Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.     

Finite element analysis of eccentrically stiffened plates in free vibration

A compound finite element model is developed to investigate eccentrically stiffened plates in free vibration. The plate elements and beam elements are treated as integral parts of a compound section, and not as independent bending components. The derivation is based on the assumptions of small deflection theory. In the orthogonally stiffened directions of the compound section, the neutral surfaces may not coincide. They lie between the middle surface of the plate and the centroidal axes of the stiffeners. The results of this study are compared with existing ones and with those of the orthotropic plate approximation. Modifications to the existing equivalent orthotropic rigidities are proposed.     

Finite element free vibration of eccentrically stiffened plates

An isoparametric stiffened plate element is introduced for the free vibration analysis of eccentrically stiffened plates. The element has the ability to accommodate irregular boundaries. Moreover, the formulation considers shear deformation, hence, the formulation is applicable to both thick and thin plates. In the present formulation, the stiffeners can be placed anywhere within the plate element and they need not necessarily follow the nodal lines. In addition, the effects of lumped and consistent mass matrices on natural frequencies of stiffened plates are investigated. The effects of several parameters of the stiffener—eccentricity, shape, torsional stiffness etc.—on the natural frequencies of the stiffened plates are studied.     

Finite element free vibration analysis of conoidal shells

Doubly curved conoidal shells are increasingly used for various industrial structures. Conoidal shells are aesthetically appealing and, being ruled surfaces, provide ease of casting. The variation of curvature is the difficulty enountered in the analysis of these shells. The finite element method is used here for the analysis of generalized doubly curved shells and is applied to truncated and full conoids of different boundary conditions, aspect ratios and degrees of truncation. An eight-noded isoparametric finite element with five degrees of freedom per node, including three translations and two rotations, is utilized. The accuracy is checked by comparing the results obtained by the present analysis with those existing in the literature. Results are presented for different conoidal shells and a set of conclusions are arrived at based on a parametric study.     

Finite element analysis of stiffened plates

A finite element method is presented in which the constraint between stiffener and member is imposed by means of Lagrange multipliers. This is performed on the functional level, forming augmented variational principles. In order to simplify the initial development and implementation of the proposed method, two-dimensional stiffened beam finite elements are developed. Several such elements are formulated, each showing monotonic convergence in numerical tests. In the development of stiffened plate finite elements, the bending and membrane behaviors are treated seperately. For each, the stiffness matrix of a standard plate element is modified to account for an added beam element (representing the stiffener) and additional terms imposing the constraint between the two. The resulting stiffened plate element was implemented in the SAPIV finite element code. Exact solutions are not known for rib-reinforced plated structures, but results of numerical tests converge monotonically to a value in the vicinity of an approximate “smeared” series solution.     

Finite element buckling analysis of stiffened plates

An isoparametric stiffened plate bending element for the buckling analysis of stiffened plates has been presented. In the present approach, the stiffener can be positioned anywhere within the plate element and need not necessarily be placed on the nodal lines. The element, being isoparametric quadratic, can readily accommodate curved boundaries, laminated materials and transverse shear deformation. The formulation is applicable to thin as well as thick plates. The buckling loads for various rectangular and skew stiffened plates with varying skew angles and stiffness parameters have been indicated. The results show good agreement with those published.     

Finite element flutter analysis of composite skew panels

A finite element method is used to study the dynamic instability of laminated composite skew panels subjected to supersonic flow. The FEM employs eight-noded isoparametric elements which take into account transverse shear deformation. The linearized Piston theory is applied to assess the aerodynamic loads. The effects of skew angle on critical aerodynamic parameters are investigated for different aspect ratios, boundary constraints, fibre orientations and lamination schemes. It is observed that the skew angle has a stabililzing effect on the flutter boundary, whereas couplings have a destabilizing effect. The higher aspect ratio is also found to exhibit a stabilizing effect on the flutter boundary.     

Finite element free flexural vibration analysis of plates having various shapes and varying rigidities

Natural frequencies of skew, curved and tapered plates have been determined using the isoparametric quadratic plate bending element. Plates having linearly varying thickness in one direction and also those having parabolically varying thickness in orthogonal directions have been analysed. A simple stepped plate approach for a linearly tapered plate has also been considered to compare the results. Two approaches have been adopted for the solution of skew plates. In one case, the boundary conditions have been exactly satisfied by transforming the rotational displacements at the boundary nodes along and normal to the edge. In the other case, only the vertical deflection was locked. A curved plate has also been analysed by the first method. Results thus obtained from both cases have been compared.     

Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively.The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.     

Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam

Many practical engineering structures can be modeled as rotating beam-like structures. Such structures involve variable coefficients in the governing equations, which in general cannot be solved analytically in closed form. In this paper, a relatively new approach called differential transformation is applied in analyzing free lateral vibrations of a centrifugally stiffened rotating Euler–Bernoulli beam. Both natural frequencies and modeshapes are obtained using differential transformation technique. Numerical examples are presented. The natural frequencies are in excellent agreement with published results.     

Free vibration analysis of multi-symmetric stiffened shells

The application of structural symmetry techniques to the free vibration analysis of cylindrical and conical shells for the prediction of natural frequencies and mode shapes is described. Appropriate boundary conditions have been developed for the analysis of only a part of the shell and have been shown to yield results comparable to the full shell analysis. Half and quarter models of the shell have been developed and analysed using semi-loof and facet shell finite elements. Unstiffened and stiffened circular cylindrical shells and stiffened conical shells have been considered.     

Design and analysis of stiffened composite panels including post-buckling and collapse

The European aircraft industry demands reduced development and operating costs, by 20% and 50% in the short and long term, respectively. Contributions to this aim are provided by the completed project POSICOSS (5th FP) and the running follow-up project COCOMAT (6th FP), both supported by the European Commission. As an important contribution to cost reduction a decrease in structural weight can be reached by exploiting considerable reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of post-buckling up to collapse. The POSICOSS team developed fast procedures for the post-buckling analysis of stiffened fibre composite panels, created comprehensive experimental data bases and derived suitable design guidelines. COCOMAT builds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The results comprise an extended experimental data base, degradation models, and improved certification and design tools as well as extended design guidelines.One major task of POSICOSS and COCOMAT is the development of improved analysis tools that are validated by experiments performed within the framework of the projects. Because the new tools must comprise a wide range of various aspects a considerable number of different structures had to be tested. These structures were designed under different objectives (e.g. large post-buckling region). For the design process, the consortiums applied state-of-the-art simulation tools and brought in their own design experience. This paper deals with the design process as performed within both projects and with the applied analysis procedures. It is focused on the DLR experience in the design and analysis of stringer-stiffened CFRP panels gained within the scope of these two projects.     

On a finite dynamic element method for free vibration analysis of structures

This paper explores the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices. Such matrices are then developed for a rectangular prestressed membrane element. Next, efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail. These are followed by suitable numerical examples which indicate that employment of such dynamic elements in conjunction with an efficient quadratic matric solution technique will result in a most significant economy in the free vibration analysis of structures.     

Finite element analysis

Current use of the finite element method in engineering practice is considered. The increasing use of finite element analysis in a CAD environment and factors influencing it are discussed.The technological state of the art is briefly reviewed. Special consideration is given to shell elements and solution methods, illustrating the progress being made in these and other areas of finite element technology. Future trends are predicted.     

高速列车浮式地板振动响应有限元分析

针对采用试验方法开发高速列车浮式地板耗时耗力,且试验规模小,不能反映整车的振动效果的问题,基于有限元法进行高速列车振动响应分析.对三明治夹芯理论、蜂窝板理论和等效板理论进行比较,确定采用等效板理论数值模拟某浮式地板中的蜂窝板;利用橡胶材料的超弹性理论拟合橡胶材料参数;建立完整模型模拟实际工况下浮式地板的振动响应,得到浮式地板的隔振效果.结果表明此浮式地板的隔振效果约为90%,满足设计要求.     

轴向运动三阶剪切变形板自由振动的有限元模型及应用

采用三阶剪切变形理论,通过虚功原理建立轴向运动板的有限元方程,利用一种包含节点挠度及其斜率和截面转角的四节点四边形单元离散求解域,随后将离散式弹簧支承这一约束首次通过系统势能的形式引入系统有限元方程中.在算例应用部分,首先考虑不同边界条件以及不同支承刚度,与ANSYS计算结果进行对比,证明方法的有效性.接着在两种边界条件下针对轴向运动薄板分别研究运动速度和弹簧刚度与系统复频率实部和虚部的关系,结果显示高速易使板失稳,而高弹簧刚度会提高系统的振动频率.最后,给出板厚与系统复频率的关系,揭示了板厚对轴向运动三阶剪切变形板稳定性的影响.     

Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge

A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.     

变频器机柜振动特性有限元分析和试验验证

根据电子设备结构振动试验标准的要求,利用ANSYS建立变频器机柜的有限元模型,获得结构的模态频率和冲击载荷下的结构响应,并与试验结果对比,验证变频器机柜有限元模型的可靠性。分析变频器机柜的振动特性,结果表明：变频器机柜顶部减振器安装位置受到的冲击能量较大,机柜内部的冲击能量较小,机柜内设备可得到有效防护。     

Finite element/difference methods in random vibration

Finite element and finite difference analyses of a class of random vibration problem are presented. The random field equations are discretized using the standard finite element/difference techniques. Recursive algorithms for the moments of the response in terms of the moments of the random loading and random initial condition are derived based on the discretized equations. The approach is straightforward and it provides an alternative to the standard normal-mode approach in the analysis of linear random structural systems. However, unlike the standard approach, the finite element/difference approach can be applied to other more complex systems. Two numerical examples are given to illustrate the application. The approximate numerical results are also compared with the exact solutions to check the accuracy of the finite element/difference analyses. It is found that for the problems considered, the finite difference algorithms provide better accuracy and efficiency than the finite element method.