Static analysis of delaminated composite shell panels using layerwise theory

In this paper, a layerwise theory and associated finite element model are presented to study the bending deformations of delaminated composite shell panels. The layerwise theory is based on the assumption of first-order shear deformation theory in each layer, and it satisfies the displacement continuity at layer interfaces. The presence of multiple discrete delaminations is modeled through the use of Heaviside step functions. Delamination movements (relative slip and opening) are included in the theory as additional degrees of freedom. The finite element model developed is validated by comparing the present results with those available in the literature. This model based on the layerwise theory is subsequently used for the first time in the literature to study the static response and delamination movements such as interfacial slipping and opening of delaminated composite shell panels.     

Interlaminar stresses in antisymmetric angle-ply cylindrical shell panels

Layerwise theory of Reddy is utilized for investigating free-edge effects in antisymmetric angle-ply laminated shell panels under uniform axial extension. Following some physical arguments, governing displacement field is divided into local and global parts. The former is discretized through the shell thickness by a zig-zag interpolation function while the latter is calculated by a first-order shear deformation theory. Local equilibrium equations are then solved through a state space approach. Accuracy of the proposed technical solution is subsequently verified by a novel analytical elasticity solution. For this end, the problem is analytically solved for specific boundary conditions along the edges. The numerical results show excellent agreement between two theories for various composite shell panels.     

Out-of-plane behaviour of infill masonry panels strengthened with composite materials

The performance of various composite materials applied to strengthen hollow masonry panels under out-of-plane actions is compared here. The strengthening solutions belong to three reinforcement Externally Bonded (EB) wet lay-up systems: (i) bidirectional composite meshes applied with inorganic matrices, i.e., Textile Reinforced Mortars (TRM); unidirectional composite textiles applied with (ii) inorganic matrices, i.e., Steel Reinforced Grouts (SRG), or (iii) organic (epoxy) matrices, i.e., Fibre Reinforced Polymers (FRP), Steel Reinforced Polymers (SRP) and Natural FRPs. Carbon FRP, flax and hemp NFRP, and basalt and glass-based TRM were examined. As inorganic matrix, a cement-based mortar was used for TRMs; in the case of SRGs, comparisons with a magnesia-based matrix were also carried out. Twenty-seven specimens were subjected to simplified four-point monotonic bending tests, aimed at reproducing in the laboratory the failure condition of infill masonry walls under out-of-plane actions. The results are compared in terms of failure mode and mechanical improvement, and provide an analytical evaluation of moment–curvature behaviour according to bilinear laws.     

Interlaminar stresses in laminated composite plates, cylindrical/spherical shell panels damaged by low-velocity impact

Prediction of damage caused by low-velocity impact in laminated composite plate cylindrical/spherical shell panels is an important problem faced by designers using composites. Not only the in-plane stresses but also the interlaminar normal and shear stresses play a role in estimating the damage caused. The work reported here is an effort in getting better predictions of damage in composite plate cylindrical/spherical shell panels subjected to low-velocity impact.

The low-velocity impact problem is treated as a quasi-static problem. First, the in-plane stresses are calculated by 2-D nonlinear finite element analysis using a 48 degrees of freedom laminated composite shell element. The damage analysis is then carried out using a Tsai-Wu quadratic failure criterion and a maximum stress criteria. Interlaminar normal and shear stresses are predicted after taking into account the in-plane damage caused by low-velocity impact. The interlaminar stresses are obtained by integrating the 3-D equations of equilibrium through the thickness. The deformed geometry is taken into account in the third equation of equilibrium (in the thickness direction). After evaluating the formulation and the computer program developed for correctness, the interlaminar stresses are predicted for composite plates/shell panels which are damaged by low-velocity impact.     

复合材料圆筒自由边效应的有限元分析

为准确预测因相邻层弹性性能不同产生的自由边应力,避免分层或横向开裂等过早破坏,基于变分渐近法构建FRP层合板的多尺度模型。利用板厚宽比很小的特点,严格将原三维各向异性弹性问题分解为代表单胞分析和二维板宏观分析。前者可提供板宏观分析所需的本构关系和三维重构关系。基于最小势能原理,通过对二维板能量泛函中主导变分项的渐近分析,得到表征板几何非线性的系列波动函数解;通过本构关系和求解得到的翘曲函数解重构自由边附近的局部三维应力场分布。通过拉伸、弯曲和扭矩共同作用下的对称铺设层合板算例表明：构建降维模型可准确预测沿自由边厚度方向和层间界面的应力分布,且计算效率大为提高,为结构设计人员在初步设计阶段对FRP层合板性能评估提供了一种简洁的途径。     

A nonlinear composite shell element with continuous interlaminar shear stresses

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear solution process. Several examples are presented to illustrate the performance of the developed numerical model.List of symbols reference surface - convected coordinates of the shell middle surface - ⁱ coordinate in thickness direction - ⁱ h thickness of layer i - X_o position vector of the reference surface - ⁱX_o position vector of midsurface of layer i - t _k orthonormal basis system in the reference configuration - ⁱ a _k orthonormal basis system of layer i - ⁱW axial vector - R_o orthonormal tensor in the reference configuration - ⁱ R orthonormal tensor of layer i - ⁱ Cauchy stress tensor - ⁱ P First Piola-Kirchhoff stress tensor - ⁱ q vector of interlaminar stresses - ⁱ n, ⁱ m vector of stress resultants and stress couple resultants - v _x components of the normal vector of boundary - ⁱ N, ⁱ Q, ⁱ M stress resultants and stress couple resultants of First Piola-Kirchhoff tensor - stress resultants and stress couple resultants of Second Piola-Kirchhoff tensor - ⁱ , ⁱ , ⁱ strains of layer i - _K transformation matrix - u_o displacement vector of layer 1 - ⁱ local rotational degrees of freedom of layer i     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

Out-of-plane failure mechanisms in LFRP composite cutting

LFRP (Long Fiber Reinforced) composites are widely used in structural components for high responsibility applications in different industrial sectors. Composite components are manufactured near final shape, however several machining operations are commonly required to achieve dimensional and assembly specifications. Machining should be carefully carried out in order to avoid workpiece damage. Despite of the interest of numerical modeling to analyze in detail the phenomena involved during composite cutting, there are only few works in the scientific literature dealing with this topic even in the simple case of orthogonal cutting. Out-of-plane failure can be accounted only if three dimensional modeling is performed. However up to date numerical analysis of cutting found in scientific literature was focused in two-dimensional approach. In this paper (2D) and three dimensional (3D) numerical modeling of orthogonal cutting of carbon LFRP composite are presented. The aim of the paper is to analyze the complex aspects involved during cutting, including out-of-plane failure.     

Optimum design for buckling of plain and stiffened composite axisymmetric shell panels/shells

The buckling of plain and discretely stiffened composite axisymmetric shell panels/shells made of repeated sublaminate construction is studied using the finite element method. In repeated sublaminate construction, a full laminate is obtained by repeating a basic sublaminate, which has a smaller number of plies. The optimum design for buckling is obtained by determining the layup sequence of the plies in the sublaminate by ranking, so as to achieve maximum buckling load for a specified thickness. For this purpose, a four-noded 48-dof quadrilateral composite thin shell element, together with fully compatible two-noded 16-dof composite meridional and parallel circle stiffener elements are used.     

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

In this paper, the free vibration analysis of simply‐supported and clamped composite laminates, especially thick laminates, is carried out. The three‐dimensional theory of elasticity is integrated into a layerwise model via differential quadrature discretization. All physical governing equations are satisfied, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in‐plane strains and stresses along the interfaces of composite laminates. Effects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional exact elasticity solutions for antisymmetric angle-ply laminated composite plates

International Journal of Mechanics and Materials in Design - This paper is concerned with the derivation of the benchmark three-dimensional exact solutions for the static analysis of rectangular...     

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN.     

Singular solutions in elasticity

Summary General solutions of the time-independent equations of motion for linear elasticity with couplestresses are studied. The completeness of a displacement potential similar to theGalerkin-Somigliana representation is proved. The fundamental singular solution of the field equations is defined with the aid of the reciprocal work theorem.

---

Zusammenfassung Allgemeine Lösungen der zeitunabhängigen Bewegungsgleichungen der linearen Elastizität mit Momentenspannungen werden studiert. Die Vollständigkeit eines Verschiebungspotentials, ähnlich dem vonGalerkin-Somigliana, wird bewiesen. Die singuläre Grundlösung der Feldgleichungen wird mit Hilfe des verallgemeinertenBettischen Reziprozitätssatzes definiert.

     

An evaluation of equivalent-single-layer and layerwise theories of composite laminates

A review of equivalent-single-layer and layerwise laminate theories is presented and their computational models are discussed. The layerwise theory advanced by the author is reviewed and a variable displacement finite element model and the mesh superposition techniques are described. The variable displacement finite elements contain several different types of assumed displacement fields. By choosing appropriate terms from the multiple displacement field, an entire array of elements with different orders of kinematic refinement can be formed. The variable kinematic finite elements can be conveniently connected together in a single domain for global-local analyses, where the local regions are modeled with refined kinematic elements. In the finite element mesh superposition technique an independent overlay mesh is superimposed on a global mesh to provide localized refinement for regions of interest regardless of the original global mesh topology. Integration of these two ideas yields a very robust and economical computational tool for global-local analysis to determine three-dimensional effects (e.g. stresses) within localized regions of interest in practical laminated composite structures.     

A comparative study of elasticity,shell and boundary layer solutions applied to axially compressed cylinders

Summary This paper deals primarily with a comparative study based on different methods of solution for the problem of axially compressed cylinders. A comprehensive discussion on the range of validity of these types of solutions is also included, and an extensive numerical analysis has been carried out.     

Fundamental solutions in micropolar elasticity

In this paper the general form of the fundamental solutions and fundamental matrices associated with the equations of the micropolar elastostatics as well as the integral representation by means of these matrices are determined. For the dynamic problem the time-periodic fundamental solutions and general fundamental solutions are determined. In this last case the explicit solution is given for $\text{ρ(γ + ?) = jμ}$.