Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers

Thermal post-buckled vibration of laminated composite doubly curved panel embedded with shape memory alloy (SMA) fiber is investigated and presented in this article. The geometry matrix and the nonlinear stiffness matrices are derived using Green–Lagrange type nonlinear kinematics in the framework of higher order shear deformation theory. In addition to that, material nonlinearity in shape memory alloy due to thermal load is incorporated by the marching technique. The developed mathematical model is discretized using a nonlinear finite element model and the sets of nonlinear governing equations are obtained using Hamilton’s principle. The equations are solved using the direct iterative method. The effect of nonlinearity both in geometric and material have been studied using the developed model and compared with those published literature. Effect of various geometric parameters such as thickness ratio, amplitude ratio, lamination scheme, support condition, prestrains of SMA, and volume fractions of SMA on the nonlinear free vibration behavior of thermally post-buckled composite flat/curved panel been studied in detail and reported.     

Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells

Summary In this paper, a model of cusped catastrophe at nonlinear dynamic buckling of a symmetrically laminated cylindrically orthotropic shallow spherical shell is presented. The shell is subjected to an axisymmetrical load. Effects of transverse shear are taken into account. Effects of the shear modulus, geometry and parameters of the material on the nonlinear dynamic buckling are discussed. Received 2 April 1997; accepted for publication 27 November 1997     

Postbuckling of pressure-loaded shear deformable laminated cylindrical panels

IntroductionInrecentyears,fiber_reinforcedcompositelaminatedpanelshavebeenwidelyusedintheaerospace,marine ,automobileandotherengineeringindustries .Theproblemofbucklingandpostbucklingofcylindricalpanelsunderaxialcompressionortorsionhasbeenextensivelystudied .Incontrast,theliteratureoncylindricalpanelsunderpressureloadingisrelativelyspares.Thesestudiesincludealinearbucklinganalysis (Singeretal.[1]) ,anonlinearbucklinganalysi(YamadaandCroll[2 ]) ,anelastoplasticbucklinganalysisusingreducedstif…     

复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降     

复合材料层合开顶扁球壳的非线性动态屈曲

研究了复合材料层合开顶扁球壳的非线性动态屈曲问题。建立了对称层合圆柱正交异性开顶扁球壳考虑横向剪切的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。     

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.     

复合材料面层夹层扁壳非线性精化理论及应用

考虑面层横向剪切变形以及横向剪应力在面层和芯层粘结处连续,应用Hamilton原理建立了正交铺设复合材料面层夹层扁壳新的非线性精化理论。在静力问题情形,控制方程和边界条件化简为用四个基本未知函数表述。作为理论的应用,分析了简支边界条件下正交铺设复合材料面层夹层圆柱壳和夹层球壳的非线性弯曲,得到了其挠度响应和层间应力响应。     

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear

The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.     

An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory

This paper deals with closed-form solutions for in-plane and out-of-plane free vibration of moderately thick laminated transversely isotropic spherical shell panels on the basis of Sanders theory without any usage of approximate methods. The governing equations of motion and the boundary conditions are derived using Hamilton’s principle. The highly coupled governing equations are recast to some uncoupled equations by introducing four potential functions. Also, some relations were presented for the unknowns of the original set of equations in terms of the unknowns of the uncoupled equations. According to the proposed analytical approach, both Navier and Lévy-type explicit solutions are developed for moderately thick laminated spherical shell panels. The efficiency and high accuracy of the present approach are investigated by comparing some of the present study with the available results in the literature and the results of 3D finite element method. The effects of various shell parameters like shear modulus ratio of transversely isotropic materials and curvature ratio on the natural frequencies are studied. Clearly, the proposed solutions can accurately predict the in-plane and out-of-plane natural frequencies of moderately thick transversely isotropic spherical shell panels.     

Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment

Influences of large deformation (geometrical non-linear) and rotary inertia on wave propagation in a long, piezoelectric cylindrically laminated shell in thermal environment is presented in this paper. Nonlinear dynamic governing equations of piezoelectric cylindrically laminated shells are derived by means of Hamilton’s principle. The wave propagation modes are obtained by solving an eigenvalue problem. Numerical examples show that the characteristics of wave propagation in piezoelectric cylindrically laminated shells are relates to the large deformation, rotary inertia and thermal environment of the piezoelectric cylindrically laminated shells. The effect of large deformation, rotary inertia and thermal load on wave propagation in the piezoelectric cylindrically laminated shells is discussed by comparing with the result from the small deformation (geometrical linear shell theory). This method may be used to investigate wave propagation in various laminated material, layers numbers and thickness of piezoelectric cylindrically laminated shells under large deformation. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｆｉｂｅｒ＿ｒｅｉｎｆｏｒｃｅｄｃｏｍｐｏｓｉｔｅｌａｍｉｎａｔｅｄｓｈｅｌｌｓｔｒｕｃｔｕｒｅｓａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｔｈｅａｅｒｏｓｐａｃｅ ,ｍａｒｉｎｅｉｎｄｕｓｔｒｙ ,ａｕｔｏｍｏｂｉｌｅｉｎｄｕｓｔｒｙａｎｄｏｔｈｅｒｅｎｇｉｎｅｅｒｉｎｇａｐｐｌｉｃａｔｉｏｎｓ.Ｄｕｒｉｎｇｔｈｅｏｐｅｒａｔｉｏｎａｌｌｉｆｅ ,ｔｈｅｖａｒｉａｎｃｅｏｆｔｅｍｐｅｒａｔｕｒｅａｎｄｍｏｉｓｔｕｒｅｒｅｄｕｃｅｓｔｈｅｅｌａｓｔｉｃｍｏｄｕｌｉ…     

爆炸冲击下复合材料层合扁球壳的动力屈曲

研究计及横向剪切的复合材料层合扁球壳在爆炸冲击载荷作用下的非线性轴对称动力屈曲问题。通过在复合材料层合扁球壳非线性稳定性的基本方程中增加横向转动惯量项并引入R.H.Cole理论的爆炸冲击力,得到爆炸冲击下复合材料层合扁球壳的动力控制方程,应用Galerkin方法得到用顶点挠度表达的爆炸冲击动力响应方程,并采用Runge-Kutta方法进行数值求解,采用Budiansky-Roth准则确定冲击屈曲的临界载荷,讨论了壳体几何尺寸对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,此方法是可行的。     

Improved torsional analysis of laminated box beams

The improved torsional analysis of the laminated box beams with single- and double-celled sections subjected to a torsional moment is performed by introducing 14 displacement parameters. For this, a thin-walled laminated box beam theory considering the effects of shear and elastic couplings is presented. The governing equations and the force-displacement relations are derived from the variation of the strain energy. The system of linear algebraic equations with non-symmetric matrix is constructed by introducing the displacement parameters and by transforming the higher order simultaneous differential equations into first order ones. This numerical technique determines eigenmodes corresponding to 12 zero and 2 non-zero eigenvalues and derives displacement functions for displacement parameters based on the undetermined parameter method. Finally, the element stiffness matrix is determined using the member force-displacement relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model using the Lagrangian interpolation polynomials and three-dimensional analysis results using the shell elements of ABAQUS for coupled laminated beams with single- and double-celled sections.     

Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties

This paper presents a study on the buckling and vibration of initially stressed composite plates with temperature-dependent material properties in thermal environments. The initial stress is taken to be a combination of a pure bending stress and an axial stress. The temperature distribution in the plate is assumed to be uniform and linear in the transverse direction. The governing equations including the transverse shear deformation effects are established using the variational method. The effects of various parameters on the buckling and vibration behaviors of laminated plates with respective temperature-dependent and temperature-independent material properties are investigated. The buckling load and natural frequency are sensitive to the thermal stresses and initial stresses. Numerical results reveal that temperature-dependent material properties should be considered in the buckling and vibration analysis for laminated plates under thermal conditions.     

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

In this study, the first-order shear deformation theory(FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets(GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young's modulus. Hamilton's principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.     

Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties

Thermal postbuckling analysis is presented for graphene-reinforced composite (GRC) laminated cylindrical shells under a uniform temperature field. The GRC layers are arranged in a functionally graded (FG) graphene reinforcement pattern by varying the graphene volume fraction in each GRC layer. The GRCs possess temperature dependent and anisotropic material properties and the extended Halpin–Tsai model is employed to evaluate the GRC material properties. The governing equations are based on a higher order shear deformation shell theory and include the von Kármán-type kinematic nonlinearity and the thermal effects. A singular perturbation method in conjunction with a two-step perturbation approach is applied to determine the thermal postbuckling equilibrium path for a GRC shell with or without geometric imperfection. An iterative scheme is developed to obtain numerical thermal buckling temperatures and thermal postbuckling load–deflection curves for the shells. The results reveal that the FG-X piece-wise FG graphene distribution can enhance the thermal postbuckling capacity of the shells when the shells are subjected to a uniform temperature loading.

     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

Nonlinear bending analysis of ring-stiffened circular and annular general angle-ply laminated plates with various boundary conditions

In this study, elastic large deflection analysis of axisymmetric ring-stiffened circular and annular general angle-ply laminated plates subjected to transverse uniform load is studied. Based on first order shear deformation theory (FSDT) and large deflection von-Karman relations, the governing equations are derived. The dynamic relaxation (DR) method in conjunction with the central finite difference discretization technique is used to solve the nonlinear equilibrium equations. A detailed parametric study is carried out to investigate the influences of plate thicknesses, stiffener width, stiffener depth, fiber orientation, stacking sequence and different types of boundary conditions. Also, some linear and nonlinear analysis is provided to consider the effect of nonlinearity on the results.     

Creep buckling and post-buckling analysis of the laminated piezoelectric viscoelastic functionally graded plates

The creep buckling and post-buckling of the laminated piezoelectric viscoelastic functionally graded material (FGM) plates are studied in this research. Considering the transverse shear deformation and geometric nonlinearity, the Von Karman geometric relation of the laminated piezoelectric viscoelastic FGM plates with initial deflection is established. And then nonlinear creep governing equations of the laminated piezoelectric viscoelastic FGM plates subjected to an in-plane compressive load are derived on the basis of the elastic piezoelectric theory and Boltzmann superposition principle. Applying the finite difference method and the Newmark scheme, the whole problem is solved by the iterative method. In numerical examples, the effects of geometric nonlinearity, transverse shear deformation, the applied electric load, the volume fraction and the geometric parameters on the creep buckling and post-buckling of laminated piezoelectric viscoelastic FGM plates with initial deflection are investigated.     

Approximate vibration analysis of laminated curved panel using higher-order shear deformation theory

An approximate analysis for free vibration of a laminated curved panel (shell) with four edges simply supported (SS2), is presented in this paper. The transverse shear deformation is considered by using a higher-order shear deformation theory. For solving the highly coupled partial differential governing equations and associated boundary conditions, a set of solution functions in the form of double trigonometric Fourier series, which are required to satisfy the geometry part of the considered boundary conditions, is assumed in advance. By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions, an approximate solution, capable of providing a reliable prediction for the global response of the panel, is obtained. Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.