Hideki Sekine

Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model

A numerical model for simulating the process of low-velocity impact damage in composite laminates using the finite element method is presented in this paper, i.e. Part I of this two part series on the study of impact. In this model, the 9-node Lagrangian element of the Mindlin plate with consideration of large deformation analysis is employed. To analyze the transient response of the laminated plates, a modified Newmark time integration algorithm previously proposed by the authors is adopted here. We also proved that the impact process between a rigid ball and laminated plates is a stiff system, therefore a kind of A(α) stable method has been advocated here to solve the motion equation of the rigid ball. Furthermore, various types of damages including delamination, matrix cracking and fiber breakage, etc. and their mutual influences are modeled and investigated in detail. To overcome the difficulty of numerical oscillation or instability in the analysis of the dynamic contact problem between delaminated layers using the traditional penalty methods, we have employed dynamic spring constraints to simulate the contact effect, which are added to the numerical model by a kind of continuous penalty function. Moreover, an effective technique to calculate the strain energy release rate based on the Mindlin plate model is proposed, which can attain high precision. Finally, some techniques of adaptive analyses have been realized for improving the computational efficiency. Based on this model, a program has been developed for numerically simulating the damage process of cross-ply fiber-reinforced carbon/epoxy composite laminates under low-velocity impact load. In Part II, this numerical model will be verified by comparing with the experimental results. Also the impact damage will be investigated in detail using this numerical approach.

A combined microstructure strengthening analysis of SiCp/Al metal matrix composites

Abstract A combined microstructure strengthening analysis was made to predict the yield strength of SiCp/Al metal matrix composites. The modified shear lag theory can be used to predict the yield strength of particlereinforced high strength aluminium composites, but the yield strength is underestimated for composites prepared from pure and cast aluminium matrices because the change of matrix microstructure after particle incorporation is not considered. The increased yield strength due to the change of matrix microstructure represents a large increment of the total increased yield strength of SiC particle-reinforced low strength aluminium composites. Several microstructure strengthening mechanisms are examined to evaluate their effects on the matrix yield strength. The result of the combined microstructure strengthening analysis is consistent with experimental results.

Buckling design of symmetrically laminated plates using lamination parameters

The paper presents an optimization approach on laminate configurations of symmetrically laminated plates to maximize buckling loads under combined loading. The coupling between bending and twisting is taken into consideration in the buckling analysis of symmetrically laminated plates. Using lamination parameters, the effect of bending-twisting coupling on the buckling is discussed for the case of simply supported or clamped edges. Optimal laminate configuration to maximize the buckling loads is obtained using a mathematical programming method where four lamination parameters are used as design variables. The relation of laminate configurations and buckling loads is clarified based on a concept of lamination parameters.

Feasible Region in General Design Space of Lamination Parameters for Laminated Composites

In the classical lamination theory and the first-order shear deformation theory, the stiffnesses of laminated composites can be expressed as linear functions of 12 lamination parameters. A method is presented for determining the feasible region in general design space of 12 lamination parameters. In some optimization problems, the local optimum can be avoided by using lamination parameters instead of layer angles and thicknesses. Thus, the lamination parameters are useful design variables in the layup optimization for mechanical properties of laminated composites. To perform the layup optimization, the feasible region of the lamination parameters needs to be known. The lamination parameters are functionals of the distribution function of fiber orientation angles through the thickness. In the determination of the feasible region, the laminate configurations are not restricted. In the method, a variational approach is applied to find the boundary of the feasible region in the general design space of 12 lamination parameters. The feasible region for any set of lamination parameters can be also obtained. With use of the method, the feasible regions in four different design spaces are examined as an example. The reliability and the validity of the method are confirmed.

Layup Optimization for Buckling of Laminated Composite Shells with Restricted Layer Angles

The layup optimization for maximizing buckling loads of long laminated composite cylindrical shells subjected to combinations of axial compression, external lateral pressure, and torsion is carried out on the basis of Flugges theory. The layer angles, that is, fiber orientation angles, of the laminated composite cylindrical shells are restricted to the values of 0, 45, -45, and 90 deg, and then nine lamination parameters are used as design variables for the layup optimization. Explicit expressions relating the nine lamination parameters are derived and used to describe the feasible region in the design space of lamination parameters. Thus, the layup optimization problem becomes a constrained nonlinear optimization problem, and the optimum lamination parameters are determined by a mathematical programming method. The laminate configurations aiming to realize the optimum lamination parameters are obtained by analytic formulas or by an unconstrained optimization procedure. It is observed that, for the laminated composite cylindrical shells with the layer angles restricted to the values of 0, 45, -45, and 90 deg, the optimum buckling loads are less than 10% lower than the optimum buckling loads obtained for unrestricted laminate configurations.

Impact analysis of composite laminates with multiple delaminations

This paper concerns with the transient response of composite laminates with multiple delaminations subjected to low-velocity impact by a rigid ball. The finite element method based on the Mindlin plate theory is employed to describe the motion and deformation of the laminates. A Hertzian-type indentation law is adopted to calculate the impact force between the laminates and the rigid ball. To deal with the dynamic contacts between delaminated layers effectively, a modified Lagrange multiplier technique is employed. For multi-body dynamic contacts, the computation of contact force between delaminated layers is addressed. Numerical results provide much information for understanding the impact phenomenon of the composite laminates with multiple delaminations.

Buckling Analysis of Elliptically Delaminated Composite Laminates with Consideration of Partial Closure of Delamination

By taking account of partial closure of delamination, the buckling analysis of elliptically delaminated composite laminates under in-plane compressive loads is made using a finite element method. In order to deal with the contact problem for the partial closure of delamination, a penalty function method is proposed. In the method, fictitious springs are inserted iteratively at all of the overlapped points. Stiffness of each spring is calculated by considering the overlap and stiffness of the structure at that point. Numerical calculations were carried out to clarify the effects of delamination size, shape, position through thickness and ply angle of delaminated layer on the buckling load and buckling mode. The results are shown in graphs.

Compressive buckling analysis of rectangular composite laminates containing multiple delaminations

Abstract The buckling analysis of rectangular composite laminates with multiple embedded delaminations under in-plane compressive load is performed using Mindlin plate elements in a finite element method. The buckling load and mode are obtained by solving an eigenproblem. Each sublaminate in the delaminated region is assigned with a separate mid-plane. The penalty function method is used to enforce constraints preventing overlap between sublaminates. Numerical results show the effect of the number, size and shape of delaminations on the buckling load and a comparison is made between the effects of multiple delaminations and a hole on the buckling load.

Buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads using lamination parameters

Abstract The buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads of axial compression and torsion are examined on the basis of Flugge’s theory. In the buckling analysis of long laminated composite cylindrical shells, 12 lamination parameters are introduced and used as design variables for layup optimization. Applying a variational approach, the feasible region in the design space of the 12 lamination parameters is numerically obtained. The buckling characteristics are discussed in the design space of the 12 lamination parameters. In the layup optimization, the optimum lamination parameters for maximizing the buckling loads and the laminate configurations for realizing the optimum lamination parameters are determined by mathematical programming methods. It is found that in case of combined loads of axial compression and torsion, the optimum laminate configurations are unsymmetric.

Compressive buckling of laminates with an embedded delamination

In this paper, a buckling analysis of laminates with an embedded delamination has been conducted by employing a finite-element method based on the Mindlin plate theory. An effective solution method has been put forward to deal with the contact problem in the buckling mode. In this method, an iterative updating process incorporating first-order sensitivity analysis and quadratic programming technique has been proposed for computing fictitious forces in the contact area, which can be used to calculate stiffness parameters of some artificial springs. Finally, the penetration between two delaminated layers in the buckling mode can be effectively prevented by inserting these artificial springs into the overlapped area in the buckling mode. Numerical examples indicated that this method is very efficient for solving the contact problem in buckling analysis. Its accuracy and convergence speed are very high. The numerical results demonstrate that the contact analysis is very important for buckling analysis in some cases. The effects of various sizes, shapes and positions of the delamination and the fiber angle of the sublaminate on the buckling load have also been investigated.