Optimum Laminate Configuration Research Articles

Approximate Solution and Optimum Design of Compression-Loaded, Postbuckled Laminated Composite Plates.

The approximate solution for the postbuckling of infinitely long and symmetrically laminated composite plates is obtained by using a simple functional representation for the buckling mode in conjunction with the Galerkin method. The results given by this solution are compared for axial compression in the longitudinal direction with the results given by the nonlinear finite element method for finite length rectangular long plates. Good agreements between the two solutions are obtained for the balanced laminate configurations, and the approximate solution appears useful for design purposes. To determine the optimum design for postbuckling, an optimization is carried out on the approximate solution using lamination parameters as design variables. The objective functions to be minimized are the maximum normal displacement and the strain given by the end shortening in the longitudinal direction. Optimum laminate configurations are determined for layer angles fixed to the common values of 0, 90, 45, and -45 deg. For high postbuckling loads the optimum laminate configurations are cross-ply laminates. When the loads decrease, the optimum laminate configurations become combinations of cross-ply and angle-ply laminates. The optimum laminate configurations for postbuckling problem are different than the optimum laminate configurations for buckling.

Multi-fidelity optimization of laminated conical shells for buckling

Optimum laminate configuration for minimum weight of filament-wound laminated conical shells is investigated subject to a buckling load constraint. In the case of a composite laminated conical shell, due to the manufacturing process, the thickness and the ply orientation are functions of the shell coordinates, which ultimately results in coordinate dependence of the stiffness matrices (A,B,D). These effects influence both the buckling load and the weight of the structure and complicate the optimization problem considerably. High computational cost is involved in calculating the buckling load by means of a high-fidelity analysis, e.g. using the computer code STAGS-A. In order to simplify the optimization procedure, a low-fidelity model based on the assumption of constant material properties throughout the shell is adopted, and buckling loads are calculated by means of a low-fidelity analysis, e.g. using the computer code BOCS. This work proposes combining the high-fidelity analysis model (based on exact material properties) with the low-fidelity model (based on nominal material properties) by using correction response surfaces, which approximate the discrepancy between buckling loads determined from different fidelity analyses. The results indicate that the proposed multi-fidelity approaches using correction response surfaces can be used to improve the computational efficiency of structural optimization problems.

Vibration characteristics of composite sandwich plates and layup optimization of their laminated FRP composite faces

This paper examines the vibration characteristics of rectangular, symmetric composite sandwich plates and the layup optimization of their top and bottom laminated FRP composite faces. The honeycomb core is modeled as a thick plate whose transverse shear deformation is taken into consideraion based on a higher-order shear deformation theory, and the top and bottom laminated FRP composite faces are modeled as a very thin sheet. A two-dimensional finite element method is developed using an eight-node isoparametric element. First, the fundamental frequency of the composite sandwich plate is discussed in the subspace of four in-plane lamination parameters of the laminated FRP composite face. Next, the layup optimization of the laminated FRP composite face for maximizing the fundamental frequency of the composite sandwich plate is performed by a nonlinear mathematical programming method, and the optimum laminate configuration of the laminated FRP composite face is determined.

Design and optimization of laminated conical shells for buckling

Optimum laminate configuration for the maximum buckling load of filament-wound laminated conical shells is investigated. In the case of a laminated conical shell, the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and the weight of the structure. Thus, optimization can be performed by maximization of the buckling load for a specific weight, or by minimization of the weight of the structure under the constraint of applied buckling load. Due to the complex nature of the problem a preliminary investigation is made into the characteristic behavior of the buckling load with respect to the volume as a function of the ply orientation. The exact buckling load is calculated by means of the computer code STAGS-A ( Structural Analysis of General Shells [Almroth BO, Brogan FA, Meller E, Zele F, Petersen HT. Collapse analysis for shells of general shape, user's manual for STAGS-A computer code. Technical report AFFDL TR-71-8; 1973]) by adding a user written subroutine WALL, see Ref. [Goldfeld Y, Arbocz J. Buckling of laminated conical shells taking into account the variations of the stiffness coefficients. AIAA J 2004; 42(3):642–649]. The optimization problem is solved using response surface methodology.

複合材サンドイッチ平板の振動特性と上下ＦＲＰ積層板表板の積層構成最適化

In this paper the vibration characteristics of rectangular, symmetric composite sandwich plates and the layup optimization of their laminated FRP composite faces are examined. The honeycomb core is modeled as a thick plate whose transverse shear deformation is taken into consideration based on a higher-order shear deformation theory, and the top and bottom FRP faces are modeled as a very thin sheet. A two-dimensional finite element method is developed using an eight-node isoparametric element. First, the fundamental frequency of the composite sandwich plate is discussed in the subspace of four in-plane lamination parameters of the FRP face. Next, the layup optimization of the FRP face for maximizing the fundamental frequency of the composite sandwich plate is performed by a nonlinear mathematical programming method, and the optimum laminate configuration of the FRP face is determined.

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

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 Flügge’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.

Layup optimization of symmetrically laminated thick plates for fundamental frequencies using lamination parameters

This paper examines the optimum laminate configurations for maximizing the fundamental frequencies of symmetrically laminated thick plates. The transverse shear effect is taken into consideration in the free vibration analysis of symmetrically laminated thick plates on the basis of the first-order shear deformation theory. Layup optimization is performed by introducing four out-of-plane and two in-plane lamination parameters that characterize the out-of-plane and the transverse shear stiffnesses, respectively. A variational approach is applied to find the boundary of the feasible region in the design space of the six lamination parameters. Using the information of the boundary of the feasible region, the optimum lamination parameters that give the maximum fundamental frequency are obtained for the cases of simply supported and clamped boundary conditions. The laminate configurations intended to realize the optimum lamination parameters are also obtained by using a mathematical programming method. The transverse shear effect on the optimum results is discussed in comparison with the optimum results obtained for classical laminated plate theory.

Design of Laminated Composite Plates Containing a Hole under In-Plane Loadings

In this work, the design of a symmetric laminated composite plate with a circular opening subject to in-plane loading is considered. Stresses are calculated using Lekhnitskii’s complex variable approach with finite width correction. To take care of the variation of stresses around the hole, Tsai-Wu quadratic failure criterion is modified with a characteristic length defined in terms of the hole size and the laminate configuration; as a result, a procedure like point stress criterion developed by Whitney and Nuismer is followed. Comparisons of strength predictions and experimental data for certain layup are presented to see the validity of the failure model developed. Optimum laminate configuration is obtained by considering the maximum first ply failure strength. An effective, quick and easy method is provided.

Optimum design of laminated composites subjected to hygrothermal residual stresses

Residual stresses in composite laminates depend on the thermoelastic properties of the material and processing temperatures. The distribution of these stresses in the various laminates is a function of the stacking sequence and ply orientation. This paper presents a theoretical investigation of the effects of hygrothermal residual stresses on the optimum design of laminated composites. Angle-ply laminates, cross-ply laminates and quasi-isotropic laminates have been considered and these laminates are subjected to different mechanical, thermal and hygroscopic loading conditions. Optimum laminate configurations have been determined by using non-linear optimization algorithms offered by the program OPTICOM. Residual stresses and strains in different layers of laminates are calculated using classical laminate theory and laminate strength ratios are determined by using the Tsai-Wu failure criterion. Hygrothermal effects on minimum thickness and in-plane strength of the laminates are then demonstrated. Analysis of the results indicates that the prediction and measurement of residual stresses are important in relation to production, design and performance of composite structures.

Composite pressure vessels with higher stiffness

A new method to design laminated composite pressure vessels under strain and strength constraints is proposed in this paper. A graphical analysis is presented to find optimum layer thicknesses for given fiber orientations. Minimum pressure vessel mass is determined from active execution of two constraints. Replacing circumferential layer by second helical layer is suggested as a new way of strain suppressing among the commonly used ways for strain suppressing such as (1) addition of extra plies and (2) use of composite material with a higher stiffness. Numerical results and graphics are given to obtain optimum laminate configuration.

Optimum in situ strength design of laminates under combined mechanical and thermal loads

In this paper, optimum laminate configurations are sought for multidirectional fibre-reinforced composite laminates under combined in-plane mechanical and thermal loads. The design objective is to enhance the value of the loads over and above the first-ply-failure loads which are judged by a transverse failure criterion and the Tsai-Hill criterion, respectively. The in situ strength parameters previously obtained are incorporated in these criteria. It is found that the optimum designs under combined mechanical and thermal loads are not the same as those under pure mechanical loads for three of the four loading cases studied. For all cases the optimum loads are significantly larger than those for a quasi-isotropic design.

The use of an energy-based criterion to determine optimum configurations of fibrous composites

The strength optimization of laminated composites under in-plane loading is considered. An effective application of a numerical optimization method has been demonstrated for the optimum laminate configuration to maximize the in-plane strength of laminated fibrous composites. Two composite materials are considered in this study; boron/epoxy and carbon/epoxy. An energy-based failure criterion is used as a first-ply-failure strength criterion. The optimization algorithm is based on the sequential linear programming method with small step limits with respect to the layer thickness. Layer thicknesses and orientations are chosen as the design variables and the total thickness of the laminate is selected as the objective function. Owing to the significance of the problem, the present paper also shows the interaction among various variables such as layer thickness, layer orientation angle, in-plane loading, stresses and energy components.

Optimal fibre orientation for simply-supported, angle-ply plates under biaxial compression

Optimum laminate configurations for laminated rectangular plates under uniaxial or biaxial compression are investigated and are obtained under buckling constraints. Complete freedom is permitted in the selection of the ply angle variation through the thickness; however, it is proved that the maximum buckling load occurs when the orientation angle in each of the layers is the same. Three types of optimal angle (directions) are obtained in terms of the material properties, the geometrical properties and the type of buckling mode. They are expressed in closed analytical form.

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.