High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Nonlinear finite element analysis of shells: Part I. three-dimensional shells

A nonlinear finite element formulation is presented for the three-dimensional quasistatic analysis of shells which accounts for large strain and rotation effects, and accommodates a fairly general class of nonlinear, finite-deformation constitutive equations. Several features of the developments are noteworthy, namely: the extension of the selective integration procedure to the general nonlinear case which, in particular, facilitates the development of a ‘heterosis-type’ nonlinear shell element; the presentation of a nonlinear constitutive algorithm which is ‘incrementally objective’ for large rotation increments, and maintains the zero normal-stress condition in the rotating stress coordinate system; and a simple treatment of finite-rotational nodal degrees-of-freedom which precludes the appearance of zero-energy in-plane rotational modes. Numerical results indicate the good behavior of the elements studied.     

Nonlinear finite element analysis of shells-part II. two-dimensional shells

A general nonlinear finite element formulation is given for two-dimensional problems. The formulation applies to the practically important cases of shells of revolution, tubes, rings, beams and frames. The approach is deduced from a corresponding three-dimensional formulation [4] and this enables a simplified implementation, especially with respect to constitutive software. Uniform reduced-integration Lagrange elements are employed and shown to be very effective for the class of problems considered.     

Least-squares finite element formulation for shear-deformable shells

We present a least-squares based finite element formulation for the numerical analysis of shear-deformable shell structures. The variational problem is obtained by minimizing the least-squares functional, defined as the sum of the squares of the shell equilibrium equations residuals measured in suitable norms of Hilbert spaces. The use of least-squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise, i.e. stability requirements such as inf–sup conditions never arise. The proposed formulation retains the generalized displacements and stress resultants as independent variables and, in view of the nature of the variational setting upon which the finite element model is built, allows for equal-order interpolation. A p-type hierarchical basis is used to construct the discrete finite element model based on the least-squares formulation. Exponentially fast decay of the least-squares functional is verified for increasing order of the modal expansions. Several well established benchmark problems are solved to demonstrate the predictive capability of the least-squares based shell elements. Shell elements based on this formulation are shown to be effective in both membrane- and bending-dominated states.     

A hybrid strain technique for finite element analysis of plates and shells

A specialization of the Hu-Washizu [1] functional wherein strains and displacements are taken as independent variables is employed in the formulation of ‘hybrid’ elements. Both the strains and displacements are independently interpolated with the strains being eliminated at the element level, leaving displacement variables only to be assembled into the global system of equations. This distinguishes such elements as ‘hybrid’, in contrast to ‘mixed’ wherein the global system of equations contains all the discretized variables. Applications including ‘thick’ plate and shell elements are considered. In many applications the hybrid strain technique appears more natural than the hybrid stress technique since stress discontinuities are accommodated quite conveniently.     

不确定性转子系统的随机有限元建模及响应分析

随机特性和随机载荷会引起转子系统动力响应的不确定性,是转子动力学分析中的重要影响因素.本文基于Timosheke梁理论,把转轴的材料和几何随机特性表示为一维随机场函数,推导出随机转轴有限元列式,建立转子系统随机动力学模型,并给出随机载荷作用下随机转子系统动力响应统计量的分析方法.分别对线性和非线性涡轮泵转子系统进行了随机动力响应分析,并同Monte Carlo仿真结果进行对比,结果表明所建立的随机有限元动力学模型和给出的随机响应分析方法是合理可行的,可以有效应用于实际转子系统随机动力学分析和设计中.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

Improving the computational efficiency in finite element analysis of shells with uncertain properties

This work is concerned with improving the computational efficiency of the most time consuming tasks performed in Monte Carlo simulation-based Finite Element Analysis (FEA) of shell structures with uncertain properties. For this purpose, stochastic field values are generated on a coarse mesh and then interpolated onto the fine mesh used for the standard FEA computations; the cost-effective TRIC shell element is used to ensure the formation of stiffness matrices in reasonable processing times; the solution of finite element equations is efficiently handled with hybrid schemes combining both iterative and direct solution concepts; additional computational gains are achieved with the use of parallel computing through the straightforward partitioning of the overall Monte Carlo simulation process. The adoption of such advanced computational approaches allows simulation-based probabilistic or stochastic FEA of shells to be performed in affordable computing times and therefore become more tractable in structural engineering practice. The computational procedures described in this work are evaluated on a cluster of 16 networked PCs using three linear elastic test problems with uncertain material and/or geometric parameters: (a) the Scordelis-Lo shell, (b) a pinched cylinder and (c) a 3D steel frame discretized with shell elements.     

Mixed isoparametric finite element models of laminated composite shells

Mixed shear-flexible isoparametric elements are presented for the stress and free vibration analysis of laminated composite shallow shells. Both triangular and quadrilateral elements are considered. The “generalized” element stiffness, consistent mass, and consistent load coefficients are obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Group-theoretic techniques are used in conjunction with computerized symbolic integration to obtain analytic expressions for the stiffness, mass and load coefficients. A procedure is outlined for efficiently handling the resulting system of algebraic equations.The accuracy of the mixed isoparametric elements developed is demonstrated by means of numerical examples, and their advantages over commonly used displacement elements are discussed.     

Stochastic linearisation of geometrically non-linear finite element models

The equivalent linearisation method is a well established approximate technique for the probabilistic analysis of non-linear structures subjected to random loads. It is shown here that this technique is readily applicable to geometrically non-linear small strain problems in which the equations of motion of the structure are derived using the Finite Element method. A general formulation for problems of this type is presented, following which the method is applied to the non-linear vibrations of an elastic beam. Good agreement with published results is obtained, demonstrating the general feasibility of the approach.     

Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells

The geometrically nonlinear analysis of elastic inplane oriented bodies, e.g. beams, frames and arches, is presented in a total Lagrangian co-ordinate system. By adopting a continuum approach, employing a paralinear isoparametric element, the formulation is applicable to structures consisting of straight or curved members. Displacements and rotations are unrestricted in magnitude. The nonlinear equilibrium equations are solved using the Newton-Raphson method for which a number of examples are given. The derivations are extended to include axisymmetric structures.     

A general finite element model for shells of arbitrary geometry

A finite element formulation is developed for the large displacement analysis of arbitrary shells. Formulation is based on a convected coordinate system and a tensorial approach is followed. The strain-displacement relationships used do not reflect the Kirchhoff hypothesis and Love's approximations. Isoparametric interpolation is used for the discretization of the problem, and the number of nodal points is variable. The numerical examples include the buckling analysis of cylindrical shells as well as two problems to test the convergence and accuracy of the algorithm.     

A finite element formulation for shells of negative Gaussian curvature

An expression for the strain energy of a shell of negative Gaussian curvature, including thickness shear deformations and without neglecting z/R in comparison with unity, is derived. Then a curved trapezoidal finite element formulation based on the principle of minimum potential energy is obtained. The shell element has eight nodes with 40 degrees of freedom and at each node there are three displacements and two rotations. The formulation is applicable for both thin and moderately thick shell analysis. The performance of this finite element is verified by applying it to some problems existing in the literature.     

Quasi-analytical finite element procedures for axisymmetric anisotropic shells and solids

Using complex series representations, a quasi-analytical finite element procedure is developed which can analyze the static and dynamic mechanical fields of anisotropic axisymmetric shells and bodies. Due to its generality the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally mechanically anisotropic materials. In this respect, in contrast to traditional quasi-analytical procedures which are limited to the ‘specially’ orthotropic case, the present treatment reveals several important effects of material and/or structural anisotropy. To illustrate the procedure as well as the significant effects of material anisotropy, several numerical examples are given along with comparisons with known analytical treatments.     

Network-distributed finite element analysis

The widespread availability of local-area networks has made the combined processing power of workstations a viable approach for compute-intensive analyses. In this paper, we describe several distributed algorithms for structural analysis using finite element methods, and we assess their performance on a conventional Ethernet-connected workstation network. Direct, iterative and hybrid equation solvers are evaluated for their performance on plane-elasticity problems, and are contrasted with respect to overall solution time and efficiency in distributing computations over a network. Equations modeling the costs of network communication and structural analysis computations are derived, and are subsequently used to predict the performance of several variations on the implemented algorithms. Our results show that each of the methods performs well on network architectures, and in particular that, while direct methods usually minimize network communication, certain iterative and hybrid methods can often be used to minimize overall solution time.     

A nine-node assumed-strain finite element for composite plates and shells

A new finite element for modeling fiber-reinforced composite plates and shells is developed and its performance for static linear problems is evaluated. The element is a nine-node degenerate solid shell element based on a modified Hellinger-Reissner principle with independent inplane and transverse shear strains. Several numerical examples are solved and the solutions are compared with other available finite solutions and with classical lamination theory. The results show that the present element yields accurate solutions for the test problems presented. Convergence characteristics are good, and the solution is relatively insensitive in element distortion. The element is also shown to be free of locking even for thin laminates.     

A semi-analytical coupled finite element formulation for shells conveying fluids

A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid–structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed.     

A doubly curved quadrilateral finite element for the analysis of laminated anisotropic thin shells of revolution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.     

Distributed structural identification and control of shells using distributed piezoelectrics: Theory and finite element analysis

Distributed dynamic identification and vibration control of high-performance flexible structures has drawn much attention in recent years. This article presents an analytical and finite-element study on a distributed piezoelectric sensor and distributed actuator coupled with flexible shells and plates. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively control the structural vibration by the direct/converse piezoelectric effects, respectively. Based on Maxwell's equations and Love's assumptions, new theories on distributed sensing and active vibration control of a generic shell using the distributed piezoelectrics are derived. These theories can be easily simplified to account for plates, cylinders, beams, etc. A new piezoelectric finite element is also formulated using the variational principle and Hamilton's principle. A piezoelectric micropositioning device was first studied; analytical solutions are compared closely with experimental and finite-element results. Distributed vibration identification and control of a zero-curvature shell-a plate-are also investigated.