Post-buckling behaviour of cylindrically orthotropic annular plates

A finite element formulation for the study of the post-buckling behaviour of cylindrically orthotropic annular plates is presented in detail. The results for radial load ratios are presented in the form of empirical formulae in terms of the deflection at the inner edge to the thickness ratios of the plates for the first time in the literature for various values of the orthotropic parameters and radii ratios.     

Post-buckling behaviour of cylindrically orthotropic annular plates with uniform internal radial load

A finite element formulation for the study of the post-buckling behaviour of cylindrically orthotropic annular plates with uniform internal radial load is presented in this paper. The results for radial load ratios are presented in the form of empirical formulae in terms of the central deflection of the annulus to the thickness ratios of the plates for the first time in the literature for various values of the orthotropic parameters and radii ratios.     

Post-buckling analysis of moderately thick elastic annular plates

Post-buckling behaviour of moderately thick elastic annular plates is studied in this paper using a simplified finite element formulation. Radial load ratios for various radii ratios and thickness parameters are presented in the form of tables bringing out clearly the effect of radii ratios and thickness parameters.     

Post-buckling behaviour of moderately thick circular plates with edges elastically restrained against bending rotation

A finite element formulation is presented to study the post-buckling behaviour of circular plates with the effects of shear deformation and elastic restraints against bending rotation at the edges of the plates considered. A set of numerical results are included which clearly bring out variation of post-buckling characteristics with the varying values of thickness of the plate and the stiffness of the spring supports.     

Post-buckling of cylindrically orthotropic linearly tapered circular plates by finite element method

The post-buckling behavior of tapered circular plates with cylindrically orthotropic material properties is studied in this paper through a finite element formulation. The results in the form of an empirical formula for the radial load ratios are presented for various values of the taper parameter and orthotropy parameter. Both simply supported and clamped boundary conditions are considered.     

Post-buckling of cylindrically orthotropic circular plates on elastic foundation with edges elastically restrained against rotation

The post-buckling behaviour of cylindrically orthotropic circular plates is investigated through a finite element formulation, with the plates resting on an elastic foundation and their edges are elastically restrained against rotation. Results are presented in the form of linear buckling load parameters and empirical formulae for radial load ratios for various values of spring stiffness, foundation stiffness and orthotropy parameter.     

Post-buckling of linearly tapered,moderately thick circular plates by finite element method

The post-buckling behaviour of linearly tapered, moderately thick circular plates subjected to an external compressive load is studied in this paper through a finite element formulation. The results in the form of an empirical formula for the radial load ratios are presented for various values of the taper parameter and central thickness to radius ratio. Both simply supported and clamped boundary conditions are considered in the present study.     

Asymmetric buckling of bimodulus thick annular plates

An annular element with Lagrangian polynomials and trigonometric functions as shape functions is developed for asymmetric finite element stability analysis. The annular element is based on the Mindlin plate theory so that the effect of transverse shear deformation is included. Using the asymmetric finite element model, the asymmetric static buckling of bimodulus thick annular plates subjected to a combination of a pure bending stress and compressive normal stress is investigated. The obtained results of non-dimensional critical buckling coefficients are shown to be very accurate when compared with the exact solutions. The effects of various parameters on the buckling coefficients are studied. The bimodulus properties are shown to have significant influences on the buckling coefficients.     

A rectangular finite element for moderately thick flat plates

This paper presents the development of a straightforward displacement type rectangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has 21 degrees of freedom consisting of nine for the lateral displacement of the midplane and 12 for rotations of the normal to the undeformed midplane of the plate (six each for rotations about the x and y axes). The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.     

Axisymmetric vibration of bimodulus thick circular and annular plates

The fundamental natural frequencies of axisymmetric circular and annular plates subjected to a combination of a pure bending stress and extensional stress in the plane of the plate are investigated. The thick plate ring element model which includes the effect of transverse shear deformation is created for axisymmetric free vibration problems. The obtained results of non-dimensional natural frequency coefficient compared with the closed form solutions for ordinary plates are shown to be very good. The effects of various parameters on the natural frequency and neutral surface locations are studied. The bimodulus properties are shown to have significant influence on the natural frequency.     

Hybrid-stress isoparametric elements for moderately thick and thin multilayer plates

A hybrid-stress formulation of isoparametric elements for the analysis of moderately thick and thin multilayer laminated composite plates is presented. The element displacement behavior is characterized by laminate reference-surface inplane and transverse displacements and laminate nonnormal crosssection rotations; as a result, the number of degrees of freedom is independent of the number of layers. All components of stress are included and are related to a set of laminate stress parameters, the number of which is independent of the number of layers. By isolating and analytically integrating all through-thickness contributions to the element matrices, the computation time for the element stiffness generation becomes nearly independent of the number of layers, and thus a computationally efficient element is produced. The formulation is used to develop an 8-node isoparametric multilayer plate element which is naturally invariant, of correct rank, and nonlocking in the thin-plate limit. Results for selected example problems show the range of applicability and convergence behavior of the element.     

Asymmetric vibration and dynamic stability of bimodulus thick annular plates

The free vibration and dynamic stability problems of asymmetric bimodulus thick annular plates are studied. The annular element with Lagrangian polynomials and trigonometric functions as shape function is developed. The element is based on the Mindlin plate theory so that the effect of transverse shear deformation is included. The dynamic stability of an annular plate subjected to a combination of a pure dynamic bending and a uniform dynamic extensional stress in the plane of the plate is investigated. The non-axisymmetric modes are shown to have significant effects in the annular bimodulus plates.     

Post-buckling behaviour of elastic circular plates using a simple finite element formulation

The post-buckling behaviour of elastic circular plates is studied in this paper using a simple finite element formulation. The final linearized eigenvalue problem is solved by using three numerical methods and all these methods are found to yield accurate results for moderately large deflections. Comparison of the present results with the results existing in literature shows the validity of this formulation.     

Inplane vibration analysis of polar orthotropic annular plates with linearly varying thickness

The natural frequencies of inplane vibrations of polar orthotropic annular plates with linearly varying thickness have been analysed. A semi-analytical method of analysis has been used where the radial and tangential displacements are expanded in the circumferential direction as Fourier series and the radial behaviour is solved using the finite element method. For the sake of comparison, results have been obtained starting with two different kinds of displacement functions. The frequencies have been studied with respect to various boundary conditions. aspect ratios, thickness ratios, ratios of moduli, and two fibre directions.     

Bending analysis of rectangular moderately thick plates using spline finite element method

A bending analysis of rectangular, moderately thick plates with general boundary conditions is presented using the spline element method. The cubic B spline interpolate functions are used to construct the field function of generalized displacements w, φ_itxand φ_ity. The spline finite element equations are derived based on the potential energy principle. For simplicity, the boundary conditions, which consist of three local spline points, are amended to fit specified boundary conditions. The shear effect is considered in the formulations. A number of numerical examples are described for rectangular, moderately thick plates. Since the cubic B spline interpolate functions have sufficient continuity and are piecewise polynomial, so the present numerical solutions show not only that the method gives accurate results, but also that the unified solutions of thick and thin plates can be directly obtained; the trouble with the so-called shear locking phenomenon does not occur here.     

矩形中厚板自由振动问题的辛本征展开定理

研究了矩形中厚板自由振动问题导出的一个Hamilton算子的本征值问题.在广义位移与内力构成的混合边界条件下,首先求解了相应算子的本征函数.接着,证明了本征函数系的完备性,这为使用分离变量法求解相应问题提供了可行性.最后,根据文中证明的展开定理获得了问题的一般解,并给出了具体的数值算例.     

Optimization of cylindrically orthotropic circular plates including geometric non-linearity with a constraint on the fundamental frequency

Optimization of cylindrically orthotropic circular plates is studied with a constraint on the fundamental frequency when the effect of geometric nonlinearity is included. Details of finite element formulation for inclusion of geometric nonlinearity, derivation of optimality criterion and recurrence relations are presented. Results for various values of orthotropy parameter are given in tables.     

Numerical analysis of nonsymmetric postbuckling behaviour of elastic annular plates

A modified shooting method is used combined with the Kantorovich orthogonalization method. An appropriate formulation of equations and an algorithm are given. Numerical examples illustrate the efficiency of the proposed method.     

Post-buckling of thick symmetric laminated plates under end-shortening and normal pressure using semi-energy finite strip method

The application of the semi-energy CLPT-FSM for the non-linear analysis of symmetric laminates is extended to include the effects of normal pressure loading in addition to the end-shortening. Moreover, a new semi-energy FSM is developed based on the concept of FSDT theory in order to attempt the large deflection solution for relatively thick laminates. It is noted that for a given level of accuracy, the developed semi-energy FSM requires a markedly lower number of degrees of freedom compared to those of FEM analysis. Hence, the semi-energy FSM is more computationally efficient than the conventional energy based schemes.