Jaehun Lee

Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

Analytical Asymptotic Solutions for Rectangular Laminated Composite Plates

An analytical solution for rectangular laminated composite plates was obtained via a formal asymptotic method. From threedimensional static equilibrium equations, the microscopic one-dimensional and macroscopic two-dimensional equations were systematically derived by scaling of the thickness coordinate with respect to the characteristic length of the plate. The onedimensional through-the-thickness analysis was performed by applying a standard finite element method. The derived twodimensional plate equations, which take the form of recursive equations, were solved under sinusoidal loading with simplysupported boundary conditions. To demonstrate the validity and accuracy of the present method, various types of composite plates were studied, such as cross-ply, anti-symmetric angle-ply and sandwich plates. The results obtained were compared to those of the classical laminated plate theory, the first-order shear deformation theory and the three-dimensional elasticity. In the present analysis, the characteristic length of each composite was dependent upon the layup configurations, which affected the convergence rate of the method. The results shown herein are promising that it can serve as an efficient tool for the analysis and design of laminated composite plates.

Free-Edge Interlaminar Stress Analysis of Composite Laminates Using Interface Modeling

AbstractInterlaminar stresses near free edges in composite laminates were analyzed by considering interface modeling. Previous regular analytical solutions for free edge stress are not rigorous in their linear elastic modeling with dissimilar interfaces between homogeneous plies of laminated composites. Singular stress is not practical in reality at the free edge because it nearly never occurs in real situations. Until now, the analytical nonsingular approximate solutions have been accepted even though they cannot show the rigorous singular behavior at the free edges; this shortcoming is corrected within linear elasticity dissimilar interface modeling. In this study, a regular analytical solution is provided, which is rigorous within the linear elastic model featuring smoothly varying material properties through the thickness of the laminates. This interface modeling provides not only nonsingular stresses but concentrated finite interlaminar stresses using the principle of complementary virtual work and t...

Finite Element for Viscoelastic Composite Plate Bending Using Efficient Higher-Order Displacement Field

Time-dependent responses of composite plate are investigated based on efficient higherorder plate theory. The constitutive equation of linear viscoelastic materials, expressed as a Boltzmann superposition integral equation, is simplified by the convolution theorem of Laplace transformation. Hence, the computational resource can be saved significantly. A triangular bending element based on an efficient higher-order plate theory is applied to the viscoelastic composite plate. To pass the shear patch tests in all configurations, a modified shape function derived by Specht has been employed. To demonstrate the element and compare with other elastic and viscoelastic theories, the static bending problem under sinusoidal loading is considered, the material properties of graphite/epoxy GY70/339 are used to describe the viscoelastic responses like creep strain and relaxation stress. The present research provides an accurate and efficient tool for time-dependent problem of laminates.

Mechanical Properties of Composite Laminates Patches with an Aluminum Substrate

A stress distribution of composite patch with an aluminum substrate was obtained by using stress functions and Kantorovich method when the substrate was under uniaxial extension and pure bending moment. The principle of complementary virtual work was applied to obtain the governing equations. The obtained three-dimensional stresses satisfied the traction free conditions at the free edges and the top surface of the patch. The stress of the bottom surfaces of the patch was obtained from the equilibrium state of patch and substrate. The interlaminar stresses reached maximum at the free edge and decreased quickly at the inner part of the patch. To demonstrate the validity and efficiency of the proposed method, cross-ply, angle-ply, and quasi-isotropic laminates patches were studied. Since the proposed analysis accurately predicts three-dimensional stresses in a composite patch not only uniaxial extension case, but also pure bending case, it is promising to use as an efficient tool for analyzing and designing such aerospace structural component.

Higher Order ZigZag Laminated Composite Shell Theory for Viscoelastic Behavior

Viscoelastic behaviors of symmetric laminated composite shell are investigated based on efficient higher order shell theory (EHOST). The constitutive equation of linear viscoelastic materials in integral form is simplified by using Laplace transform. Moreover, the free top and bottom condition and continuity condition at interface layers can be applied to reduce the number of unknown variables conveniently. All the displacement fields, equilibrium equation for orthogonal curvilinear coordinate system are obtained in Laplace domain. Finally, the results of strain, stress distributions are converted to real time domain for both creep and relaxation process by using the numerical inverse Laplace transform.

An Asymptotic Approach for the Analysis of Composite Plates Having Interfacial Imperfections

An asymptotic method based plate analysis is carried out for composite laminates including interfacial imperfections. By scaling of the thickness coordinate with respect to the characteristic length of the plate, the initial three-dimensional governing equations are separated into the microscopic through-the-thickness equations and macroscopic plate equations. In the microscopic 1D analysis, finite element method along the thickness direction is applied to obtain the deformation modes and equivalent stiffnesses. In order to describe the interfacial imperfection effects, a spring layer model is introduced, which can be easily combined with the existing 1D finite element formulation. From the microscopic analysis, the macroscopic plate equations which take the form of recursive equations are refined maintaining the form of classical plate theory. Herein the present studies, various layups including sandwich plate are taken into account to demonstrate the validity of the present analysis. Since the suggested method can easily and accurately predict the behavior of the composite plate having interfacial imperfections, it can be used as an efficient analyzing and designing tool.

Layup Optimization of Laminated Composite Patches Considering Uncertainty of Material Properties

The layup of the maximum strength of laminated composite patch was optimized using genetic algorithm (GA). To calculate the three dimensional stress distribution of the composite patch efficiently, a stress function-based analytic method was applied. The principle of complementary virtual work was adopted to obtain the governing equations. In the process of GA, a repair strategy was used to satisfy given constraints. Moreover, multiple elitism was implemented to find multiple global optima effectively. A convex modeling method was applied to consider the bounded uncertainty of material properties. The results of the optimization were compared with those of optimization with nominal values. Since the GA optimization combined with convex modeling can practically offer the global optima considered the uncertainty of material properties, it is promising to use the proposed method as an efficient tool for analyzing and designing such aerospace composite structural components.