C. T. Sun

A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates

Abstract In view of the increasing interest in using composite materials for aerospace structures, the analysis of laminated composite plates becomes essential. A three-dimensional eight-node hybrid stress finite element method is developed for the analysis of laminated plates. The hybrid stress model is based on the modified complementary energy principle and takes into account the transverse shear deformation effects. The displacement field is interpolated through shape functions and nodal displacements. All three displacement components are assumed to vary linearly through the thickness of each lamina. The stress field is interpolated through assumed stress polynomials with 55 stress parameters for each lamina. All six stresses are included and satisfy the homogeneous equilibrium equations. The validity of the hybrid stress finite element model is determined by comparing the predicted numerical results with the existing three-dimensional elasticity solutions. Excellent accuracy and fast convergence are observed in the numerical results.

The influence of fiber length and fiber orientation on damping and stiffness of polymer composite materials

This paper describes the theoretical analysis, the experimental results and the curve-fitting of the analytical model to the experimental results on the influence of fiber length and fiber orientation on damping and stiffness of polymer-composite materials. The experimental results show that, as predicted, very low fiber aspect ratios are required to produce significant improvements in damping. Measurements and predictions also indicate that the control of lamina orientation in a continuous fiber-reinforced laminate may be a better approach to the improvement of damping than the control of the fiber aspect ratio.

Complex moduli of aligned discontinuous fibre-reinforced polymer composites

This paper describes recent analytical and experimental efforts to determine the effects of fibre aspect ratio, fibre spacing, and the viscoelastic properties of constituent materials on the damping and stiffness of aligned discontinuous fibre-reinforced polymer matrix composites. This includes the analysis of trade-offs between damping and stiffness as the above parameters are varied. Two different analytical models show that there is an optimum fibre aspect ratio for maximum damping, and that the predicted optimum aspect ratios lie in the range of actual aspect ratios for whiskers and microfibres when the fibre damping is small. When the fibre damping is great enough, however, the optimum fibre aspect ratio corresponds to continuous fibre reinforcement. Experimental data for E-glass/epoxy specimens are presented for comparison with predictions.

Internal damping of short-fiber reinforced polymer matrix composites

Abstract This paper describes an analytical study to optimize the internal damping of shortfiber polymer matrix composites. Two different analytical methods—force balance model and finite-element numerical scheme were used to obtain numerical results. The loss factor is optimized in terms of many important parameters such as; fiber aspect ratio, the angle θ between the applied tensile load and the fiber direction, stiffness ratio between the fiber and matrix materials and the damping ratio between the fiber and matrix materials. The numerical results show that, for given fiber and matrix materials and given fiber volume fraction, there exists an optimum fiber aspect ratio and an optimum angle γ for maximum damping of the composite. The predicted optimum aspect ratios lie in the range of actual aspect ratios for whiskers and microfibers for small fiber damping and increases as the damping ratio between the fiber and matrix increases. The predicted optimum angle θ lies between 0 and 30°.

Failure analysis of laminated composites by using iterative three-dimensional finite element method

Abstract In this paper, a failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, we first propose three different modes of failure, namely, fiber breakage, matrix cracking and delamination. The first-ply failure load is then evaluated. As the applied load exceeds the first-ply failure load, localized structural failure occurs and the global structural stiffness should change. We modify the global stiffness matrix by taking nonlinearity due to partial failures within a laminate into consideration. The first-ply failure load is analyzed by using an iterative mixed field in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include a three-layered cross-ply (0/90/0) E-glass-epoxy and an angle-ply four-layer Thornel 300 graphite-934 resin epoxy laminates under uniaxial tension in both cases. First-ply failure loads as well as the final loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. First-ply failure loads and final failure loads are obtained by using the finite element program. Excellent correlation with the experimental data is observed.

Prediction of material damping of laminated polymer matrix composites

In this study the material damping of laminated composites is derived analytically. The derivation is based on the classical lamination theory in which there are eighteen material constants in the constitutive equations of laminated composites. Six of them are the extensional stiffnesses designated by [A] six of them are the coupling stiffnesses designated by [B] and the remaining six are the flexural stiffnesses designated by [D]. The derivation of damping of [A], [B] and [D] is achieved by first expressing [A], [B] and [D] in terms of the stiffness matrix [Q](k) andhk of each lamina and then using the relations ofQij(k) in terms of the four basic engineering constantsEL,ET, GLT andvLT. Next we apply elastic and viscoelastic correspondence principle by replacingEL,ET...by the corresponding complex modulusEL*,ET*,..., and [A] by [A]*, [B] by [B]* and [D] by [D]* and then equate the real parts and the imaginary parts respectively. Thus we have expressedAij′,Ay″,Bij′,Bij″, andDij″ in terms of the material damping ηL(k) and ηT(k)...of each lamina. The damping ηL(k), ηT(k)...have been derived analytically by the authors in their earlier publications. Numerical results of extensional damping lηij =Aij″/Aij′ coupling dampingcηij =Bij″/Bij′ and flexural damping Fηij =Dij″/Dij″ are presented as functions of a number of parameters such as fibre aspect ratiol/d, fibre orientation θ, and stacking sequence of the laminate.

Finite element analysis of a laminated composite plate subjected to circularly distributed central impact loading

Abstract A two dimensional finite element analysis has been made for a fiber-reinforced composite laminate subjected to circularly distributed impact load which results, for example, from impacting the plate with a blunt-ended projectile. A finite element displacement model which includes the effects of transverse shear deformation and rotary inertia was used along with Hamiltons principle to derive the finite element matrices. Newmarks direct integration technique was used to integrate with respect to time. The interaction force between the projectile and the plate was calculated by using the Hertzian law of contact. Results for laminate deformations are shown to compare quantitatively with experimental results. Numerical values for stresses in the plate were calculated.

Bending of shape-memory alloy-reinforced composite beam

Based on the one-dimensional thermo-mechanical constitutive relation of a shape-memory alloy (SMA) in which the dependence of the elastic modulus of SMA upon the martensite fraction is considered, a constitutive relation for the bending of a composite beam with eccentrically embedded SMA wires has been developed. The deflection-temperature relation upon heating and cooling has been analysed for the SMA-reinforced composite beam.

One-dimensional constitutive relation for shape-memory alloy-reinforced composite lamina

Based on the one-dimensional thermo-mechanical constitutive relation of a shape-memory alloy (SMA) in which the dependence of the elastic modulus of SMA upon the martensite fraction is considered, a one-dimensional constitutive relation for SMA-reinforced composite lamina has been developed. The stress-strain relation under constant temperature, the free recovery and the restrained recovery under variable temperature, have been analysed for the SMA-reinforced lamina.

Hygrothermal effects on structural stiffness and structural damping of laminated composites

In this paper the hygrothermal effects on structural stiffness and damping of laminated composites are investigated. Since the hygrothermal influence on properties of composite materials is primarily matrix dominated, we first determine experimentally the effects of temperature and moisture on the storage modulus, Poissons ratio and material damping of the epoxy matrix. With the experimentally determined properties of the epoxy material, we then determine the complex moduli (EL*,ET*,GLT* andvLT*) of unidirectional glass-epoxy and graphite-epoxy composites. The structural stiffness (extensional and flexural) and damping of symmetric angle-ply laminates of glass-epoxy and graphite-epoxy are then investigated both analytically and experimentally for temperatues of 20° C and 80° C, respectively. Three moisture contents which are the dry, saturated and a non-uniform moisture gradient states corresponding to each temperature case are considered. Numerical and limited experimental results show that the effects of moisture on the real part ofA11*,A66*,D11* andD66* at room temperature, 20° C, are negligible for all the considered cases. But as temperature increases, the moisture and temperature combined influence induces significant changes in the complex stiffnessA11*A66*,D11*, andD66* especially for the matrix dominated terms.