze composite laminate problems.An analytical solution for the free edge effect of composite laminates is obtained,showing the effectiveness of the symplectic dual method in analyzing composite laminates.

Multilayers Plates Buckling by Mixed Finite Elements

It is presented a buckling analysis ofmultilayered plates by the finite elements method with mixed unknowns （displacement and rotations, and transverse interlaminar stresses）. In the mixed model, each layer is analyzed as a single plate, where the continuity of displacement is ensured by Lagrange multipliers which represent static variables. This procedure is easy to be implemented from the computational point of view. A methodology to solve the eigen problem is presented based on the inverse iteration method. The model is verified successfully with results obtained by other authors.

STUDY ON THE TENSILE FATIGUE DAMAGE OF QUASI-ISOTROPIC COMPOSITE LAMINATES

Quasi-isotropic laminates have isotropic elastic properties in all in-plane directions. Therefore, this kind of laminate is widely used for structural elements. The simplest stacking sequence of quasi-isotropic laminates is [0/-60/60]s. When the direction of applied axial load to [0/-60/60]S laminate is inclined at a 30-degree angle, we have the other quasi-isotropic laminate [30/-30/90]s under axial load. The failure mechanisms of these two laminates are, however, entirely different from each other because these two laminates have different distribution of the interlaminar stresses. It was confirmed by tensile fatigue tests that the [0/-60/60]s laminate does not show any visible fatigue damage, but the [30/-30/90]s laminate develops edge-delamination during cyclic loading. The analytical results were in good agreement with the experimental results.

Analysis of Cutout Fiber as Source of Delamination in Composites System Using FEM

Delamination in composite structures can be a serious threat to the safety of the structure. Delamination leads to loss of stiffness and strength of laminates under some conditions. This is particularly so in the case of compressively loaded structures as the loss of stiffness may lead to separation of layers, the consequences of which can be catastrophic. Causes of delamination are many. In aerospace applications, this includes manufacturing defects, as well as operationally induced defects such as bird strikes, hits due to runway debris and tool drops. In this work one of the main causes of delamination that is dealt with, is the one that redistribution of the stress state due to some defects all mostly like here is broken single fiber （cutout fiber） in composite system already initiated by one of the above causes. When a laminate is subjected to in-plane tension, the effects of delamination on the stiffness and strength may be characterized by analytical results concerning the onset of delamination growth and its subsequent development. Many of the analytical treatments deal with just free-edge delamination. In mean time the redistribution and the gradient of the stress state in composite system is playing an important role for causing delamination. The main task of this work is to analyze single fiber with and without cutout embedded in matrix. Different FE models were generated, from the results, the redistribution of the stress state around the defected fiber were presented and discussed. Finally concluded remarks were indicated.

INFLUENCE OF THE MIDDLE WEAK LAYER ON THE IMPACT BEHAVIOR OF LAMINATED STRUCTURES

In this paper, a calculation model based on the subsection displacement theory and the large deflection analysis is developed to describe the dynamic response of isotropic laminated circular plates impacted by a soft body. The model takes into account the interlaminar shear effect induced by the middle weak layer. It is proved by numerical examples that the difference between the model developed in this paper and that based on the classical laminated theory mainly depends on three factors, the elastic modulus of the glue, the radius of the circular plate and the impact force.