Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model

Nonlinear free vibration behavior of laminated composite curved panel under hygrothermal environment is investigated in this article. The mathematical model of the laminated panel is developed using Green–Lagrange-type geometrical nonlinearity in the framework of higher-order mid-plane kinematics. The corrugated composite properties are evaluated through the micromechanical model and all the nonlinear higher-order terms are included in the present model for the sake of generality. The equation of vibrated panel is obtained using Hamilton's principle and discretized with the help of the finite element steps. The solutions are computed numerically using the direct iterative method. The effect of parameters on the nonlinear vibration responses is examined thoroughly by solving the wide variety of numerical examples.     

Active damping of geometrically nonlinear vibrations of doubly curved laminated composite shells

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of doubly curved laminated composite shells. Vertically/obliquely reinforced 1–3 piezoelectric composite (PZC) and active fiber composite (AFC) materials are used as the materials of the constraining layer of theACLD treatment. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory (FSDT) and the Von Kármán type non-linear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element (FE) model of doubly curved laminated smart composite shells integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear transient vibrations of the shells. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the doubly curved laminated cross-ply and angle-ply shells for suppressing their geometrically nonlinear transient vibrations. It is found that the performance of the ACLD patch with its constraining layer being made of the AFC is significantly higher than that of the ACLD patch with vertically/obliquely reinforced 1–3 PZC constraining layer. The effects of variation of piezoelectric fiber orientation in both the obliquely reinforced 1–3 PZC and the AFC constraining layers on the control authority of the ACLD patches have also been investigated.     

Geometrically nonlinear formulation for the curved shell elements

This paper presents a geometrically nonlinear formulation using total lagrangian approach for the three-dimensional curved shell elements. The basic element geometry is constructed using the coordinates of the middle surface nodes and the mid-surface nodal point normals. The element displacement field is described using three translations of the mid-surface nodes and the two rotations about the local axes. The existing shell element formulations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements.     

Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates

This research present the development of geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Geometric nonlinearity is accounted for in Von-Karman sense. A family of NURBS elements are constructed from refinement processes and validated using various examples. k-refined NURBS elements are developed to study thin plates. Isotropic, orthotropic and laminated composite plates are studied for various boundary conditions, length to thickness ratios and ply-angles. Computed center deflection is found to be in an excellent agreement with the literature. For thin plate analysis, linear and k-refined quadratic NURBS element is found to remedy the shear locking problem. k-refined quadratic NURBS element provide stabilized response to distorted, coarse meshes without increasing the order of the polynomial, owing to the increased smoothness of solution space.     

Asymptotic finite strip analysis of doubly curved laminated shells

On the basis of the Hellinger–Reissner (H–R) principle, an asymptotic finite strip method (FSM) for the analysis of doubly curved laminated shells is presented by means of perturbation. In the formulation the displacements and transverse stresses are taken as the functions subject to variation. Imposition of the stationary condition of the H–R functional, the weak formulation associated with the Euler–Lagrange equations of three-dimensional (3D) elasticity is obtained. Upon introducing a set of appropriate dimensionless scaling and bringing the transverse shear deformations to the stage at the leading-order level, the weak formulation is asymptotically expanded as a series of weak-form equations for various orders. An asymptotic FSM according to the present formulation is then developed where the field variables are interpolated as a finite series of products of trigonometric functions and crosswise polynomial functions independently. Through successive integration, the present formulation turns out that three mid-surface displacement degrees-of-freedom (DOF) and two rotation DOF for each node in a strip element are taken as the independent unknowns in the system equations for various orders. The solution procedure for the leading-order level can be repeatedly applied level-by-level in a consistent and hierarchic way. Application of the asymptotic FSM to a benchmark problem is demonstrated.     

Nonlinear free vibration analysis of shape memory alloy embedded laminated composite shell panel

High specific strength and stiffness are characteristics desired for aircraft and launch vehicle domains to enhance the payload gain and performance. The mechanical properties of the composites can be further tailored by embedding structural components, such as shape memory alloys, into the passive composite structure. The present study is primarily focused on the nonlinear free vibration analysis of spherical and cylindrical composite shell panels embedded with shape memory alloy fibers. The nonlinear finite element governing equations based on the higher-order shear deformation plate theory and principle of virtual work with nonlinear von-Karman strain displacement relations are employed for the analysis. The temperature-dependent material properties of shape memory alloy are considered in the formulation. A nine-noded isoperimetric element is accounted for synthesizing the element for the finite formulation. The Young's modulus and the recovery stress vary with temperature and higher nonlinearity. The incremental method is used to generate the inputs for the temperature-dependent nonlinear properties of materials. The temperature change is divided by many small temperature increments. The temperature-dependent material properties are assumed constant during the small increment. The mechanics of shape memory alloy in substrate are presented and the governing equation of laminated composite with shape memory alloy is obtained and implemented in the MATLAB 7.8 program.     

Stochastic post buckling analysis of laminated composite cylindrical shell panel subjected to hygrothermomechanical loading

In this paper, the effect of random system properties on the post buckling load of geometrically nonlinear laminated composite cylindrical shell panel subjected to hygrothermomechanical loading is investigated. System parameters are assumed as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic formulation. The elastic and hygrothermal properties of the composite material are considered to be dependent on temperature and moisture concentration using micromechanical approach. A direct iterative based C⁰ nonlinear finite element method in conjunction with first-order perturbation technique proposed by present author for the plate is extended for shell panel subjected to hygrothermomechanical loading to compute the second-order statistics (mean and variances) of laminated composite cylindrical shell panel. The effect of random system properties, plate geometry, stacking sequences, support conditions, fiber volume fractions and temperature and moisture distributions on hygrothermomechanical post-buckling load of the laminated cylindrical shell panel are presented. The performance of outlined stochastic approach has been validated by comparing the present results with those available in the literature and independent Monte Carlo simulation.     

Effects of in-plane constraints on the free vibration of a symmetrically laminated doubly curved panel

Summary. For a symmetrically laminated curved panel, although the stretching-bending anisotropic coupling stiffnesses are zero, but due to presence of the curvature, the in-plane and out-of-plane behaviors of the panel are still coupled, and hence the in-plane constraints at the boundaries have influences on the transverse behavior of the panel. Such effects of in-plane constraints on the free vibration of the symmetrically laminated curved panel are investigated using a modified Galerkin method in this study. Transverse shear deformation of the panel is considered by using first-order shear deformation theory. Numerical results of the symmetric angle-ply and cross-ply laminated panel with simply supported boundary conditions (SS2 and SS3) are presented. Results show that the in-plane boundary constraints have significant effects on the vibration behavior of the symmetrically laminated curved panel, and the effects strongly depend on the radius of curvature, thickness and lamination schemes, etc. Effects of bending-twisting anisotropic coupling of symmetric angle-ply laminate on the vibration behavior are also discussed.     

Geometrically nonlinear analysis for some axially compressed laminated cylindrical panels

Mainly, this paper deals with cylindrical laminated panels, axially compressed under the constraint of four simply-supported edges.By imposing uniform increasing end-shortening to the two opposite circular edges, characteristic equilibrium paths have been obtained in correspondence to numerical evaluations with finite element models subject to geometric non linearity. A peculiar link among different branches of the total path, each of which is connected to a proper deformed configuration, is pointed out in the axial load/end-shortening space.Convergence problems and mesh sensibility are also examined.     

Geometrically nonlinear axisymmetric analysis of thick laminated annular plate using FSDT

This paper presents geometrically nonlinear, axisymmetric, static and transient, moderately large deflection response of a laminated, composite, moderately thick annular plate subjected to uniformly distributed ring loads. The layers are considered to be polar orthotropic. Rotational inertia is included but the inplane inertia is neglected. First-order shear deformation theory is used in terms of the deflection w, rotation ψ of the midplane and the stress function Φ. The governing equations are solved by the orthogonal point collocation method and Newmark-β scheme. The effect of the radius-to-thickness ratio of the plate on the deflection and stress response is studied for symmetrically and unsymmetrically laminated plates.     

Completely hierarchical p-version curved shell element for laminated composite plates and shells

This paper presents a new completely hierarchical three dimensional curved shell finite element formulation for linear static analysis of laminated composite plates and shells. The element displacement approximation can be of arbitrary polynomial orders p , p and p in the , , and directions thereby permitting strains of at least (p –1), (p –1) and (p –1) order. The element approximation functions as well as the nodal variables are hierarchical. The element formulation ensures C ⁰ continuity. The lamina properties are incorporated by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. The geometry of the laminated shell element is described by the coordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The element formulation is equally effective for very thin as well as very thick laminated plates and curved shells. The results obtained from the present formulation are compared with those available in the literature as well as available analytical solutions.     

Materially nonlinear analysis of laminated composite plates

A materially nonlinear analysis of laminated composite plates is presented. The Reissner-Mindlin type plate theory and a fully three-dimensional elasticity theory of laminated composites are used to analyze the bending of plates under transverse loads. The modified Ramberg-Osgood relationship is used to compute the principal elastic moduli in each lamina. Results are also presented using the modified elastic-plastic criterion of Hill. The results agree well with those available in the literature. Many of the results presented here should serve as references for future investigations.     

A general doubly curved laminate shell theory

The aim of the work summarized in this paper is the theoretical modelling of laminated composite shells of arbitrary shape, in order to: improve the calculus of shear stresses, and especially to avoid shear correction factors; account for continuity conditions of displacements and transverse shear stresses at layer interfaces as well as compatibility conditions of transverse shear stresses on the bonding surfaces; estimate the relevance of shear refinements, of membrane refinements and of the transverse stretching beyond standard kinematics; and to analyse the sensitivity to edge effects for significant boundary conditions.     

Geometrically nonlinear composite beam structures: design sensitivity analysis

The purpose of this paper is to develop a finite element model for optimal design of composite laminated thin-walled beam structures, with geometrically nonlinear behavior, including post-critical behavior. A continuation paper will be presented with design optimization applications of this model. The structural deformation is described by an updated Lagrangean formulation. The structural response is determined by a displacement controlled continuation method. A two-node Hermitean beam element is used. The beams are made from an assembly of flat-layered laminated composite panels. Beam cross-section mass and stiffness property matrices are presented.

Design sensitivities are imbedded into the finite element modeling and assembled in order to perform the structural design sensitivity analysis. The adjoint structure method is used. The lamina orientation and the laminate thickness are selected as the design variables. Displacement, failure index, critical load and natural frequency are considered as performance measures. The critical load constraint calculated as the limit point of the nonlinear response is also considered, but a new method is proposed, replacing it by a displacement constraint.     

Analysis of laminated bimodulus composite thin shells of revolution using a doubly curved quadrilateral finite element

This paper presents a finite element analysis of laminated bimodulus composite thin shells of revolution using a 48 d.o.f. doubly curved quadrilateral finite element. All the three displacements of the shell element reference surface are expressed as products of one-dimensional first-order Hermite interpolation polynomials. The constitutive relationship for a bimodulus composite is assumed to depend on the fibre-direction strain experienced by each orthotropic layer. Consequently the true state of strain and the corresponding constitutive relationship in a bimodulus composite structure are to be determined iteratively. The true state of stress/strain is obtained by specifying a maximum error in the locations of the two neutral surfaces (one along each of the orthogonal reference axes) in the shell. The use of the quadrilateral shell finite element is validated by solving the problem of (i) a freely supported single layer (0°) bimodulus composite square plate and (ii) a freely supported single layer (0°) cylindrical panel, which are subjected to sinusoidal transverse loading and for which analytical solutions are available. Next, the problems of a single layer (90°) pinched cylindrical shell and a single layer (0°) open crown hemispherical shell are solved to show the ability of the present program.     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.     

几何非线性高性能复合材料筋混凝土梁Heterosis组合壳单元

对于高性能碳纤维增强聚合物复合材料(CFRP)筋混凝土梁,研究几何非线性组合壳单元模型,对预应力CFRP筋混凝土梁进行了全过程分析。引入Von Karman理论,推导了局部坐标系下Piola2Kirchhoff 应力矩阵和几何刚度矩阵;分别采用组合壳单元和分层壳单元模拟预应力CFRP 筋和玻璃纤维增强聚合物复合材料(GFRP)筋,并推导了CFRP筋对组合壳单元刚度矩阵的贡献,同时采用Heterosis选择积分技术以避免剪切锁定和零能量模式,研制了相应的非线性计算程序。计算结果与试验数据对比可知,挠度发展规律和预应力CFRP筋应变发展规律均吻合良好,说明了研究单元的有效性及研制程序的正确性;CFRP筋具有高强度性能,梁试件破坏时CFRP筋均未失效;利用预应力CFRP筋应变重分布系数研究了梁的刚度退化规律,表明采用GFRP筋代替普通钢筋在加载后期会使梁的刚度退化减小。      

Progressive failure analysis of laminated composite with hole under flexural loading

Abstract

Understanding the progressive failure of laminated composite plays an important role in the structural integrity analysis of a structure. Continuum damage mechanics-based approach is one of the powerful tools to analyze the failure of laminated composite structures. The present paper investigates the damage evolution and progression in laminated composites with a hole under flexural loading. The presence of high-stress concentrations along with the free edge stresses at the vicinity of the hole in laminated composite leads to complex failure mechanisms. The influence of the change in thickness and lamina configuration on the strength characteristics is presented.     

Delamination modeling in doubly curved laminated shells for free vibration analysis using zigzag theory-based facet shell element and hybrid continuity method

We present a finite element (FE) formulation for the free vibration analysis of doubly curved laminated composite and sandwich shells having multiple delaminations, employing a facet shell element based on the efficient third-order zigzag theory and the region approach of modeling delaminations. The methodology, hitherto not attempted, is general for delaminations occurring at multiple interfacial and spatial locations. A recently developed hybrid method is used for satisfying the continuity of the nonlinear layerwise displacement field at the delamination fronts. The formulation is shown to yield very accurate results with reference to full-field three-dimensional FE solutions, for the natural frequencies and mode shapes of delaminated shallow and deep, composite and highly inhomogeneous soft-core sandwich shells of different geometries and boundary conditions, with a significant computational advantage. The accuracy is sensitive to the continuity method used at the delamination fronts, the usual point continuity method yielding rather poor accuracy, and the proposed hybrid method giving the best accuracy. Such efficient modeling of laminated shells with delamination damage will be of immense use for model-based techniques for structural health monitoring of laminated shell-type structures.