The present paper presents an innovative numerical model for predicting stress concentrations in composite materials in a multi-physics context. The numerical approach is based on the Carrera unified ...formulation, a numerical tool able to handle any kinematic model using a unified and compact notation. A general formulation for one-, two- and three-dimensional higher-order models has been presented. Equivalent single-layer and layer-wise models have been considered since they are the most effective in the analysis of composite materials. A hygro-thermo-elastic multi-physics formulation has been considered. The model has been used to investigate stress concentrations considering different configurations. Mechanical, thermal and hygroscopic loads have been considered. An innovative global-local analysis technique has been used to reduce the computational cost preserving the accuracy of the solution.
This article is part of the theme issue ‘Ageing and durability of composite materials’.
•A three-dimensional formulation is developed to analyze the stresses in composite panel under transverse loading.•An analytical solution is presented for the governing equations.•The presented ...formulation demonstrate high stress gradient for interlaminar stresses near the free and clamped edges.•Numerical predictions for out of plane stresses satisfy the traction conditions on the top and bottom surface of the panel.•The effect of radius to thickness, width to thickness ratio and boundary conditions are investigated on edge stresses.
In this study, a formulation is developed for investigation of three-dimensional edge stresses in cylindrical composite shell panels under distributed transverse loading. The formulation is obtained by employing the Galerkin weak formulation of the equilibrium equations. The obtained governing equations for the panel are solved via an analytical method for Levy-type boundary conditions including free and clamped edges. The presented formulation is capable of prediction of three-dimensional and boundary layer stresses in the composite panels subjected to transverse loading. The edge stresses in free edge, clamped edge and simple edge of transversally loaded cylindrical composite panel are studied. Comparison of numerical results with the available results of exact elasticity solution in the literature confirms the accuracy and the efficiency of the formulation.
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An analytical procedure for the analysis of interlaminar shear stresses in symmetric laminates is presented. The approach is based on the fact that the coupling effects of each part of the laminate ...are compensated by the adjacent parts. In a first step, a half of the laminate is considered for determining forces and moments per unit length that prevent the global deformation of the whole laminate. These forces and moments are obtained by solving a homogeneous second order differential equation. Then, the interlaminar shear stresses are computed by applying the stress equilibrium equations and by imposing the continuity of the stresses in the layer interfaces. The analytical results are checked by means of Finite Element Method in the case of quasi-isotropic laminates.
•A Galerkin based Layer-wise formulation is presented for thick composite panel subjected to bending moment.•An analytical solution is presented for governing equations of the panel considering free ...edge conditions.•Free edge stresses in bending of thick panel with general layer stacking is studied for the first time.•The predictions satisfy the free edge and free surface conditions.•The effect of geometrical parameters and layer stacking are investigated.
A thick composite cylindrical shell panel with general layer stacking is studied to investigate the free edge and 3D stresses in the panel which is subjected to pure bending moment. To this aim, a Galerkin based layerwise formulation is presented to discretize the governing equation of the panel to ordinary differential equations. Employing a reduced displacement field for the cylindrical panel, the governing equations for thick panel are developed in terms of displacements and a set of coupled ordinary differential equations is obtained. The governing equations are solved analytically for free edge boundary conditions and applied pure bending moment. The accuracy of numerical results is examined and the distribution of interlaminar and in-plane stresses is studied. The free edge stresses are studied and the effect of radius to thickness ratio, width to thickness ratio and layer stacking on the distribution of stresses is investigated. The focus of numerical results is on the prediction of boundary layer and free edge stress distribution.
A three-dimensional piezoelasticity based iterative analytical solution is presented for the multiphysics problem of free edge stresses in hybrid composite panels integrated with piezoelectric ...transducer layers. The formulation, applicable for general laminate configurations with arbitrary layup and materials properties, considers extension, bending, twisting and electric field actuation loadings with full electromechanical coupling. A mixed formulation approach based on the Reissner-type mixed variational principle is adopted to ensure exact point-wise satisfaction of all boundary and interlaminar continuity conditions, which is key to obtaining accurate results for the localized stresses near free edges. The solution is obtained using the recently developed mixed-field multiterm extended Kantorovich method, whose robustness, convergence and accuracy are illustrated for various laminates and loadings. The solution successfully captures singular nature of free edge interlaminar stresses under different loadings. The results show a significant effect of electromechanical coupling on the free edge stresses in hybrid laminates under mechanical loading. The effect of actuator thickness on the interfacial stress distributions under electric load is studied. Finally, it is shown how the free edge stresses due to extension, bending and twisting loads can be controlled by applying appropriate actuation potential.
•Formulate a semi-analytic method for determining interfacial stresses of hard coatings.•Investigate the dependency of interfacial stresses upon structural and material parameters.•Determine the ...spacing of progressive cracking in hard coatings based on an energy criterion with refined stress field.
Surface coatings are broadly used in cutting tools, protective surface, and recently developed flexible electronics. This paper provides a simple semi-analytic strain energy approach to analysis of the interfacial stresses and progressive cracking in hard coatings subjected to mechanical and thermomechanical loads. The problem is formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses in cracked coating layers are determined by means of an efficient semi-analytic stress-function variational method formulated by the authors recently. Criterion for progressive cracking in the coating layers is established in the sense of energy conservation. The crack spacing is determined as a function with respect to the geometries, material properties, and external loads. Dependencies of the free-edge stresses and crack spacing upon the geometries and material parameters of the coating system as well as external loads are demonstrated. Numerical results show that given a coating system, the threshold load increases rapidly with the decrease of crack spacing; the thicker and stiffer the coating layer is, the easier the progressive cracking is. A universal scaling number on progressive cracking is obtained. The model is also validated by the results in the literature. The present phenomenological model is applicable for scaling analysis of cracking tolerance of surface coatings, data reduction of coating experiments, design of property-tailorable surface coating systems, etc.
A top-down approach has been proposed to achieve the free-edge stresses in a θ/−θs rectangular laminate under a longitudinal tensile load. At the first stage, the laminate is subdivided into two ...antisymmetric parts and the upper one is analyzed by including an unknown twisting moment. This problem has been solved by extending an analytical solution for torsion of orthotropic laminates to antisymmetric laminates. At the second stage, the upper lamina was analyzed alone by including the shear force induced by the lower lamina. In this way, closed-form solutions for in-plane and out-of-plane stresses were obtained. The results for the case of a 45/−45s strip have been compared to other analytical and numerical results. θ/−θs laminates of different widths have been analyzed and analytical results have been compared with results obtained by the FEM, after applying the submodeling technique.
Large free-edge interfacial stresses induced in adhesively bonded joints (ABJs) are responsible for the commonly observed debonding failure in ABJs. Accurate and efficient stress analysis of ABJs is ...important to the design, structural optimization, and failure analysis of ABJs subjected to external mechanical and thermomechanical loads. This paper generalizes the high-efficiency semi-analytic stress-function variational methods developed by the authors for accurate free-edge interfacial stress analysis of ABJs of various geometrical configurations. Numerical results of the interfacial stresses of two types of common ABJs, i.e., adhesively bonded single-lap joints and adhesively single-sided joints, are demonstrated by using the present method, which are further validated by finite element analysis (FEA). The numerical procedure formulated in this study indicates that the present semi-analytic stress-function variational method can be conveniently implemented for accurate free-edge interfacial stress analysis of various type of ABJs by only slightly modifying the force boundary conditions. This method is applicable for strength analysis and structural design of broad ABJs made of multi-materials such as composite laminates, smart materials, etc.
An elasticity formulation for finite general cross-ply (symmetric and unsymmetric) laminates subjected to extension and/or a layerwise temperature distribution is developed. It is shown that the ...edge-effect problem of such laminates is actually a quasi-three-dimensional problem and its stress analysis can be restricted to a generic two-dimensional cross-section of the laminates. A layerwise theory is used to investigate analytically the interlaminar stresses near the free edges of general cross-ply composite laminates. The results obtained from this theory are compared with those available in the literature. It is found that the theory can predict very accurately the stresses in the interior region and near the free edges of composite laminates.
This paper presents efficient modeling technique using multi-dimensional method for prediction of free edge stresses in laminate plates. For the efficient modeling, the p-convergent transition ...element based on two-dimensional layer elements is proposed in order to connect discrete layer elements. The elements considered are on the basis of subparametric element concept. The results obtained by this proposed model are compared with those available in literatures. Especially, three-dimensional out-of-plane stresses in the interior and near the free edges are evaluated. The present models using the p-convergent transition element are demonstrated to be more practical and economical than previously p-version FEM using only single element type.
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