Optimal Laminate Configurations Research Articles

Free vibrations and flutter analysis of cylindrical shells

The paper present the free vibration and the flutter of multi-layered cylindrical shells using the Rayleigh-Ritz method. The optimal design with constraints imposed on the eigenfrequencies is particularly useful in the selection of dynamic characteristics of structures. For composite cylindrical shells, the fiber orientation variations in individual layers results in an increase (decrease) the critical value of free vibrations. Optimal fibre orientations depends on the shell support and on the geometric parameters of a structure. In the case of the optimal laminate configuration finding, the optimization task cannot be solved using standard FEM software the application and genetic algorithms are required.

Peculiarities in the Material Design of Buckling Resistance for Tensioned Laminated Composite Panels with Elliptical Cut-Outs.

The results of analytical and numerical studies of the buckling behavior of laminated multilayered tensioned sheets with circular and elliptical openings are presented. The analysis shows the significant influence of stress concentration effects on buckling modes and loads, particularly taking into consideration variations in the E1/E2 and E1/G12 ratios. The results of finite element (FE) computations prove that the buckling mode cannot be described by a single buckle localized at the apex of the hole. The optimal design of such structures seems to be much more complicated than classical buckling problems of compressed laminated panels without holes. However, the obtained results indicate that the optimal laminate configurations occur at the boundaries of the feasible regions of the introduced design space. Both continuous and discrete fibre orientations are considered. For continuous fibre orientations, the optimal stacking sequence corresponds to angle-ply symmetric laminates.

Damping optimization of symmetrically laminated plates with transverse shear deformation using lamination parameters

This paper deals with the damping characteristics of symmetrically laminated plates with transverse shear deformation. First, the effect of laminate configuration on the damping characteristics is investigated for cantilevered laminated plates based on the Reissner–Mindlin’s first-order shear deformation theory. To examine the effect of laminate configuration, the concept of specific damping capacity is introduced and the damping characteristics are represented on the lamination parameter plane, where the damped stiffness invariants in transverse shear are newly proposed in this paper. Next, the optimal laminate configurations for the cantilevered laminated plates with maximal damping are determined taking into account the transverse shear effect by using differential evolution in which lamination parameters are used as intermediate design variables. The relation between the laminate configurations and the damping characteristics is discussed based on the concept of lamination parameters.

Impact perforation of polymer–metal laminates: Projectile nose shape sensitivity

Recent research has established that polymer–metal laminates are able to provide enhanced impact perforation resistance compared to monolithic metallic plates of the same mass. A number of mechanisms have been proposed to explain this benefit, including the dissipation of energy within the polymer itself, and the polymer deformation enhancing dissipation within the metallic layer. This understanding of the layer interactions and synergies informs the optimisation of the laminate. However, the effect of the nose shape geometry of the projectile on perforation resistance of a particular laminate configuration has not been established. An optimal laminate configuration for one projectile may be sub-optimal for another. This investigation aims to clarify this nose shape sensitivity for both the quasi-static and impact perforation resistance of light-weight polymer–metal laminates. Bi-layer plates are investigated, with a polyethylene layer positioned on either the impacted or distal face of a thin aluminium alloy substrate. Three contrasting nose shapes are considered: blunt, hemi-spherical and conical. These have been shown to induce distinctly different deformation and fracture modes when impacting monolithic metallic targets. For all projectile nose shapes, placing a polyethylene layer on the impacted (rather than distal) face of the bi-layer plate results in an increase in perforation resistance compared to the bare substrate, by promoting plastic deformation in the metal backing. However, the effectiveness of the polymer in enhancing perforation resistance is sensitive to both the thickness of the polymer layer and the nose shape of the projectile. For a thin polyethylene layer placed on the impacted face, the perforation resistance is greatest for the blunt projectile, followed by the hemi-spherical and conical nose geometries. As the thickness of the polymer facing layer approaches the projectile radius, there is a convergence in both failure mode and perforation energy for all three nose shapes. Bi-layer targets can outperform monolithic metallic targets on an equal mass basis, though this is sensitive to the type of polyethylene used, the polymer layer thickness and the projectile nose shape. The greatest benefit of bi-layer construction (on an equal mass basis) is seen for blunt projectiles, using a polyethylene that maintains a high degree of strain hardening at high strain rates (i.e. UHMWPE), and a polymer thickness just sufficient to switch the failure mode in the metal layer from discing (failure at the projectile perimeter) to tensile failure at the plate centre.

Optimal design of symmetrically laminated plates for damping characteristics using lamination parameters

The present paper deals with the damping characteristics of symmetrically laminated plates. First, the effect of laminate configuration on the damping characteristics is investigated for cantilevered laminated plates. To examine the effect of laminate configuration, the concept of specific damping capacity is introduced and the damping characteristics are represented on the lamination parameter plane, where the damped stiffness invariants are newly proposed in this paper. Next, the optimal laminate configurations for the cantilevered laminated plates with maximal damping subjected to the constraints on the natural frequencies are determined by using differential evolution in which lamination parameters are used as intermediate design variables. The relation between the laminate configurations and the damping characteristics is discussed based on the concept of lamination parameters.

Structural Optimization of Composite Panel with Lamination Parameters and Equivalent Stiffness Laminate Method

Firstly, a two-level optimization procedure for composite structure is investigated with lamination parameters as design variables and MSC.Nastran as analysis tool. The details using lamination parameters as MSC.Nastran input parameters are presented. Secondly, with a proper equivalent stiffness laminate built to substitute for the lamination parameters, a two-level optimization method based on the equivalent stiffness laminate is proposed. Compared with the lamination parameters-based method, the layer thicknesses of the equivalent stiffness laminate are adopted as continuous design variables at the first level. The corresponding lamination parameters are calculated from the optimal layer thicknesses. At the second level, genetic algorithm (GA) is applied to identify an optimal laminate configuration to target the lamination parameters obtained. The numerical example shows that the proposed method without considering constraints of lamination parameters can obtain better optimal results.

Panel Flutter Design of Symmetrically Laminated Plates Using Lamination Parameters.

The present paper examines the optimal laminate configuration to maximize the flutter boundary for simply-supported symmetrically laminated plates with bending-twisting coupling. The Rayleigh-Ritz method is used to solve the natural vibration, and modal analysis using several lowest natural modes is applied to obtain the supersonic panel flutter boundary. First, the flutter characteristics are clarified with use of lamination parameters. Next, the optimal laminate configuration to maximize the flutter boundary is obtained using mathematical programming method where the lamination parameters are adopted as intermediate design variables.

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.

Layup Optimization of Laminated Composites in Flexural Design.

A layup optimization method of symmetrically laminated plates is proposed for minimizing the maximum deflection. The bending-twisting coupling is taken into consideration in the flexural analysis of symmetrically laminated plates subject to a uniformly distributed transverse load. With the use of lamination parameters, the effect of bending-twisting coupling on the maximum deflection is discussed for the case of simply supported or clamped plates. Optimal laminate configurations to minimize the maximum transverse deflection are also obtained by using a mathematical programming method in which four lamination parameters are used as design variables. It is shown that the optimal laminate configuration consists of either an angle-ply laminate or a cross-ply laminate.

Optimal Design of Symmetric Laminated Plates for Fundamental Frequency

The optimal laminate configurations of symmetric laminated plates for maximizing fundamental frequencies are examined. The coupling between bending and twisting is taken into consideration in the free vibration analysis of symmetric laminated plates. With the use of lamination parameters, the effect of bending-twisting coupling on the fundamental frequencies is discussed for the cases of simply supported or clamped edges.The optimal laminate configuration to maximize the fundamental frequencies is also obtained by using a mathematical programming method in which four lamination parameters are used as design variables. The relation between the laminate configurations and the fundamental frequencies is discussed on the basis of the concept of lamination parameters.

Optimal laminate configurations with symmetric lay-ups for maximum postbuckling stiffness

Optimal designs of symmetrically laminated angle-ply plates are obtained with the objective of maximizing the initial postbuckling stiffness. The design involves optimization over the ply angles and the stacking sequence to obtain the best laminate configuration. The stacking sequence is chosen from amongst five candidate designs. It is shown that the best configuration depends on the ratio of the in-plane loads in the x and y directions. Results are also given for two additional configurations which do not exhibit bending-twisting coupling.

Buckling Optimization of Symmetrically Laminated Plates under Combined Loading.

In the present paper we examine optimal laminate configurations to maximize combined buckling loads for symmetrically laminated plates with bending-twisting coupling. Various loading cases are discussed in this paper, that is, compressive, shear, and the combined loads. First, the buckling characteristics under combined loading are clarified with use of the lamination parameters. Next, optimal laminate configurations to maximize the combined buckling loads are obtained using a mathematical programming method where lamination parameters are adopted as intermediate design variables.

Optimal Hybridization of Symmetric, Cross‐Ply Laminates against Biaxial Buckling

Optimal ratio of the thickness of the inner layers made of a low‐stiffness fiber‐reinforced material to the total laminate thickness is determined for sandwich hybrid laminates, with the objective of maximizing the buckling load for a given laminate thickness. The sandwich plate is constructed as a symmetric, cross‐ply laminate with outer layers made of a high‐stiffness fiber composite material and inner layers made of a low‐stiffness fiber‐composite material. The fiber orientations of high‐ and low‐stiffness materials (0° or 90°) are determined optimally, noting that the orientations of outer and inner layers affect the maximum buckling load in the case of hybrid laminates. The relative stiffness of outer layers to inner layers is shown to affect the optimal level of hybridization. The optimal laminate configurations are shown to be sensitive to the relative magnitudes of biaxial buckling loads as well as to the changes in the aspect ratio.

OPTIMAL HYBRIDIZATION OF ANTISYMMETRIC, ANGLE-PLY LAMINATES UNDERGOING FREE VIBRATIONS

The optimal ratio of the thickness of a low-stiffness fiber composite material to the total thickness is determined for sandwich hybrid laminates. The objective of optimization is to maximize the fundamental frequency or the separation between two adjacent frequencies of the laminate subject to a mass or thickness constraint. The sandwich plate is constructed as an antisymmetric, angle-ply laminate which has outer layers made of a high-stiffness fiber composite material and inner layers of a low- stiffness fiber composite material. Such hybrid constructions produce cost-effective structures by making maximum use of expensive fibers. Optimal hybridization further increases the efficiency of the construction by determining the best thicknesses of layers containing high and low stiffness fibers. Comparative numerical results are given in graphical form for boron/glass hybrid and non-hybrid laminates. In the maximum fundamental frequency problem, the optimal laminate configuration is found to be a hybrid one ...

Minimum Weight Design of Laminated Composite Panels under Strength and Displacement Constraints

The present paper treats a minimum weight design of laminated composite panels under in-plane loading. Constraints consist of strength and displacement conditions. Layer orientation angles as well as layer thicknesses are used as design variables. An approximation method is applied to generate a high-quality approximate optimization problem. Stress components are evaluated using a linear approximation of stress resultants while displacements are approximated in a linear form. Transformed design variables with respect to the layer angles are also introduced to reduce the nonlinearity between the strength constraints and the layer angles. It is shown that optimal laminate configurations can be obtained with fewer than ten iterations.

Design of antisymmetric hybrid laminates for maximum buckling load: II. Optimal layer thickness

Antisymmetric, angle-ply laminates under biaxial compression are optimized with respect to layer thicknesses. The laminates are constructed with inner layers of a low-stiffness fibre composite material and outer layers of a high-stiffness fibre composite material. The optimal design problem consists of determining the ratio of inner layer thickness to the total laminate thickness so as to maximize the buckling load subject to a mass or thickness constraint. Numerical results are given for laminates of equal total thickness and equal mass made of boron, kevlar and glass fibre reinforced plastics. The optimal laminate configuration is found to be consisting of layers of high-stiffness or low-stiffness material or a combination of both depending on the ply angles and the materials. The optimal layer thickness is observed to have jump discontinuities with respect to fibre orientation.

Simplified Design Techniques for Laminated Cylindrical Pressure Vessels under Stiffness and Strength Constraints

This paper treats the optimum design of graphite/epoxy laminated composite cylindrical pressure vessels under stiffness and strength constraints based upon the membrane theory. Stiffness constraints are specified as strain conditions both in the axial and circumferential directions. Tsai-Wu failure criterion is used for determining a first-ply-failure strength. The stiffness and strength characteristics of the laminate are discussed based upon the concept of lamination parameters. For small values of allowable axial and circumferential strains, the strain (or stiffness) condition is critical, while for large values of allowable strains the strength condition is critical. The optimal laminate configurations are determined for the various kinds of strain and strength constraints.

On Laminate Configurations for Simultaneous Failure

A particular class of laminated composites is presented where all layers fail simul taneously. Lamiante configurations and loading conditions for simultaneous failure are ob tained for laminated composites under in-plane loads. The present paper also shows the optimal laminate configurations to maximize the in-plane strength for graphite/epoxy composites. Tsai-Wu criterion is used as a first ply failure strength criterion. The particular failure strength characteristics are shown for graphite/epoxy composites. The strength characteristics of the laminate configurations for simultaneous failure are compared with those of the optimal ones. It is shown that the laminate configurations for simultaneous failure are optimal only for a special loading condition.

網目理論による積層板・殻の剛性最適化

The present paper treats the optimal design problems of laminated composite plates and shells based upon the netting theory in which the stiffnesses other than the longitudinal Young's modulus are neglected. Some stiffness characteristics are examined, that is, the vibration and buckling characteristics of laminated composite plates and the buckling characteristics of laminated composite cylindrical shells. Optimal laminate configurations for the vibration and the buckling are also obtained by using the netting theory and compared with the results based upon the lamination theory. Applicability and limitation of the netting theory to the laminated plates and shells are verified through the numerical examples.

Optimal laminate configurations of cylindrical shells for axial buckling

Optimum laminate configurations for laminated cylindrical shells under axial compression are investigated and obtained under buckling constraints. Complete freedom is given in the selection of the ply angle variation through the thickness. Twelve lamination parameters are introduced to describe laminate properties, and the optimal values of these parameters are obtained numerically. It is shown that there are many different optimal configurations which give the same buckling load. The optimality condition for the laminate configurations is derived semiempirically from the numerical results in terms of the lamination parameters. The maximum buckling load is obtained in terms of material properties. Some examples of optimal laminate configurations are presented. It is shown that one of the optimal laminate configurations can be obtained when an infinite number of infinitely thin layers are arranged so that the shell becomes quasi-isotropic in the shell surface and quasihomogeneous through the thickness.