Lamination Angle Research Articles

OPTIMAL ROBUST DESIGN OF NOVEL MATERIALS: PROBLEMS OF STABILITY AND VIBRATIONS

A numerical method for the optimal design of thin anisotropic laminates is presented, layer thicknesses and lamination angles being the design variables. An optimal solution is pursued with respect to frequency domain objectives, e.g. fundamental frequency and Euler critical load. A special feature of the method is the semi-analytical second order design sensitivity that is computed with the aid of a Rayleigh-Ritz analysis approach. A modified sequential quadratic programming scheme is then introduced, where standard quasi-Newton approximations are avoided by an exact calculation of the Hessian matrix. Furthermore, the robustness of the method with respect to scatter in material properties such as mass density and elastic moduli is assessed. A stochastic extension of the Rayleigh-Ritz approach is developed on this purpose that allows the location of those regions in the design space that are most sensitive to physical parameter randomness. This allows the use of a modified objective function that penalizes sensitive solution.

A comparative study of failure criteria in probabilistic fields and stochastic failure envelopes of composite materials

One of the major objectives of this paper is to offer a practical tool for materials design of unidirectional composite laminates under in-plane multiaxial load. Design-oriented failure criteria of composite materials are applied to construct the evaluation model of probabilistic safety based on the extended structural reliability theory. Typical failure criteria such as maximum stress, maximum strain and quadratic polynomial failure criteria are compared from the viewpoint of reliability-oriented materials design of composite materials. The new design diagram which shows the feasible region on in-plane strain space and corresponds to safety index or failure probability is also proposed. These stochastic failure envelope diagrams which are drawn in in-plane strain space enable one to evaluate the stochastic behavior of a composite laminate with any lamination angle under multi-axial stress or strain condition. Numerical analysis for a graphite/epoxy laminate of T300/5208 is shown for the comparative verification of failure criteria under the various combinations of multi-axial load conditions and lamination angles. The stochastic failure envelopes of T300/5208 were also described in in-plane strain space.

ACTIVE CONTROL OF SOUND FIELDS FROM A COMPOSITE PLATE USING THE ANISOTROPY AND SHAPE OF DISTRIBUTED PVDF ACTUATORS

Compared to piezoceramic material, polyvinylidene fluoride polymer has anisotropic electromechanical material properties. Using the fact that the anisotropy and shape of distributed piezopolymer actuators have coupling effects with the vibration modes of structures, studies on the design of distributed piezopolymer actuators are performed in order to improve the effectiveness of active control of the sound fields radiated from composite structures. The sound fields induced by the complicated dynamic behaviors of a composite structure was analyzed using coupled finite element and boundary element methods. Active control of sound fields is attempted through minimization of the radiated sound power from a plate. Some numerical results of sound control problems are presented with actuators of various shapes and lamination angles. The results indicate that the anisotropy and shape of distributed piezopolymer actuators are promising factors in the design of distributed piezoelectric actuators for controlling acoustic radiation from structures.

On the response of MMC laminated plates to non-uniform temperature loading: the effect of temperature-dependent material properties

Thermal response of antisymmetrically laminated metal matrix composite (MMC) plates subjected to non-uniform temperature field is analysed. Temperature dependence of both elastic and viscoplastic properties of the metallic matrix is taken into account; this suggests that a non-uniformly heated plate should be considered as a non-homogeneous structure. A micro-to-macro approach is employed to establish the instantaneous thermo-inelastic constitutive law at each point of the plate and to perform the structural analysis. Results are presented for simply-supported and clamped graphitealuminium plates. The effects of boundary conditions, lamination angle, length-to-thickness ratio and different types of spatial temperature distributions are illustrated. Comparisons with the results obtained using an approach that treats the effect of temperature-dependent material properties in a simplified manner are shown. Comparisons with the corresponding elastic solutions (which neglect the inelastic effects in the metallic matrix) are given.

Piezothermoelastic Solution for Angle-Ply Laminated Cylindrical Panel

A three dimensional solution is presented for simply supported, angle-ply laminated hybrid cylindrical panel under cylindrical bending. The differential equations with variable coefficients are solved by the modified Frobenius method. Numerical results are presented for sinusoidal loads to illustrate the effect of the thickness parameter and the lamination angle. The two dimensional classical lamination theory and first order shear deformation theory are assessed by comparison with the three dimensional solution.

面外せん断変形を考慮した複合材料積層板の二軸圧縮座屈解析

The buckling analysis of laminated composite plates compressed in two perpendicular directions is presented by using the pb-2 Ritz functions, which consist of the product of a basic function and a two dimensional polynomial function. The out-plane shear deformation is also taken into consideration in this analysis. It is shown that the convergence of solutions for the buckling load is good when the number of polynomials is more than 20. Numerical results are obtained for cross-ply and angle-ply laminated composite plates compressed in two perpendicular directions. The effects of material properties, plate aspect ratio, number of layers and lamination angle on buckling load are also investigated under simple supported, clamped edges and combined edge conditions. It is shown that the presented method considering the out-of-plane shear deformation can be widely used to analyze the buckling behavior of composite plates with general boundary conditions.

The effect of temperature-dependent material properties on elasto-viscoplastic buckling behaviour of non-uniformly heated MMC plates

An inelastic bifurcation buckling of symmetrically laminated metal matrix composite (MMC) plates under non-uniform thermal loading is analyzed. The metallic matrix is modeled as a thermoelasto-viscoplastic material with temperature-dependent properties (both elastic and viscoplastic). This suggests that, in the prebuckling state, a MMC plate should be considered as a statistically non-homogeneous thermoelasto-viscoplastic structure. To treat the problem, a method based on a combination of micromechanical and structural analyses is used. As a result, a buckling criterion, incorporating the effective instantaneous constitutive behaviour at every point of the plate at each increment of thermal loading, is obtained. Results are presented for simply supported and clamped SiC/Ti plates. The effects of length-to-thickness and aspect ratios, lamination angle, fiber volume fraction, and different types of spatial temperature distributions on the critical buckling temperature are illustrated. Comparisons with the results obtained using an approach that treats the effect, of temperature-dependent material properties in a simplified manner, are presented. Comparisons with the corresponding elastic solutions, obtained by neglecting the inelastic effects in the metallic matrix, are given.

Buckling behaviour of laminated composite structures using a discrete higher-order displacement model

A higher-order theory is used to develop a discrete finite element model for the linear buckling analysis of multilaminated composite plate-shell structures. This model is based on an eight node isoparametric element with 10 degrees of freedom per node. The geometric stiffness matrix is developed by taking into consideration the effects of the higher order terms on the initial in-plane and transverse shear stresses. The model is applied to study several cases that take into consideration different number of layers, lamination angles, length-to-thickness ratio, as well as symmetry and non-symmetry on the laminates. The accuracy of the present formulation is evaluated by comparing the present results with alternative solutions.

Response of metal matrix laminated cylindrical panels to combined uniform temperature change and edge displacements

A quasistatic response of metal matrix laminated cylindrical panels subjected to a combination of uniform thermal loading and applied edge displacements is addressed. To treat the problem, an approach based on a micro-to-macro analysis is proposed. A micromechanical analysis enables one to account for the thermo-viscoplastic behavior of the metallic matrix and its interaction with the thermo-elastic fibers, and provides the overall constitutive behavior of metal matrix composite (MMC). This is further employed in a structural analysis to obtain the response of simply supported MMC laminated panels. Results are presented for unidirectional and antisymmetric angle-ply SiC/Ti panels, both geometrically perfect and imperfect. The elastic and viscoplastic material properties of Ti matrix are considered as temperature-dependent. The effect of mechanical pre-loading on the following thermal response is illustrated. The influence of the panel curvature, length-to-thickness ratio, amplitude of initial geometrical imperfections, lamination angle, and the effect of heating followed by cooling are investigated. Comparisons with the corresponding elastic solutions, obtained by neglecting the inelastic effects in the metallic matrix, are presented.

Development of a Thermal Insulating Support System Using Fiber-Reinforced Plastics for MAGLEV Trains.

A new type of load support system for the superconducting magnet of MAGLEV trains has been developed. This connects a coil case kept at liquid helium temperature (4.2K) with an outer case kept at ambient temperature (about 300K). Thus, this support system possesses low thermal conductivity as well as high and sufficient strength. In this paper we show how this new support system is developed. First, we define a characteristic parameter stiffness which is the product of support system multiplied by thermal resistance. Then, we evaluate this specific for various structural shapes, such as bars, cylinders and cones. On the basis of these evaluations we select a cone-shaped support system made of alumina-FRP. The optimization of cone angle and lamination angle by finite element analysis is discussed. Finally, measured results from several new cone-shaped support systems are presented, including thermal conductivity, stiffness, stress distributions and strength.

アングルプライ積層円筒殻の曲げ座屈に及ぼす積層構成効果

Advanced fiber-reinforced composite materials have been used for structural members, because of their high specific strength and stiffness. In general, laminated cylindrical shells behave differently from isotropic and homogeneous orthotropic cylinders due to the effect of lamination constitution associated with their anisotropy and unsymmetric lamination.In this paper, the effect of lamination constitution on the buckling stress of carbon fiber/epoxy (CFRP) angle-ply laminated cylindrical shells under bending is reported. The effect of various factors, such as stacking sequence, number of layers, lamination angle, dimension of cylinders, and buckling modes, on the buckling value are analyzed by assuming the buckling patterns which satisfy the Flügge-type equilibrium equations. It is clarified that the buckling stress is significantly affected by the effect of lamination constitution.

Sound–structure interaction analysis of composite panels using coupled boundary and finite element methods

Sound–structure interaction problems frequently arise in the aerospace and automotive industries. In this paper, the boundary element method is coupled with the finite element method to accurately model sound–structure interaction of a composite panel resting on an acoustic cavity. First, the approach is validated by comparing the numerical solutions with known analytical and experimental results for isotropic panels. However, for composite panels, exact solutions are difficult or impossible to compute. Also, until today, very little effort has been made to obtain experimental results for composite panels undergoing sound–structure interaction. As the first step toward exploring this area of sound–structure interaction, this study offers numerical results on an acoustic cavity-backed composite panel by harnessing the strengths of the coupled BEM–FEM technique. The results indicate that the transmission loss values for composite panels are very sensitive to the lamination angle of the fibers in the different layers of the composite panel.

Finite element analysis of laminated composite plates with multi-pin joints considering friction

In this paper the problems in multi-pin joints of laminated composite plates considering friction effects in the contact boundary are analyzed. The coulomb friction law is used and the contact constraint are handled by extended interior penalty methods. The perturbed variational principle is adopted to treat the non-differential term due to the coulomb friction, and the obtained equilibrium equation is discretized by the finite element method. The normal contact pressures and the tangential forces due to the frictional effect in the contact area are obtained by the penalty term without the increment of the number of unknowns, as in the Lagrange multiplier method. As numerical experiments, the joint problem with a single pin hole is, first, solved for various lamination angles of the plate and parameters such as clearances between pins and holes, friction coefficients and geometric factors of the plate. The computed results are compared with the existing ones by the previous workers and these agree well. The joint systems with two pin holes in series and in parallel are also analyzed in a similar manner. It is concluded that the formulation of composite joint problems considering frictional contact by utilizing the extended interior penalty method and the regularization process for the non-differentiable term is mathematically sound, physically reasonable and numerically efficient.

Vibration of cantilevered composite triangular and trapezoidal doubly-curved shallow shells

The first known vibration analysis of composite cantilevered shallow shells having right triangular and trapezoidal planforms is conducted. Accurate frequencies are obtained using the Ritz method with algebraic polynomials. This is demonstrated by detailed convergence studies. The lowest six natural frequencies for these shallow shells with double curvature are listed. Effects of curvature, material orthotropy and lamination angle on the natural frequencies are investigated.

THERMAL POSTBUCKLING OF METAL MATRIX LAMINATED PLATES

The postbuckling response of metal matrix laminated plates that are subjected to thermal loading is investigated A micromechanical analysis, which accounts the thermo-viscoplastic behavior of the metallic matrix and its interaction with the elastic fibers and provides the overall constitutive response of metal matrix composite (MMC), is performed. This is further employed in a structural analysis to obtain the thermal postbuckling behavior of MMC laminated plates. Results are presented for unidirectional and angle-ply graphite / aluminum and boron /aluminum geometrically imperfect plates that are subjected to uniform temperature loadings. The influences of the amplitude of initial geometrical imperfections, the lamination angle, the length-to-thickness ratio, and the effect of heating followed by a subsequent cooling are investigated. Comparisons with the corresponding elastic solutions, which are obtained by neglecting the inelastic effects in the metallic matrix, are presented

Dynamic Response of Angle-Ply Laminated Cylindrical Shells under Axial Compressive Impact Loads.

This study is concerned with the problem of dynamic response of angle-ply laminated cylindrical shells under axial compressive impact loads. A mathematical formulation of shell theory is based on the Kirchhoff-Love hypothesis. Cylindrical shells are analyzed using the Donnell-type equations under the boundary condition for simply supported edges. Subsequently, certain perturbations are superimposed on this motion, and their behavior in time is investigated. The symmetric state of motion of the shell is called stable if the perturbations remain bounded. The solutions for the prebuckling motion and the perturbed motion are obtained using the Galerkin method. The inevitability of dynamically unstable behavior is proved analytically and the effects of various factors, such as compressive load ratio, lamination angle, dynamic unstable mode and dimensions of the cylinder are clarified.

Natural vibration of free, laminated composite triangular and trapezoidal shallow shells

Natural vibration of completely free, laminated shallow shells having triangular and trapezoidal planforms is studied. Algebraic polynomials are used in a Ritz analysis to determine the natural frequencies. Detailed convergence studies are made and showed that relatively accurate results can be obtained. The lowest six frequencies for various shell configuration and material lamination angle are listed. Both right and symmetrical triangular and trapezoidal shell configurations are considered. The methods can be used for generally shaped planforms, general lamination angle and stacking sequence and general material properties.

Experimental study of the natural frequencies of rotating thin-walled composite blades

The paper presents an experimental method for detecting the natural frequencies of helicopter-like thin-walled rotating composite blades, and a study of their dependency in the lamination angles and in the rotor angular velocity. The tests were carried out in a vacuum chamber which allowed the isolation of the structural dynamic effects. Both symmetric and antisymmetric box-beam specimens were tested. The blades were excited by an impulse force during rotation and the time history of the resulting strain distributions were recorded. Natural frequencies have been obtained by numerical analysis of the time response. The results demonstrate high repeatability and clear trends of the natural frequencies variation as a function of the blade lamination modes and their angular velocity.

FINITE ELEMENT ANALYSIS OF OUT-OF-PLANE DEFORMATION IN LAMINATED SHEET METALS BASED ON AN ANISOTROPIC PLASTICITY MODEL

An anisotropic plastic constitutive model is applied to a three-dimensional finite element method based on the up-dated Lagrangian type formulation, and out-of-plane deformation of the laminated sheet metal which comprises different materials of stainless steel sheet and aluminum sheet is analyzed. The constitutive model involves a fourth order tensor in its representation, by which not only the initial orthotropy but also the subsequent skewed-anisotropy can be predicted. The variation of anisotropic axis is taken into account with reference to the kinematic relationship of the axis before and after the deformation. The conventional laws of both a power formula for work-hardening and a normality rule for plastic flow are employed in the model. Before the analysis, simple tension tests in various directions are performed to identify the anisotropic material parameters of each component layer. Since the mechanical properties vary in the thickness direction, a fully three-dimensional scheme is adopted in the numerical analysis. Here, we examine the following three kinds of loading patterns; (a) curl in transverse direction under a simple tension, (b) deflection at longitudinal direction in unloaded state following the tension, and (c) strain localization behavior in large deformation regime. The effect of thickness ratio is discussed from the viewpoint of the reduction of out-of-plane deformation, and the difference due to lamination angle is also examined to clarify the combination effect of planer anisotropy.

Free vibration of laminated composite plates—a simple finite element based on higher order theory

A four-noded rectangular element with seven degrees of freedom at each node is developed for the vibration analysis of laminated composite plate structures having a constant thickness of any individual layer. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. The mass matrix is derived in a consistent manner. Rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of highly anisotropic composite materials are considered. Two sets of material properties are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. Results are compared with existing analytical and numerical solutions. The present element formulation confirms its applicability for a wide variety of laminated plates.