Laminate Composite Shell Research Articles

Investigation of the macroscopic behaviour of laminates shells (MBLS) under varying loads using low order CSFE-sh FEM and the N-T's 2-D shell equations.

The target in this survey is to investigate deformations of laminates shells (DLS), due to asymmetric and axisymmetric loads, including several other loadings using N-T shell equations. We point out here, the contribution of the metric change in thickness for the analysis of static and linear behavior of laminated composite shells. To achieve this objective, we've applied N-T's shells equations on the same monolayer laminate composite shell and derive the law of MBLS. The macrostructure is analyzed under static loads and implemented using low order curved shell finite elements with shifted Lagrange (CSFE-sh). We tested this element on benchmarks found within the literature. The analysis of cylindrical and spherical shells subjected to uniform sinusoidal pressures and asymmetric pressures reveals excellent accuracy compared to others. The results found without any correction factor were compared with those obtained by the analytical method and other finite element models.

Viscoelastic damped response of laminated composite shells subjected to various dynamic loads

In this study, viscoelastic damped dynamic behaviors of laminated composite shells (LCS) under different dynamic loads were investigated. In order to obtain better numerical stability, the truncated series method was used in the formation of equations governing the system. While deriving the equations governing the system, the z/R terms are usually neglected, whereas only 3 and higher order terms are truncated here. The method of truncated equations has been used for the first time as suggested here to obtain viscoelastic damped behavior of dynamically loaded LCS. The governing equation of composite shells was obtained with the help of Hamilton’s principle. Afterwards, time dependent partial differential equations were obtained by applying Navier solution method to these valid equations. These equations were transformed into Laplace space in order to solve time dependent partial differential equations. The transformation of the resulting calculations from Laplace domain into the time domain was conducted with the help of Modified Durbin algorithm. In addition, one of the goals of this research is to highlight the importance of including the (1+z/R) part in the equations to account for the curvature effect of the shells. The addition of these effects and truncated series method to the equations and the investigation of their effects are the originalities of the present study. The present work obtained values were compared with the results obtained with Newmark’s approach and ANSYS finite element methods. The numerical results showed that the proposed approach is a highly effective and efficient solution that can be easily applied to laminated viscoelastic shell problems.

Dynamic response of laminated composite shells under various impact loads

This paper investigates the dynamic behavior of laminated composite shells (LCS) under the effect of dynamic loads. The governing equations for composite shells have been derived by using Hamilton’s principle. Then, these governing equations have been obtained by using Navier solution method. Many researchers do not use the term of ($1+z/R$) in the stress equations. However, these equations with the term of ($1+z/R$) have been obtained to get a more realistic model in the proposed study. It is aimed to emphasize the importance of the term ($1+z/R$) to take into account the effect of the radius of curvature in the calculation of the equations of the shell elements. In addition, the truncated series are used for a better numerical stability in the solution of the motion equations. The differential equations governing the system are derived by using the dynamic virtual displacements. Time-dependent ordinary differential equations are transformed into the Laplace space. Equations dependent on the parameters are then solved in this space. Calculations are transformed from the Laplace space into the time space by the help of modified Durbin’s algorithm. In order to verify the methodology, the results obtained in this study are compared with those obtained by Newmark and ANSYS finite element methods. The results of numerical studies for the dynamic response of laminated composite shells (LCS) are demonstrated and compared with previous studies in the literature.

Global-local model coupling for composite shell structures in the framework of isogeometric analysis

Nitsche’s method had recently demonstrated its potential for a seamless and continuity-preserving coupling of NURBS patches in isogeometric shell analysis. Trimmed and non-conforming patches and even blended models including classical thin-shell and solid-shell formulations can be coupled successfully while preserving a continuous flux along the coupling interfaces. In this paper, we take advantage of the method’s modeling flexibility for an extension to NURBS-based laminate composite shell structures. We introduce a global-local model coupling approach to enrich laminate composite thin-shell Kirchhoff-Love models locally with a full three-dimensional continuum solution. The approach provides a reliable coupling of the classical lamina theory with a layerwise formulation revealing the full interlaminar stress state at reduced computational cost. The layerwise shell model is based purely on a mid-surface NURBS description of the shell body thus supporting the direct application of a surface-defined CAD data representation of shells. We apply a refined finite cell approach to handle efficiently trimmed geometries, as common in CAD models. We demonstrate reliability, accuracy of the coupling approach and efficiency in terms of numerical costs and modeling effort of our approach with several examples.

A layerwise isogeometric approach for NURBS-derived laminate composite shells

Layerwise theories provide an accurate prediction of the three-dimensional stress state of composite structures which is in many cases a prerequisite for a successful prediction of failure mechanism. We focus on such a model for laminate composite plate and shell models in the framework of isogeometric analysis. We apply an exact but dimensionally reduced geometry description based on a computer-aided design (CAD) derived mid-surface NURBS model and a layerwise through-thickness B-spline description. Using the unique and characteristic refinement capabilities of isogeometric analysis we simplify the modeling process while keeping the higher order and higher continuity properties of NURBS. Trimmed geometries, as common in CAD models are efficiently handled by an embedded domain method which treats trimmed areas as a fictitious extension domain in the computational model. We verify our approach with several examples for moderately thick laminate plate and shell models and compare our results to existing 3D solutions.

J1010104 一般的な外圧条件を考慮した偏平FRPパネルの座屈最適化

Composite materials are well known to have superior specific stiffness and strength to conventional metal materials. Due to the excellent material properties, composites contribute to lighten the structures in various industrial fields. Moreover, it is known that engineers can intentionally change dynamic properties of composites by designing their lay-up configuration. Among the composites, shell structures are often found in the automotive and aerospace industries, but this type of structures has technical problem causing the buckling due to various external loads. Therefore, it is important to investigate buckling response of those structures on the safety design. In this study, the effect of generally shaped pressure on buckling eigenvalues of laminated composite shells is studied and those lay-up configurations are optimized to maximize non-dimensional buckling load or buckling parameters. First, stress distributions of shells under general external pressure are calculated by the Ritz method. Then, eigenvalues as critical buckling loads under in-plane stresses are derived by the Ritz method again where in-plane stress distributions determined in the first step are included as the potential energy. Finally, the layerwise optimization (LO) method is applied to optimize lay-ups and to maximize buckling load of laminated composites shells, and obtained optimum solutions are successfully result in higher buckling load compared with the typical lay-ups.

Multi-objective optimal design of laminate composite shells and stiffened shells

This paper presents a multi-objective evolutionary algorithm for combinatorial optimisation and applied for design optimisation of fiber reinforced composite structures. The proposed algorithm closely follows the implementation of Pareto Archive Evolutionary strategy (PAES) proposed in the literature. The modifications suggested include a customized neighbourhood search algorithm in place of mutation operator to improve intensification mechanism and a cross over operator to improve diversification mechanism. Further, an external archive is maintained to collect the historical Pareto optimal solutions. The design constraints are handled in this paper by treating them as additional objectives. Numerical studies have been carried out by solving a hybrid fiber reinforced laminate composite cylindrical shell, stiffened composite cylindrical shell and pressure vessel with varied number of design objectives. The studies presented in this paper clearly indicate that well spread Pareto optimal solutions can be obtained employing the proposed algorithm.

Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells

This study introduces a non-linear finite element analysis approach to the procedure of modeling hybrid laminate composite shells with embedded shape memory alloy (SMA) wire subjected to coupled structural and thermal loading. Numerical analyses of SMA wire reinforced composite laminates were carried out by synergizing the non-linear laminate shell element with Brison's model of the SMA constitutive law. To verify the proposed procedure, the present illustrative applications involve rectangular laminated panels clamped along one side. Analysis results were compared with corresponding experimental results from a prior study. Several test cases that depend on the volume fraction of SMA, temperature, and ply angles are presented to illustrate the highly entangled thermo-mechanical behavior of shape memory alloy hybrid composites (SMAHCs). The results of the numerical analysis show the ability of the suggested procedure to compute the thermo-mechanical behavior of a SMAHC in accordance with the SMA's internal phase transformations induced by stress and temperature variation and demonstrate very good agreement with experimental results.

Geometrically nonlinear static and dynamic analysis of composite laminates shells with a triangular finite element

Geometrically nonlinear static and dynamic behaviour of laminate composite shells are analyzed in this work using the Finite Element Method (FEM). Triangular elements with three nodes and six degrees of freedom per node (three displacement and three rotation components) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases with finite rotations and displacements an iterative-incremental scheme is employed. Numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes.

A postprocess method for laminated shells with a doubly curved nine-noded finite element

A numerical method that predicts through-the-thickness stresses accurately by using in-plane displacement of Efficient Higher Order Shell Theory (EHOST) as a postprocessor is implemented in nine-noded doubly curved shell element. In the present study, an efficient postprocess method is developed in the framework of shell finite element without losing the accuracy of solutions. This method consists of two steps. First is to obtain the relationship between shear angles of First Order Shear Deformation Theory (FSDT) and EHOST. Second is to construct accurate displacement and stress fields from the FSDT solution by using EHOST displacement fields as a postprocessor. To obtain accurate transverse shear stresses, integration of equilibrium equation approach is used. In the course of calculating transverse shear stresses, the computation of third derivatives of transverse deflection is required. Simply supported curved panels and finite cylinder problems demonstrate economical and accurate solution of laminate composite shells provided by the present method. The present postprocess method should work as an efficient tool in the stress analysis of multilayered thick shells.

A postprocess method using a displacement field of higher-order shell theory

A new method that predicts through-the-thickness stresses accurately by using in-plane displacement of EHOST (Efficient Higher-Order Shell Theory) as a postprocessor is proposed. Higher-order theories produce realistic displacement fields with a small number of dependent variables which is independent of the number of layers. However, these shell theories require tedious computations since their in-plane displacements are more complicated than that of first-order shell theory. In this study, a simple and economical method is proposed without losing the accuracy of solutions. This method consists of two steps. First is to obtain the relationship between shear angles of FSDT (First-order Shear Deformation Theory) and EHOST. Second is to obtain accurate displacement and stress fields from the FSDT solution by using EHOST displacement fields as a postprocessor. Simply supported static cylindrical shell problems demonstrate an economical and accurate solution of laminate composite shells provided by the present method.

A quasi-conforming triangular laminated composite shell element based on a refined first-order theory

A “quasi-conforming” triangular laminated shell element based on a refined first-order shear deformation theory is presented. The Hu-Washizu variational principle, involving strain and displacement fields as variables, with stresses being considered as Lagrange multipliers, is used to develop the laminate composite shell element. Both strains and displacements are discretized in the element, while displacements alone are discretized at the boundary. The inter-element C 1 continuity is satisfied a posteriori in a weak form. Due to the importance of rotations and shear deformation in the geometrically non-linear analyses of shells, 7 degrees of freedom per node are chosen, viz. three displacements, two first-derivatives in the in-plane directions of the out-of-plane displacement, and two transverse shear strains at each node. To consider the effect of transverse shear deformation on the global behavior of the laminated composite shell, the Reissner-Mindlin first-order theory, with shear correction factors of Chow and Whitney, is adopted. The transverse shear stresses are obtained through the integration of the 3-D equilibrium equations; and the warping induced by transverse shear is considered in the calculation of the in-plane stresses to improve their accuracy. Numerical examples show that the element has good convergence properties and leads to highly accurate stresses.