Layerwise Higher-order Shear Deformation Theory Research Articles

Application of layerwise HSDT and fracture analysis in the ultimate strength of composite plates with delamination in bending

To obtain the flexural response and the load-carrying capacity of composite plates with delamination, an efficient closed-form analytical solution is presented. Layerwise Higher-order Shear Deformation Theory and Rayleigh-Ritz approximation technique are applied. Fracture analysis is used to obtain the load-carrying capacity and primary steps of delamination propagation. The results include continuous functions. Furthermore, a considerable experimental study has been performed with specimens of various geometries and delamination types. The experimental investigation includes the fabrication procedure, tension experiments to obtain material properties and three-point bending tests of the delaminated plates.

Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

Analysis of composite laminates containing through-the-width and embedded delamination under bending using layerwise HSDT

The effects of different boundary conditions on the composite laminate containing embedded and through-the-width delamination under bending load are investigated analytically based on a developed Layerwise Higher Order Shear Deformation Theory (LHSDT) and the results are compared with the three-dimensional Finite Element Method (FEM). Contact energy has been calculated. The results demonstrate the ability of the presented method of predicting the displacement fields of a composite laminate containing delamination and obtaining stress-strain curves in bending condition. Moreover, strain energy release rate can be achieved using the obtained displacements to evaluate the initiation of delamination propagation around the boundaries of the considered delaminated region. Furthermore, the failure of the laminate will be predicted using conventional theories such as Tsai-Wu.

Experimental, numerical and analytical study of buckling of rectangular composite laminates

The deflection of composite laminates and their maximum compressive and tensile strains under in-plane compression, buckling and post-buckling conditions are investigated in this study. For this purpose, different equivalent single layer and layer wise theories based on polynomial and trigonometric shape functions are used. Then the Rayleigh–Ritz approximation technique and the principle of minimum potential energy are applied to obtain the unknown coefficients of the displacement fields. The results are compared with a three-dimensional finite element analysis and an experimental program is conducted to produce data for validation of theoretical and numerical methods. Mesh independency is also studied to evaluate the accuracy of the finite element results. Regarding to the computational costs and agreement of the analytical and numerical results with the experimental ones, the layer wise higher order shear deformation theory (LHSDT) based on polynomial shape functions is the most efficient and flexible theory in calculation of the deflection and strains for the very thin to thick laminates in the buckling and post-buckling conditions.

Analysis of laminated composite and sandwich plate structures using generalized layerwise HSDT and improved meshfree radial point interpolation method

This paper presents a generalized layerwise higher-order shear deformation theory for static, free vibration and buckling analyses of symmetric laminated composite and sandwich plates using improved meshfree radial point interpolation method (iRPIM). The approach comes from a layerwise model combined with a generalized higher-order shear deformation theory. In other words, we impose the continuity on the interface of each layer for the in-plane displacements and transverse shear stresses. This yields more adequate solution for sandwich structures which present the significant difference of properties between the core sheet and the face ones. As a result, transverse shear stresses are accurately achieved as compared with the analytical ones. The present iRPIM shows stability and high accuracy with respect to the uniquely proposed correlation function. A simple but effective enforcement based on the concept of the rotation-free of essential boundary conditions yields significant advantage of computations. The numerical results are provided and compared well with other published solutions.

A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis

This paper presents a generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates. We exploit a higher-order shear deformation theory in each layer such that the continuity of the displacement and transverse shear stresses at the layer interfaces is ensured. Thanks for enforcing the continuity of the displacement and transverse shear stresses at an inner-laminar layer, the minimum number of variables is retained from the present theory in comparison with other layerwise theories. The method requires only five variables, the same as what obtained from the first- and higher-order shear deformation theories. In comparison with the shear deformation theories based on the equivalent single layer, the present theory is capable of producing a higher accuracy for inner-laminar layer shear stresses. The free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate are fulfilled without any shear correction factors. The discrete system equations are derived from the Galerkin weak form, and the solution is obtained by isogeometric analysis (IGA). The discrete form requires the C1 continuity of the transverse displacement, and hence NURBS basis functions in IGA naturally ensure this condition. The laminated composite and sandwich plates with various geometries, aspect ratios, stiffness ratios and boundary conditions are studied. The obtained results are compared with the 3D elasticity solution, the analytical as well as numerical solutions based on various plate theories.

Two-dimensional sublamination theory for analysis of functionally graded plates

Presented is a two-dimensional sublamination theory for analysis of plates made of functionally graded materials. The sublamination plate theory extends a layer-wise higher-order shear-deformation theory for laminated plates by considering material properties being continuous functions of the thickness coordinate and using a new concept of sublamination to increase the degrees of freedom. The theory accommodates free shear stress conditions on the bonding surfaces, accounts for non-uniform deformation-dependent distributions of transverse shear stresses through the thickness, can be used for evaluating boundary restraint effects, and can be used for analyzing thin and thick plates with any boundary conditions. A sublamination plate element based on this theory is developed and validated for static and dynamic analysis. The degrees of freedom of the element is adaptable. For an element away from boundaries, it's degrees of freedom can be reduced at the elemental level without loss of accuracy. Analytical shear warping functions are presented. Moreover, modal analysis of functionally graded plates with different boundary conditions is performed to show the capability and accuracy of the theory.

Total-Lagrangian Formulation and Finite-Element Analysis of Highly Flexible Plates and Shells

Presented here is a new total-Lagrangian displacement-based finite-element formulation for plates and shells undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities, general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a first-order shear deformation theory with shear correction factors obtained by matching the shear strain energy and stress resultants with those of a general layerwise higher-order shear deformation theory. Large static deformations of several different plates and shells under different loading and boundary conditions are obtained. Comparison with available results in the literature reveals that the finite-element model is accurate in predicting large deformations of highly flexible two-dimensional structures.

A higher-order sandwich plate theory accounting for 3-D stresses

In this paper we extend a layerwise higher-order shear-deformation theory to model a sandwich plate impacting with an elastic foundation at a low velocity. A new concept of sublaminates is introduced, and the new sandwich plate theory satisfies the continuity conditions of interlaminar shear and normal stresses, accommodates the normal and shear stresses on the bonding surfaces, and accounts for non-uniform distributions of transverse shear stresses in each layer. Moreover, the use of sublaminates enables the modeling of shear warpings that change with the spatial location, vibration frequency, and loading and boundary conditions. A finite-element model based on this sandwich plate theory is derived for performing direct transient analyses to predict the initiation and location of critical matrix crack and the threshold of impact damage. Moreover, analytical shear warping functions, shear coupling functions, and normal strain functions due to in-plane stretching, bending, transverse shearing, and surface loading are presented.

A new look at shear correction factors and warping functions of anisotropic laminates

Shear warpings of a composite laminate are shown to be functions of its stacking sequence, its ply angles, and the material properties of layers. Moreover, a new formulation of shear correction factors is derived by matching the exact shear stress resultants and shear strain energy with those of the equivalent first-order shear deformation theory. Without solving a plate problem with specified loading and boundary conditions, approximate analytical shear warping functions of a composite laminate can be derived by using the continuity conditions of in-plane displacements and interlaminar shear stresses and the free shear stress conditions on the bonding surfaces. The approach results in a layerwise higher-order shear deformation theory that contains most shear deformation theories as special cases and reveals the shear coupling effect of angle-ply laminates. A combination of the present method of deriving shear warping functions and the new formulation of shear correction factors can be used to obtain fairly accurate a priori estimates of shear correction factors for the use of the first-order shear deformation theory in analyzing highly anisotropic laminates. For isotropic plates, the shear correction factor obtained is 5/6. For orthotropic laminates, the shear correction factors obtained are compared with those results in the literature that are obtained by using predictor-corrector procedures. Shear correction factors for some symmetric and asymmetric angle-ply laminates, of which the shear correction factor accounting for the shear coupling effect is non-trivial, are also presented.